1st Periodical Examination 2024-2025.docx

**FIRST QUARTERLY EXAMINATION IN MATHEMATICS 8** **DIRECTION: 1.** *Read each question carefully; 2. Shade the letter that corresponds to your answer; 3. Do not use mobile phone or any gadget while the test is going on.* 1\. What is the process of finding the factors of an expression? a.) Factori...

**FIRST QUARTERLY EXAMINATION IN MATHEMATICS 8** **DIRECTION: 1.** *Read each question carefully; 2. Shade the letter that corresponds to your answer; 3. Do not use mobile phone or any gadget while the test is going on.* 1\. What is the process of finding the factors of an expression? a.) Factoring c.) Rationalization b.) Special Product d.) Continuous Division 2\. What is the GCF of 20, 24, and 40? a.) 1 c.) 8 b.) 4 d.) 20 3\. What is the GCF of [*xy*^6^, *x*^2*y*^3^^]{.math.inline}and [*x*^3^*y*?]{.math.inline} a.) [xy]{.math.inline} c.) [*x*^3^*y*^6^]{.math.inline} b.) [*xy*^6^]{.math.inline} d.) [*x*^3^*y*]{.math.inline} 4\. What are the complete factors of 7x + 7? a.) 7(x - 1) c.) x (x + 7) b.) 7(x + 1) d.) 7x + 1 5\. Find the complete factors of [*x*^2^− *x*^9^.]{.math.inline} a.) [*x*^2^(1−*x*^7^)]{.math.inline} c.) [*x*(*x* − *x*^8^)]{.math.inline} b.) [*x*^2^(*x*−*x*^7^)]{.math.inline} d.) [*x*^9^(*x*^2^− 1)]{.math.inline} 6\. Find the complete factors of [2*x*^6^− 12*x*^4^.]{.math.inline} a.) [2*x*^6^(2−6*x*^2^)]{.math.inline} c.) [*x*(2*x*^5^−12*x*^3^)]{.math.inline} b.) [2*x*^4^(*x*^2^−6)]{.math.inline} d.) [2(*x*^6^− 6*x*^4^)]{.math.inline} 7\. If one factor of [4*x*^2^+ 6]{.math.inline} is 2, what is the other factor? a.) [2*x*^2^+ 3]{.math.inline} c.) [4*x* + 6]{.math.inline} b.) [2*x* + 6]{.math.inline} d.) [2*x* + 3]{.math.inline} 8\. Which of the following is a perfect square expression? a.) [3*x*]{.math.inline} c.) [9*x*^3^]{.math.inline} b.) [4*x*^2^]{.math.inline} d.) [12*x*^4^]{.math.inline} 9\. Which of the following is a perfect square? a.) [16*x*^2^*y*^2^]{.math.inline} c.) [36*x*^6^*y*^7^]{.math.inline} b.) [25*x*^5^*y*^6^]{.math.inline} d.) [40*x*^8^*y*^8^]{.math.inline} 10\. Which of the following expressions has factors \ [(2*x*−*y*)(2*x*+*y*)?]{.math.display}\ a.) [4*x*^2^ + *y*^2^]{.math.inline} c.) [2*x*^2^ + *y*^2^]{.math.inline} b.) [4*x*^2^− *y*^2^]{.math.inline} d.) [2*x*^2^ − *y*^2^]{.math.inline} 11\. If one factor of the difference of two squares is [*x* + 2,]{.math.inline} what is the other factor? a.) [*x*^2^ − 4]{.math.inline} c.) [*x* − 2]{.math.inline} b.) [*x*^2^ + 4]{.math.inline} d.) [ *x* + 2]{.math.inline} 12\. What is the complete factored form of [*x*^2^ − 16?]{.math.inline} a.) [(*x*^2^+4)(*x*^2^−4)]{.math.inline} c.) [(*x* − 4)(*x* − 4)]{.math.inline} b.) [(*x*+4)(*x*+4)]{.math.inline} d.) [(*x*+4)(*x*−4)]{.math.inline} 13\. What is the complete factored form of [*x*^2^*y*^2^ − 1?]{.math.inline} a.) [(*x*^2^*y*^2^+1)(*x*^2^*y*^2^−1)]{.math.inline} b.) [(*xy*−1)(*xy*−1)]{.math.inline} c.) [(*xy*+1)(*xy*−1)]{.math.inline} d.) [(*x*+*y*)(*x*−*y*)]{.math.inline} 14\. Which of the following is a perfect cube? a.) [8*x*]{.math.inline} c.) [64*x*^4^]{.math.inline} b.) [25*x*^2^]{.math.inline} d.) [81*x*^6^]{.math.inline} 15\. Which of the following is the complete factored form of \ [*x*^3^ − 8?]{.math.display}\ a.) [(*x*^2^)(*x*^2^+2*x*+4)]{.math.inline} b.) [(*x*−2)(*x*^2^−2*x*−4)]{.math.inline} c.) [(*x*−2)(*x*^2^+2*x*+4)]{.math.inline} d.) [(*x*−2)(*x*^2^−2*x*+4)]{.math.inline} 16\. Using the pattern for factoring the sum of cubes, we know that factoring [8 + *b*^3^]{.math.inline} gives \_\_\_\_\_. a.) [(2+*b*)(4+2*b*−*b*^2^)]{.math.inline} b.) [(2+*b*)(4−2*b*−*b*^2^)]{.math.inline} c.) [(2+*b*)(4+2*b*+*b*^2^)]{.math.inline} d.) [(2+*b*)(4−2*b*+*b*^2^)]{.math.inline} 17\. What is the complete factored form of [*x*^3^*y*^3^ + 1?]{.math.inline} a.) [(*xy*+1)(*x*^2^*y*^2^−*xy*−1) ]{.math.inline} b.) [(*xy*+1)(*x*^2^*y*^2^+*xy*−1)]{.math.inline} c.) [(*xy*+1)(*x*^2^*y*^2^−*xy*+1)]{.math.inline} d.) [(*xy*+1)(*x*^2^*y*^2^+*xy*+1)]{.math.inline} 18\. What is the complete factored form of [27 − *x*^6^?]{.math.inline} a.) [(3−*x*)(9−3*x*+*x*^2^)]{.math.inline} b.) [(3−*x*)(9+3*x*+*x*^2^)]{.math.inline} c.)[(3−*x*^2^)(9−3*x*^2^+*x*^4^)]{.math.inline} d.) [(3−*x*^2^)(9−3*x*^2^+*x*^4^)]{.math.inline} 19\. Factor completely: [64*x*^3^ − *y*^3^]{.math.inline} a.) [(4*x*−*y*)(16*x*^2^−4*xy*+*y*^2^)]{.math.inline} b.) [(4*x*−*y*)(16*x*^2^+4*xy*−*y*^2^)]{.math.inline} c.) [(4*x*−*y*)(16*x*^2^+4*xy*+*y*^2^)]{.math.inline} d.) [(4*x*−*y*)(16*x*^2^−4*xy*+*y*^2^)]{.math.inline} 20\. If one factor of [*x*^6^ + 1000]{.math.inline} is [*x*^4^ − 10*x*^2^ + 100,]{.math.inline} what is the other factor? a.) [*x*^2^ + 100]{.math.inline} c.) [*x*^2^ − 10]{.math.inline} b.) [*x*^2^ − 100]{.math.inline} d.) [*x*^2^ + 10]{.math.inline} 21\. Supply the missing expression to make it true, \ [10 + 270*y*^3^ = 10(\_\_\_\_)(1−3*y*+9*y*^2^).]{.math.display}\ a.) [1 + 3*y*]{.math.inline} c.) [1 + 27*y*]{.math.inline} b.) [1 − 3*y*]{.math.inline} d.) [1 − 27*y*]{.math.inline} 22\. Which of the following is a perfect square trinomial? a.) [*y*^2^ − 5*y* + 4]{.math.inline} c.) [8*a*^2^ − 6*a* + 1]{.math.inline} b.) [*a*^2^ − 4*a* − 4]{.math.inline} d.) [4*m*^2^ − 4*m* + 1]{.math.inline} 23\. Which of the following is a perfect square trinomial? a.) [*x*^2^ + 10*x*  + 25]{.math.inline} c.) [*x*^2^ + 10*x*  + 20]{.math.inline} b.) [*x*^2^ + 5*x*  + 10]{.math.inline} d.) [*x*^2^ + 10*x*  + 50]{.math.inline} 24\. Which value of b would make [16*x*^2^ − *bx* + 25]{.math.inline} a perfect square trinomial? a.) {.math.inline} c.) {.math.inline} b.) 5 d.) {.math.inline} 25\. Which method could be used to factor [9*x*^2^ + 24*x* + 16?]{.math.inline} a.) Perfect Square Trinomial c.) Factor by grouping b.) Difference of Two Squares d.) Factor out the GCF 26\. What is the complete factorization of [*x*^2^ − 8*x* + 16?]{.math.inline} a.) [(*x* − 8)(*x* − 8)]{.math.inline} c.) [(*x* + 4)(*x* + 4)]{.math.inline} b.) [(*x*+8)(*x*+8)]{.math.inline} d.) [(*x*−4)(*x*−4)]{.math.inline} 27\. Determine whether [*x*^2^ − 6*x* − 9]{.math.inline} is a perfect square trinomial. If so, choose the correct factorization. a.) Yes; [(*x*−3)^2^]{.math.inline} c.) Yes; ([*x* + 3)(*x* − 3)]{.math.inline} b.) Yes; [(*x*+3)^2^]{.math.inline} d.) No 28\. Which of the following is equal to [*x*^2^ − 6*xy* + 9*y*^2^?]{.math.inline} a.) [(*x*+2*y*)^2^]{.math.inline} c.) [(*x*+3*y*)^2^]{.math.inline} b.) [(*x*−2*y*)^2^]{.math.inline} d.) [(*x*−3*y*)^2^]{.math.inline} 29\. What are the two numbers whose sum is 1 and whose product is -12? a.) -3 and 4 c.) -3 and -4 b.) 3 and -4 d.) 3 and 4 30\. What are the two expressions whose sum is 7x and whose product is [10*x*^2^?]{.math.inline} a.) 2x and -5x c.) -2x and -5x b.) -2x and 5x d.) 2x and 5x 31\. If one factor of [*x*^2^ − 5*x* − 24]{.math.inline} is [*x* + 3]{.math.inline}, what is the other factor? a.) [*x* − 3]{.math.inline} c.) [*x* + 8]{.math.inline} b.) [*x* − 8]{.math.inline} d.) [*x* + 3]{.math.inline} 32\. What is the complete factored form of [*x*^2^ + 7*x* + 10?]{.math.inline} a.) [(*x* + 1)(*x* + 10)]{.math.inline} c.) [(*x* + 2)(*x* + 5)]{.math.inline} b.) [(*x*−1)(*x*−10)]{.math.inline} d.) [(*x*−2)(*x*−5)]{.math.inline} 33\. What is the complete factored form of [2*x*^2^ + 5*x* − 3?]{.math.inline} a.) [(2*x* + 1)(*x* − 3)]{.math.inline} c.) [(2*x* − 1)(*x* − 3)]{.math.inline} b.) [(2*x*−1)(*x*+3)]{.math.inline} d.) [(2*x*+1)(*x*+3)]{.math.inline} 34\. If one factor of [3*x*^2^ + 17*x* + 10 ]{.math.inline}is [3*x* + 2]{.math.inline}, What is the other factor? a.) [3*x* − 2]{.math.inline} c.) [*x* + 5]{.math.inline} b.) [2*x* + 5]{.math.inline} d.) [*x* − 5]{.math.inline} 35\. Which of the following trinomials is factorable? a.) [*x*^2^ − 6*x* + 7]{.math.inline} c.) [2*x*^2^ + 5*x* + 10]{.math.inline} b.) [*x*^2^ + 3*x* + 2]{.math.inline} d.) [3*x*^2^ − 6*x* + 12]{.math.inline} 36\. The area of a rectangular garden is [9*t*^2^ − 64]{.math.inline} square units. If one side is [3*t* − 8]{.math.inline}, what is the other side? a.) [*t* + 8]{.math.inline} c.) [3*t* + 8]{.math.inline} b.) [*t* − 8]{.math.inline} d.) [3*t* − 8]{.math.inline} 37\. Your classmate was asked to square [(2*x*−3),]{.math.inline} he answered [4*x*^2^ − 9]{.math.inline}. Is his answer correct? a.) No, because the answer must be [4*x*^2^ + 9.]{.math.inline} b.) No, because squaring a binomial always produces a trinomial product. c.) Yes, because product rule is correctly applied. d.) Yes, because squaring a binomial always produces a binomial product. 38\. A rectangular garden has an area by [6*x*^2^ + *x* − 2]{.math.inline} square meter. If the length is represented by [3*x* + 2,]{.math.inline} find a binomial that represents the width. a.) [*x* − 2]{.math.inline} c.) [2*x* − 1]{.math.inline} b.) [*x* + 2]{.math.inline} d.) [2*x* + 1]{.math.inline} 39\. The rectangle has an area of [2*x*^2^ + 8*x* + 8]{.math.inline} square units. If the length is ([2*x* + 4)]{.math.inline} units, find the width of the rectangle. a.) ([*x* − 2)]{.math.inline} units c.) [(*x*−4)]{.math.inline} units b.) [(*x*+2)]{.math.inline} units d.) [(*x*+4)]{.math.inline} units 40\. The area of a square is [*x*^2^ + 8*x* + 16]{.math.inline} square units. Find the length and the width of a square. a.) [(*x*+4)(*x*−4)]{.math.inline} units c.) [(*x*+4)(*x*+4)]{.math.inline} units b.) [(*x*−4)(*x*+4)]{.math.inline} units d.) [(*x*−4)(*x*−4)]{.math.inline} units