Podcast
Questions and Answers
What is the greatest common factor (GCF) of the polynomial $12x^3y + 8xy - 6xy$?
What is the greatest common factor (GCF) of the polynomial $12x^3y + 8xy - 6xy$?
- $2xy$ (correct)
- $6x^3y$
- $4x^2y$
- $2x^2y$
What is the result of dividing the polynomial $25x^7 - 10x^2 + 30x$ by $5x$?
What is the result of dividing the polynomial $25x^7 - 10x^2 + 30x$ by $5x$?
- $5x^6 - 2x + 6$ (correct)
- $5x^6 - 2x^2 + 6x$
- $5x^7 - 10x^2 + 30x$
- $5x^6 - 10x^2 + 30x$
Which of the following represents the factored form of the quadratic expression $x^2 - 11x + 18$?
Which of the following represents the factored form of the quadratic expression $x^2 - 11x + 18$?
- $(x - 1)(x - 18)$
- $(x - 3)(x - 6)$
- $(x - 2)(x - 9)$ (correct)
- $(x + 2)(x + 9)$
Given the polynomial $6x^2$ + 4 - 3, what expression was multiplied by $2xy$ to obtain the polynomial $12x^3y+8xy-6xy$?
Given the polynomial $6x^2$ + 4 - 3, what expression was multiplied by $2xy$ to obtain the polynomial $12x^3y+8xy-6xy$?
Consider the factored form of the expression $x^2 - 11x + 18$, which is $(x - 2)(x - 9)$. If you were to change the constant term from 18 to -18, which of the following factored forms would be possible?
Consider the factored form of the expression $x^2 - 11x + 18$, which is $(x - 2)(x - 9)$. If you were to change the constant term from 18 to -18, which of the following factored forms would be possible?
Given the expression (3x + 2x^2 - 4x) + 3x^2 - 5x, which of the following correctly represents the simplified expression in standard form?
Given the expression (3x + 2x^2 - 4x) + 3x^2 - 5x, which of the following correctly represents the simplified expression in standard form?
What is the degree of the polynomial resulting from the sum of $(-2x^2 + 3x - 4) + (3x^2 + 4x + 6)$?
What is the degree of the polynomial resulting from the sum of $(-2x^2 + 3x - 4) + (3x^2 + 4x + 6)$?
Using the FOIL method to multiply $(2x + 4)(-4x - 7)$, what is the resulting expression after combining like terms?
Using the FOIL method to multiply $(2x + 4)(-4x - 7)$, what is the resulting expression after combining like terms?
A monomial is given as $8x^{2+5}yz^0$. What is the degree of this monomial?
A monomial is given as $8x^{2+5}yz^0$. What is the degree of this monomial?
After simplifying a polynomial expression, it is found to have two terms. According to the number of terms, how is this polynomial classified?
After simplifying a polynomial expression, it is found to have two terms. According to the number of terms, how is this polynomial classified?
Flashcards
Combine Like Terms
Combine Like Terms
Combining terms with the same variable and exponent to simplify an expression.
Standard Form (Polynomial)
Standard Form (Polynomial)
Writing a polynomial with the term of highest degree first, then decreasing order.
Degree of a Monomial
Degree of a Monomial
The sum of the exponents of the variables in a monomial.
Degree of a Polynomial
Degree of a Polynomial
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FOIL Method
FOIL Method
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What is the Greatest Common Factor (GCF)?
What is the Greatest Common Factor (GCF)?
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How to find the GCF of a polynomial?
How to find the GCF of a polynomial?
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Factoring using GCF
Factoring using GCF
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Dividing Polynomials by a Monomial
Dividing Polynomials by a Monomial
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What is Factored Form?
What is Factored Form?
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Study Notes
- The notes cover content for Topic 6 - Quiz.
Question 1
- Part A involves simplifying the expression (3x - 4x - 5x) + (2x² + 3x²).
- Combining like terms simplifies the expression to -6x + 5x², which can be rewritten as 5x² - 6x.
- Part B requires writing the simplified expression in standard form, resulting in 5x² - 6x.
- Part C asks to write the degree of each monomial in the expression.
- The degree of 5x² (D1) is 2, and the degree of -6x (D2) is 1.
- Part D is to write the degree of the monomial 8xyz^5 which is 14 (7+2+5).
Question 2
- The task is to find the sum of the polynomials (-2x² + 3x + 4) and (3x² + 4x + 6).
- After eliminating parentheses and combining like terms, the sum is x² + 7x + 2.
Question 3
- The FOIL method is utilized to multiply the binomials (2x + 4) and (4x - 7)
- Multiplying First terms: 2x * 4x = 8x²
- Multiplying Outer terms: 2x * -7 = -14x
- Multiplying Inner terms: 4 * 4x = 16x
- Multiplying Last terms: 4 * -7 = -28
- Combining these results gives the expanded form: 8x² + 2x - 28.
Question 4
- The objective is to factor the polynomial 12x^5y^3 + 8x^4y^2 - 6x^3y using the Greatest Common Factor (GCF).
- First, find the factors of 12, 8, and 6 which are 223, 222, 2*3.
- Determine the lowest number of x and y's in the equation, 3 x's, 1 y.
- The GCF of 12x^5y^3 + 8x^4y^2 - 6x^3y is 2x^3y
- The resulting terms in the equation are (6x^2y^2 + 4xy - 3)
Question 5
- Divide polynomials by 5x of 25x^7 - 10x^2 + 30x
- Dividing each term results in: 5x^6 - 2x + 6
- Note: x^0 = 1
Question 6
- Factored form of x^2 - 11x + 18
- Factors of 18: 1,18; 2,9; 3,6
- -2 + -9 = -11
- Factored form: (x - 2)(x - 9)
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Description
Simplify polynomial expressions by combining like terms. Includes finding the degree of monomials and using the FOIL method. Sum two polynomials by eliminating parentheses and combining like terms.
