Podcast
Questions and Answers
Which of the following trinomials can be factored into two binomials with a positive constant term and a negative coefficient for the $x$ term?
Which of the following trinomials can be factored into two binomials with a positive constant term and a negative coefficient for the $x$ term?
If the factors of a trinomial have a product of 15 and a sum of 8, what is the trinomial?
If the factors of a trinomial have a product of 15 and a sum of 8, what is the trinomial?
What is the incorrect statement about the factors of the trinomial $x^2 - 5x - 14$?
What is the incorrect statement about the factors of the trinomial $x^2 - 5x - 14$?
A student claims that the trinomial $x^2 + 14x + 48$ can be factored into $(x+8)$ and $(x-6)$. Which statement correctly identifies the student's error?
A student claims that the trinomial $x^2 + 14x + 48$ can be factored into $(x+8)$ and $(x-6)$. Which statement correctly identifies the student's error?
Signup and view all the answers
Which statement about trinomials with factors that have a negative product is true?
Which statement about trinomials with factors that have a negative product is true?
Signup and view all the answers
Study Notes
Factoring Polynomials
- Polynomials can be factored into simpler expressions
- A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
- Factoring involves finding the factors which when multiplied gives the actual expression.
- Different methods exist to factor different types of polynomials, such as Trinomials
Trinomial Factoring
- To factor a trinomial of the form ax² + bx + c, find two numbers that multiply to ac and add to b
- For instance, if we have x² + 5x - 24, we look for two numbers that multiply to -24 and add to 5. These numbers are 8 and -3
- The factored form in this case is (x + 8)(x - 3)
Example Polynomials to Factor
-
8x - 65 : This is a binomial, not a trinomial, so this cannot be factored using the method described here.
-
23x + 60: This is a binomial, not a trinomial, so this cannot be factored using the method described here.
-
x² - 12x + 32: Factoring this trinomial, we look for two numbers that multiply to 32 and add to -12. These two numbers would be (-8 and -4), therefore factorization is (x-8)(x-4).
-
x² + 15x + 44: Two numbers that multiply to 44 and add to 15 are 11 and 4. Factoring, we get (x+11)(x+4).
-
6x² - 72: Factoring shows it is 6(x-2 * (x+2))
-
x² + 5x - 84: Factoring shows it is (x+12)(x-7)
-
x² + 6x - 27: Factoring shows it is (x+9)(x-3)
-
x² - 14x + 33: Factoring shows it is (x-11)(x-3)
-
x² + 5x - 84: Factoring this trinomial, we look for two numbers that multiply to -84 and add to 5. These numbers are 12 and -7, therefore factorization is (x+12)(x-7).
Identifying Incorrect Statements
- Students might make errors in the way they factor
- Pay attention to the sign of the factors when determining the correctness of the factored form
- The product and sum should be correctly calculated
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz covers the essential techniques for factoring polynomials, specifically focusing on trinomials. You will learn how to identify the factors of polynomial expressions and apply methods to factor them effectively. Test your understanding with examples and practice problems.
