Factorization with the Factor Theorem

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What is the correct factorization of y^2 - 5y + 6 using the Factor Theorem?

(y - 2)(y - 3) (correct)

(y + 2)(y - 3)

(y + 1)(y - 6)

(y - 1)(y - 6)

How did the Factor Theorem help in finding the factors of y^2 - 5y + 6?

By using the trial and error method to test all possible factor combinations.

By identifying that the constant term is the product of the roots of the polynomial. (correct)

By splitting the middle term of the polynomial to identify the root values.

By simplifying the polynomial expression to its simplest form.

Why is the splitting method deemed inappropriate for factorizing cubic polynomials initially?

Cubic polynomials have a more complex root structure that requires a different approach.

Factors of cubic polynomials need to be identified first to effectively use the splitting method. (correct)

It is based on trial and error, making it inefficient for cubic polynomials.

The splitting method may lead to multiple factor pairs that need to be refined further.

In the given expression ax2 + bx + c, which of the following statements is true?

b is the sum of two numbers ps and qr. Signup and view all the answers

For factorizing 6x2 + 17x + 5 using the splitting method, what are the correct pairs of factors for 30 that lead to p + q = 17?

2 and 15 Signup and view all the answers

Using the Factor Theorem, if p(x) = 6x2 + 17x + 5, what are the correct roots (zeroes) of p(x)?

-1 and -5/6 Signup and view all the answers

If x - 2 is a factor of the polynomial p(x) = x^3 + 4x^2 + 3x - 2, what is the value of p(2)?

0 Signup and view all the answers

For the polynomial q(x) = 2x^3 - 5x^2 + 4x - 1, which one of the following is NOT a factor of q(x)?

(2x + 1) Signup and view all the answers

Given the polynomial r(x) = x^3 - 6x^2 + 11x - 6, what value of k would make (x - 2) a factor of r(x)?

-6 Signup and view all the answers

If x + 3 is a factor of the polynomial s(x) = 3x^3 - x^2 - 10x + 6, what would be the result when s(-3) is calculated?

0 Signup and view all the answers

Factorization with the Factor Theorem

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Questions and Answers

What is the correct factorization of y^2 - 5y + 6 using the Factor Theorem?

How did the Factor Theorem help in finding the factors of y^2 - 5y + 6?

Why is the splitting method deemed inappropriate for factorizing cubic polynomials initially?

In the given expression ax2 + bx + c, which of the following statements is true?

For factorizing 6x2 + 17x + 5 using the splitting method, what are the correct pairs of factors for 30 that lead to p + q = 17?

Using the Factor Theorem, if p(x) = 6x2 + 17x + 5, what are the correct roots (zeroes) of p(x)?

If x - 2 is a factor of the polynomial p(x) = x^3 + 4x^2 + 3x - 2, what is the value of p(2)?

For the polynomial q(x) = 2x^3 - 5x^2 + 4x - 1, which one of the following is NOT a factor of q(x)?

Given the polynomial r(x) = x^3 - 6x^2 + 11x - 6, what value of k would make (x - 2) a factor of r(x)?

If x + 3 is a factor of the polynomial s(x) = 3x^3 - x^2 - 10x + 6, what would be the result when s(-3) is calculated?

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