IBEW Polynomial Factoring Methods 3

Question 1

Factor: 4x² - 25

Accepted Answer

(2x - 5)(2x + 5)

Answer

4x² − 25 is a difference of squares: (2x)² − 5² = (2x − 5)(2x + 5).

Question 2

What is the GCF of 12x³, 18x², and 6x?

Accepted Answer

6x

Answer

The GCF of 12, 18, and 6 is 6, and the lowest power of x is x¹, so GCF = 6x.

Question 3

Factor completely: x⁴ - 16

Accepted Answer

(x - 2)(x + 2)(x² + 4)

Answer

x⁴ − 16 = (x² − 4)(x² + 4) = (x − 2)(x + 2)(x² + 4); x² + 4 cannot be factored further over integers.

Question 4

Factor: x² - x - 12

Accepted Answer

(x - 4)(x + 3)

Answer

Find numbers multiplying to −12 and adding to −1: −4 and 3, giving (x − 4)(x + 3).

Question 5

If one factor of x² - 7x + 10 is (x - 2), what is the other factor?

Accepted Answer

(x - 5)

Answer

Dividing x² − 7x + 10 by (x − 2) gives (x − 5), verified by −2 × −5 = 10 and −2 + −5 = −7.

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