IBEW Polynomial Factoring Methods 2

Question 1

Factor the trinomial: x² + 11x + 30

Accepted Answer

(x + 3)(x + 10)

Answer

Find two numbers that multiply to 30 and add to 11: 3 and 10, giving (x + 3)(x + 10).

Question 2

Which expression is a perfect square trinomial?

Accepted Answer

x² + 6x + 9

Answer

x² + 6x + 9 = (x + 3)² because the middle term equals 2 times the square root of the last term times x.

Question 3

Factor completely: 3x² - 12

Accepted Answer

3(x - 2)(x + 2)

Answer

Factor out 3 to get 3(x² − 4), then factor the difference of squares to get 3(x − 2)(x + 2).

Question 4

What are the factors of x² - 10x + 25?

Accepted Answer

(x - 5)²

Answer

x² − 10x + 25 is a perfect square trinomial equal to (x − 5)².

Question 5

Factor: 2x² + 5x + 3

Accepted Answer

(2x + 3)(x + 1)

Answer

Using the AC method: 2×3=6; factors of 6 summing to 5 are 2 and 3, giving (2x + 3)(x + 1).

IBEW - Aptitude Test Practice Test