IBEW Aptitude Test Polynomial Factoring Methods Questions and Answers 2

Question 1

Factor: x² - 16

Accepted Answer

(x - 4)(x + 4)

Answer

Difference of squares: x² - 4² = (x-4)(x+4).

Question 2

What are the roots of x² - 5x + 6 = 0?

Accepted Answer

x = 2 and x = 3

Answer

Factor: (x-2)(x-3) = 0. So x = 2 or x = 3.

Question 3

Factor by grouping: x³ + 2x² + 3x + 6

Accepted Answer

(x + 2)(x² + 3)

Answer

Group: (x³+2x²) + (3x+6). Factor each: x²(x+2) + 3(x+2). Factor out (x+2): (x+2)(x²+3).

Question 4

Which is a perfect square trinomial?

Accepted Answer

x² + 6x + 9

Answer

x² + 6x + 9 = (x+3)². Check: 2×1×3=6 (middle term), 3²=9 (constant). Perfect square.

Question 5

Factor completely: 2x³ - 8x

Accepted Answer

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

Answer

Factor out 2x: 2x(x²-4). Factor difference of squares: 2x(x-2)(x+2).

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