IBEW Polynomial Factoring Methods 4

Question 1

Factor the sum of cubes: 8x³ + 27

Accepted Answer

(2x + 3)(4x² - 6x + 9)

Answer

Using a³ + b³ = (a + b)(a² − ab + b²) with a = 2x and b = 3: (2x + 3)(4x² − 6x + 9).

Question 2

Which polynomial CANNOT be factored over integers?

Accepted Answer

x² + 9

Answer

x² + 9 is a sum of squares, which cannot be factored over the integers.

Question 3

Factor by grouping: 2ax + 2ay + bx + by

Accepted Answer

(2a + b)(x + y)

Answer

Group as (2ax + 2ay) + (bx + by) = 2a(x + y) + b(x + y) = (2a + b)(x + y).

Question 4

What value of c makes x² + 8x + c a perfect square trinomial?

Accepted Answer

16

Answer

For a perfect square, c = (8/2)² = 4² = 16, giving (x + 4)².

Question 5

Factor completely: 5x³ - 45x

Accepted Answer

5x(x - 3)(x + 3)

Answer

Factor out 5x to get 5x(x² − 9), then factor the difference of squares: 5x(x − 3)(x + 3).

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