IBEW Polynomial Factoring Methods 5

Question 1

Factor: x³ + 8

Accepted Answer

(x + 2)(x² - 2x + 4)

Answer

Sum of cubes: x³ + 2³ = (x + 2)(x² − 2x + 4) using a³ + b³ = (a + b)(a² − ab + b²).

Question 2

Factor: 4x² + 12x + 9

Accepted Answer

(2x + 3)²

Answer

4x² + 12x + 9 = (2x)² + 2(2x)(3) + 3² = (2x + 3)², a perfect square trinomial.

Question 3

Which is the fully factored form of 2x³ - 8x?

Accepted Answer

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

Answer

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

Question 4

Factor: 3x² + 10x - 8

Accepted Answer

(3x - 2)(x + 4)

Answer

AC method: 3×(−8)=−24; factors summing to 10 are 12 and −2; grouping gives (3x − 2)(x + 4).

Question 5

What technique is most efficient for factoring x⁶ - 64?

Accepted Answer

Difference of squares applied twice

Answer

x⁶ − 64 = (x³)² − 8² = (x³ − 8)(x³ + 8), then each cubic can be factored further.

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