IBEW Aptitude Test Polynomials and Factoring Questions and Answers 3

Question 1

Factor completely: 2x² - 8

Accepted Answer

2(x - 2)(x + 2)

Answer

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

Question 2

Expand and simplify: (2x - 3)²

Accepted Answer

4x² - 12x + 9

Answer

(2x-3)² = (2x)² - 2(2x)(3) + 3² = 4x² - 12x + 9.

Question 3

Factor: x² - 7x + 12

Accepted Answer

(x - 3)(x - 4)

Answer

Find two numbers with product=12 and sum=-7: -3 and -4. Factored: (x-3)(x-4).

Question 4

What is the value of p(2) if p(x) = x³ - 3x² + 2x - 5?

Accepted Answer

-5

Answer

p(2) = 8 - 12 + 4 - 5 = -5.

Question 5

Add the polynomials: (3x² - 2x + 5) + (x² + 4x - 3)

Accepted Answer

4x² + 2x + 2

Answer

Combine like terms: (3x²+x²) + (-2x+4x) + (5-3) = 4x² + 2x + 2.

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