IBEW Aptitude Test Polynomials and Factoring Questions and Answers 2

Question 1

Factor: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

x² - 9 is a difference of squares: a² - b² = (a-b)(a+b). Here a=x, b=3. So (x-3)(x+3).

Question 2

Expand: (x + 4)(x + 3)

Accepted Answer

x² + 7x + 12

Answer

FOIL: x·x + x·3 + 4·x + 4·3 = x² + 3x + 4x + 12 = x² + 7x + 12.

Question 3

Factor: 6x² + 9x

Accepted Answer

3x(2x + 3)

Answer

GCF of 6x² and 9x is 3x. Factor out: 3x(2x + 3).

Question 4

What is the degree of the polynomial 4x³ - 2x² + 7x - 1?

Accepted Answer

3

Answer

The degree is the highest power of x, which is 3 (from 4x³).

Question 5

Factor: x² + 5x + 6

Accepted Answer

(x + 2)(x + 3)

Answer

Find two numbers that multiply to 6 and add to 5: 2 and 3. Factored: (x+2)(x+3).

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