IBEW Polynomials and Factoring 2

Question 1

Factor completely: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

This is a difference of squares: a² - b² = (a+b)(a-b). x² - 9 = x² - 3² = (x+3)(x-3).

Question 2

Multiply: (2x + 3)(x - 4)

Accepted Answer

2x² - 5x - 12

Answer

FOIL: 2x·x + 2x·(-4) + 3·x + 3·(-4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12.

Question 3

Factor: x² + 7x + 12

Accepted Answer

(x + 3)(x + 4)

Answer

Find two numbers that multiply to 12 and add to 7: 3 and 4. So (x+3)(x+4).

Question 4

What is the GCF of 12x³y², 18x²y, and 24xy³?

Accepted Answer

6xy

Answer

GCF of 12, 18, 24 is 6. Lowest power of x is x¹. Lowest power of y is y¹. GCF = 6xy.

Question 5

Factor completely: 3x² - 12

Accepted Answer

3(x + 2)(x - 2)

Answer

Factor out 3: 3(x² - 4). Then factor difference of squares: 3(x+2)(x-2).

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