Factor:

6x² + 13x − 5 = 0

A. (2x + 5)(3x − 1) = 0
Correct! The factors are equivalent to the quadratic expression.

B. (2x − 5)(3x + 1) = 0
Incorrect. Check the signs within each factor.

C. (2x + 5)(3x + 1) = 0
Incorrect. Check the signs of one of the factors.

D. (2x − 5)(3x − 1) = 0
Incorrect. Check the signs of one of the factors.

Solve:

x² + 8x + 15 = 0

A. 5 and 3
Incorrect. Set the factors equal to 0 and solve for x.

B. -5 and -3
Correct! – 5 and – 3 make the equation true.

C. 8 and 15
Incorrect. Factor the expression and then set the factors equal to 0.

D. 0 and 15
Incorrect. Factor the expression and then set the factors equal to 0.

Solve:

4x² + 2 = 11

A. ± 3 2
Correct!

B. No solution
Incorrect. To solve this equation using factoring, subtract 11 from both sides of the equation, and then factor the binomial difference of two perfect squares.

C. ± 2 3
Incorrect. When you apply the Zero Product Property, you will set each factor equal to 0 and then solve for x. You will either add or subtract 3, and then divide by the coefficient of x, which is 2.

D. 3, 11
Incorrect. To solve this equation using factoring, subtract 11 from both sides of the equation, and then factor the binomial difference of two perfect squares.

The solutions for the following quadratic equation are -1 and 7. Determine the constant that would make the following equation true.

6x² − 42x + ____= 0

A. -7
Incorrect. Set up the factors of the quadratic and then distribute.

B. -48
Correct!

C. 7
Incorrect. Set up the factors of the quadratic and then distribute.

D. 48
Incorrect. Set up the factors of the quadratic and then distribute.

The solutions for the following quadratic equation are both -5. Determine the missing value that would make the following equation true.

x² + 10x + ____= 3

A. 5
Incorrect. Set up the factors for the quadratic, distribute, and then subtract 3 to determine the constant.

B. -5
Incorrect. Set up the factors for the quadratic, distribute, and then subtract 3 to determine the constant.

C. 10
Incorrect. Set up the factors for the quadratic, distribute, and then subtract 3 to determine the constant.

D. 28
Correct!