What are the factors and zeros of g(x)=2x^2+9x−5?

Question

Select from the drop-down menus to correctly complete the sentences.

The factors are       and      

answer choices: (2x+1), (2x-1), (2x+5), (2x-5) and (x-5), (x+5), (x-2), (x+2)

the zeros are       and      

answer choices: -5/2, 5/2, -1/2, 1/2 and 1, -1, 5, -5

Answer 1

Factoring:

g(x) = 2x² + 9x - 5 = 2x² + 10x - x - 5 = (2x² + 10x) - (x + 5) = 2x(x + 5) - (x + 5) = (x + 5)(2x -1)

Calculating roots/zeros:

x + 5 = 0

x = -5

2x -1 = 0

x = 1/2

Answer 2

Hello, Alesia,

I believe this equation can be factored to (x+5) and (2x-1). I believe those will result in the original equation when multiplied together. Check my math, to be certain.

If these are correct, the zeros would be -5 and 1/2.

Please check these values.

Bob