Question

Which expression is a factor of 2x^2 + 9x -35

A. x - 7
B. x + 5
C. 2x-5
D. 2x+7

Answer 1

To determine which expression is a factor of the quadratic \(2x^2 + 9x - 35\), we can use the factoring process.

The quadratic can generally be factored into the form \((ax + b)(cx + d)\). For \(2x^2 + 9x - 35\), we want to find two numbers that multiply to \(2 \times -35 = -70\) and add up to \(9\).

The pairs of factors of \(-70\) that add to \(9\) are \(14\) and \(-5\), since \(14 + (-5) = 9\).

Now we can rewrite the middle term \(9x\) using these numbers:
\[
2x^2 + 14x - 5x - 35
\]

Next, we can group the terms:
\[
(2x^2 + 14x) + (-5x - 35)
\]

Factoring out the common factors gives us:
\[
2x(x + 7) - 5(x + 7)
\]

Now we can factor by grouping:
\[
(2x - 5)(x + 7)
\]

From this factored form, we see that the factors of the expression are \((2x - 5)\) and \((x + 7)\).

Therefore, the answer to which expression is a factor of \(2x^2 + 9x - 35\) is:
**C. \(2x - 5\)**.