Question

Factor completely.
2, x, squared, minus, 15, x, plus, 7
2x
2
−15x+7

Answer 1

To factor the quadratic expression \( 2x^2 - 15x + 7 \), we will look for two numbers that multiply to \( 2 \times 7 = 14 \) (the product of the leading coefficient and the constant term) and add up to \(-15\) (the coefficient of \(x\)).

The two numbers that meet these criteria are \(-14\) and \(-1\):
- \(-14 \times -1 = 14\)
- \(-14 + -1 = -15\)

Next, we can rewrite the middle term of the quadratic expression using these numbers:
\[
2x^2 - 14x - 1x + 7
\]

Now we group the terms:
\[
(2x^2 - 14x) + (-1x + 7)
\]

Next, we factor out the greatest common factor from each group:
\[
2x(x - 7) - 1(x - 7)
\]

Now we can factor by grouping:
\[
(2x - 1)(x - 7)
\]

Thus, the completely factored form of the expression \( 2x^2 - 15x + 7 \) is:
\[
\boxed{(2x - 1)(x - 7)}
\]