To factor the quadratic expression [tex]\(-8 x^2 + 54 x + 140\)[/tex], we need to express it as a product of two binomials.
Upon factoring the given quadratic expression, we end up with the following factored form:
[tex]\[
-2 \cdot (x + 2) \cdot (4x - 35)
\][/tex]
This can be checked by expanding back to the original quadratic expression, confirming its correctness.
Let's go through the process to match this result with one of the given options:
1. [tex]\((x-70)(-8 x+2)\)[/tex]
- This does not match our factored form.
2. [tex]\((x+1)(8 x-140)\)[/tex]
- This does not match our factored form either.
3. [tex]\((x-8)(2 x+70)\)[/tex]
- This also does not match our factored form.
4. [tex]\((x+2)(-8 x+70)\)[/tex]
- This expression is close to our form. However, it needs a factor of [tex]\(-2\)[/tex]. When we include this factor, this matches:
[tex]\[
-2 \cdot (x + 2) \cdot (4x - 35)
\][/tex]
Thus, the correct option is:
[tex]\[
(x+2)(-8x + 70)
\][/tex]
