1018rihanna
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Which expression represents [tex]\(-8x^2 + 54x + 140\)[/tex] in factored form?

A. [tex]\((x-70)(-8x+2)\)[/tex]
B. [tex]\((x+1)(8x-140)\)[/tex]
C. [tex]\((x-8)(2x+70)\)[/tex]
D. [tex]\((x+2)(-8x+70)\)[/tex]

Sagot :

GinnyAnswer
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]
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