Question

Perform the operation(s) and simplify completely.
(4-2x) (-6x^2+10x+21/4-2x)
A. -x^3+5x^2-6x+3
B. -x^2+2x-8
C. -6x^2+10x+21
D. -x^2-2x+12

Answer 1

To simplify the expression \((4-2x) \left(-\frac{6x^2 + 10x + 21}{4-2x}\right)\), we can first notice that \(4 - 2x\) is a common factor in the numerator and the denominator.

We can rewrite the expression as follows:

\[
(4-2x) \left(-\frac{6x^2 + 10x + 21}{4-2x}\right) = - (6x^2 + 10x + 21)
\]

This simplifies to:

\[
- (6x^2 + 10x + 21) = -6x^2 - 10x - 21
\]

Thus, the final expression is:

\[
-6x^2 - 10x - 21
\]

Now we need to check if any of the given options match this result. None of the options provided exactly match, however, we can check if \( - (6x^2 + 10x + 21) \) can still lead to a equivalent option:

Rewriting \(-6x^2 - 10x - 21\):

Now from the options:

A. \(-x^3 + 5x^2 - 6x + 3\)

B. \(-x^2 + 2x - 8\)

C. \(-6x^2 + 10x + 21\) (This is simply \(-6\) times what we have, not a match.)

D. \(-x^2 - 2x + 12\)

None of the options provided directly match the simplification.

So we double-check:

1. Start again with the original:

\((4-2x) \left(-\frac{6x^2 + 10x + 21}{4-2x}\right)\)

Cancelling \((4 - 2x)\):

Which gives us \(- (6x^2 + 10x + 21)\), keeping an eye for correct signs, yield the same result.

Thus, the closest to my result is \(C\) but not quite equal, so make sure of values inserted:

After testing back:

None of the options fit. The simplification yields \(-6x^2 - 10x - 21\).

Final result doesn't match any of those provided correctly.