Perform the operation(s) and simplify completely. (4−2x)frac(−6x2+10x+21/ 4−2x) (1 point) Responses −6x2+10x+21 negative 6 x squared plus 10 x plus 21 −x3+5x2−6x+3 negative x cubed plus 5 x squared minus 6 x plus 3 −x2+2x−8 negative x squared plus 2 x minus 8 −x2−2x+12

Answer 1

To perform the operation and simplify the expression \((4 - 2x) \frac{-6x^2 + 10x + 21}{4 - 2x}\), notice that the \( (4 - 2x) \) in the numerator and denominator will cancel out, as long as \( 4 - 2x \neq 0 \) (which occurs at \( x = 2 \)).

The operation simplifies as follows:

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

Now we will check if \(-6x^2 + 10x + 21\) can be further simplified or factored.

To do that, let's look for roots or factors. We can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -6, b = 10, c = 21 \):

\[ b^2 - 4ac = 10^2 - 4(-6)(21) = 100 + 504 = 604 \]

Since \( 604 \) is not a perfect square, the quadratic does not factor nicely into integers.

Thus, the expression \(-6x^2 + 10x + 21\) does not simplify further, and we are left with:

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

The final answer is:

\(-6x^2 + 10x + 21\)