Clear my choice
If $-2 x^{3}-6 x^{2}+5 x-7$ is divided by $x-7$ to give a quotient of $-2 x^{2}$ and a remainder of -952 , then which of the following is true?
Select one:
a. $(x-7)\left(-2 x^{2}-20 x-135\right)=-952$
b. $-2 x^{3}-6 x^{2}+5 x-7=(x-7)\left(-2 x^{2}-20 x-135\right)+952$
C. $(x-7)\left(-2 x^{2}-20 x-135\right)=952$
d. $-2 x^{3}-6 x^{2}+5 x-7=(x-7)\left(-2 x^{2}-20 x-135\right)-952$
Glear my choice
Answer
\(\boxed{\text{d. }-2 x^{3}-6 x^{2}+5 x-7=(x-7)left(-2 x^{2}-20 x-135 ight)-952}\)
Step 1 ：Given that the polynomial $-2x^3 - 6x^2 + 5x - 7$ is divided by $x-7$ to give a quotient of $-2x^2$ and a remainder of -952.
Step 2 ：Using the division formula: Dividend = (Divisor * Quotient) + Remainder
Step 3 ：Substitute the given values: $-2x^3 - 6x^2 + 5x - 7 = (x-7)(-2x^2) + (-952)$
Step 4 ：Comparing the given options, we find that option d matches the equation: $-2 x^{3}-6 x^{2}+5 x-7=(x-7)left(-2 x^{2}-20 x-135 ight)-952$
Step 5 ：\(\boxed{\text{d. }-2 x^{3}-6 x^{2}+5 x-7=(x-7)left(-2 x^{2}-20 x-135 ight)-952}\)
