fill in the missing values below one at a time to find the quotient when -16x^3 + 12x^2 + 28x - 21 is…

Explanation:

Step1: Divide first - term of dividend by first - term of divisor

To get the first term of the quotient $4x^{2}$, we divide $-16x^{3}$ (first term of $-16x^{3}+12x^{2}+28x - 21$) by $-4x$ (first term of $-4x + 3$), i.e., $\frac{-16x^{3}}{-4x}=4x^{2}$.

Step2: Multiply divisor by first - term of quotient

Multiply $-4x + 3$ by $4x^{2}$. We get $4x^{2}(-4x)=-16x^{3}$ and $4x^{2}(3)=12x^{2}$.

Step3: Find the second - term of the quotient

The remaining part of the dividend after subtracting the product of the first - term of the quotient and the divisor from the dividend is $(12x^{2}+28x - 21)-12x^{2}=28x - 21$. Divide the first term of this new polynomial $28x$ by the first term of the divisor $-4x$. So, $\frac{28x}{-4x}=-7$. The second - term of the quotient is $-7$.

Step4: Multiply divisor by second - term of quotient

Multiply $-4x + 3$ by $-7$. We have $-7(-4x)=28x$ and $-7(3)=-21$.

The completed table:

	$4x^{2}$	$-7$
$-4x$	$-16x^{3}$	$28x$
$+3$	$12x^{2}$	$-21$

Answer:

The quotient is $4x^{2}-7$.