Question

period:____ 3.5.2 quiz b find each quotient using long division. 1. $(7x^3 - 44x^2 + 49x - 21) \div (x - 5)$

Explanation:

Step1: Divide leading terms

$\frac{7x^3}{x} = 7x^2$
Multiply divisor by $7x^2$:
$7x^2(x-5) = 7x^3 - 35x^2$
Subtract from dividend:
$(7x^3 - 44x^2 + 49x - 21) - (7x^3 - 35x^2) = -9x^2 + 49x - 21$

Step2: Divide new leading terms

$\frac{-9x^2}{x} = -9x$
Multiply divisor by $-9x$:
$-9x(x-5) = -9x^2 + 45x$
Subtract from current polynomial:
$(-9x^2 + 49x - 21) - (-9x^2 + 45x) = 4x - 21$

Step3: Divide new leading terms

$\frac{4x}{x} = 4$
Multiply divisor by $4$:
$4(x-5) = 4x - 20$
Subtract from current polynomial:
$(4x - 21) - (4x - 20) = -1$

Answer:

The quotient is $7x^2 - 9x + 4$ with a remainder of $-1$, or written as $7x^2 - 9x + 4 - \frac{1}{x-5}$