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TEKS A.10(C) Determine the quotient of divided by a polynomial of degree one a exceed the degree of the dividend (SUPF
PROBLEM
Y
Which expression is equivalent to

(x^(2)+3x-32)÷(x-4)" ? "
A
x+7-(4)/(x-4)
B
x+8

cx+7

TEKS A. $10$ (C) Determine the quotient of divided by a polynomial of degree one a exceed the degree of the dividend (SUPF $\newline$ PROBLEM $Y$ $\newline$ Which expression is equivalent to $\newline$ $\left(x^{2}+3 x-32\right) \div(x-4) \text { ? }$ $\newline$ A $x+7-\frac{4}{x-4}$ $\newline$ B $x+8$ $\newline$ $c x+7$

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Conjugate root theorems

Full solution

Q. TEKS A.

10

(C) Determine the quotient of divided by a polynomial of degree one a exceed the degree of the dividend (SUPF

\newline

PROBLEM

Y

\newline

Which expression is equivalent to

\newline

\left(x^{2}+3 x-32\right) \div(x-4) \text { ? }

\newline

A

x+7-\frac{4}{x-4}

\newline

B

x+8

\newline

c x+7

Divide using polynomial long division: : Let's do polynomial long division to divide $(x^2 + 3x - 32)$ by $(x - 4)$ .
Multiply by $7$ : : Now, $x$ goes into $7x$ , $7$ times. Multiply $(x - 4)$ by $7$ to get $7x - 28$ . Subtract that from $7x - 32$ to get $-4$ .
Identify the remainder: : Since $-4$ is a constant and we're dividing by a linear polynomial, this is the remainder. Write the remainder as a fraction over the divisor.
Write the final expression: : The quotient is $x + 7$ with a remainder of $-4$ , so the expression is $x + 7 - \frac{4}{x - 4}$ .

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