Question

question 3 of 25
what is the quotient when (x + 3) is divided into the polynomial $2x^2 + 3x - 9$?

a. $2x + 1$ with no remainder
b. $2x - 5$ with no remainder
c. $x + 3$ with a remainder of -2
d. $2x - 3$ with no remainder

Explanation:

Step1: Divide leading terms

$\frac{2x^2}{x} = 2x$

Step2: Multiply divisor by 2x

$2x(x + 3) = 2x^2 + 6x$

Step3: Subtract from polynomial

$(2x^2 + 3x - 9) - (2x^2 + 6x) = -3x - 9$

Step4: Divide new leading term

$\frac{-3x}{x} = -3$

Step5: Multiply divisor by -3

$-3(x + 3) = -3x - 9$

Step6: Subtract to find remainder

$(-3x - 9) - (-3x - 9) = 0$

Answer:

D. 2x - 3 with no remainder