MATH SOLVE

5 months ago

Q:
# PLEASE HELP ME!! It's a real struggle manWhich of the following expressions is this one equivalent to? [tex]\frac{4x^{3}+2x^{2}+x+3}{x+2}[/tex]A.) [tex]4x^{3} -6x+13+\frac{23}{x+2}[/tex]B.) [tex]4x^{2} -6x+13-\frac{23}{x+2}[/tex]C.) [tex]4x-6+\frac{13}{x+2}[/tex]D.) [tex]4x^{2} +13-\frac{2}{x+2}[/tex]

Accepted Solution

A:

Answer:Option B.Step-by-step explanation:The given expression is [tex]\frac{4x^{3}+2x^{2}+x+3}{x+2}[/tex]Now we will divide the numerator by the given denominator.x + 2 ) 4x³ + 2x² + x + 3 ( 4x² - 6x + 13 4x³ + 8x² -6x² + x -6x² -12 x 13x + 3 13x + 26 - 23 Therefore, remainder is (-23) and quotient is (4x² - 6x + 13) forms the expression as 4x³ - 6x + 13 - [tex]\frac{23}{x + 2}[/tex]Option B. is the answer.