Next End of Semester Test: Algebra 2A
11
Select the correct answer.
Using long division, what is the quotient of $3 x^{4}+20 x^{3}+14 x^{2}+17 x+30$ and $x+6$ ?
A. $2 x^{3}+14 x^{2}+17 x+30$
B. $3 x^{2}+2 x+2$
C. $3 x^{3}+2 x^{2}+2 x+5$
D. $3 x^{3}-2 x^{2}+2 x-5$
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\(\boxed{3x^{3}+2x^{2}+2x+5}\)
Step 1 :Perform long division of the given polynomial by the divisor:
Step 2 :\(\frac{3x^{4}+20x^{3}+14x^{2}+17x+30}{x+6}\)
Step 3 :Find the quotient:
Step 4 :\(3x^{3}+2x^{2}+2x+5\)
Step 5 :\(\boxed{3x^{3}+2x^{2}+2x+5}\)