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QuizMultiple Choice

Synthetic Division and the Remainder Theorem — Quiz

Question 1 • Algebra II

Use synthetic division to solve open paren 2 x cubed plus 4 x squared minus 35 x plus 15 close paren divided by open paren x minus 3 close paren What is the quotient?

Answer
A
2 x cubed plus 10 x squared minus 5 x
B
2 x squared plus 10 x minus 5
C
2 x squared minus 2 x minus 29 plus the fraction with numerator 102 and denominator x minus 3
D
2 x squared minus 2 x minus 29 plus the fraction with numerator 102 and denominator x plus 3

Explanation

For division by x − 3, use 3 in synthetic division with coefficients 2, 4, −35, and 15. Bring down 2; then 2 × 3 = 6, giving 10; 10 × 3 = 30, giving −5; and −5 × 3 = −15, giving remainder 0. The quotient is 2x² + 10x − 5, choice A.

AI-written and checked against the verified answer.

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