Use synthetic division to express $P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35$ in the form (divisor)(quotient)+ remainder for the divisor x - 5.

A) $( x - 3 ) \left( 25 x ^ { 2 } + 5 x + 2 \right) - 25$
B) $( x - 5 ) \left( 3 x ^ { 2 } + 5 x + 2 \right) - 25$
C) $( x - 5 ) \left( 3 x ^ { 2 } + 2 \right) - 25$
D) $( x - 5 ) \left( 3 x ^ { 2 } + x + 2 \right)$
E)none of these

Question

Use synthetic division to express $P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35$ in the form (divisor)(quotient)+ remainder for the divisor x - 5.
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A) $( x - 3 ) \left( 25 x ^ { 2 } + 5 x + 2 \right) - 25$
B) $( x - 5 ) \left( 3 x ^ { 2 } + 5 x + 2 \right) - 25$
C) $( x - 5 ) \left( 3 x ^ { 2 } + 2 \right) - 25$
D) $( x - 5 ) \left( 3 x ^ { 2 } + x + 2 \right)$
E)none of these

Quizplus · Accepted Answer

Using synthetic division with the divisor $x - 5$, we find the quotient to be $3x^2 + 5x + 2$ and the remainder to be $-25$. Therefore, the expression can be written as $(x - 5)(3x^2 + 5x + 2) - 25$.

Use Synthetic Division to Express P(x)=3x3−10x2−23x−35P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35P(x)=3x3−10x2−23x−35

Use Synthetic Division to Express $P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35$