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11. True or False: If 2x^3 − 9x^2 + 13x + k is divisible by x − 2, then it is also divisible by x − 1. Justify your answer fully with work.
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11. True or False:

If 2x^3 − 9x^2 + 13x + k is divisible by x − 2, then it is also divisible by x − 1.

Justify your answer fully with work.

User Crisboot
by
8.8k points

1 Answer

4 votes

Answer:

Hi,

True.

Explanation:


If\ P(x)=2x^3- 9x^2 + 13x + k\ is\ divisible\ by\ x - 2\ then\\P(2)=2*2^3-9*2^2+13*2+k=0\\6+k=0\\k=-6\\P(1)=2*1-9*1+13*1-6=0\\\\P(x)\ is \ divisible\ by\ x-1.\\

User Digvijay Sawant
by
8.2k points
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