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Question

Using factor theorem find which of the following is a factor of the polynomial p(x)=3x2+10x+7.

A
(x+1)
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B
(x+7)
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C
(x1)
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D
(x7)
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Solution

The correct option is A (x+1)
Given polynomial: p(x)=3x2+10x+7

By factor theorem, if (xa)is a factor of p(x),then p(a)=0

Checking (x+1):
p(1)=3×(1)2+10×(1)+7
p(1)=0
Hence, (x+1) is a factor of p(x).

Checking (x+7):
p(7)=3×(7)2+10×(7)+7
p(7)=14770+7=840
Hence, (x+7) is not a factor of p(x).

Checking (x1):
p(1)=3×(1)2+10×(1)+7
p(1)=20
Hence, (x1) is a not factor of p(x).

Checking (x7):
p(7)=3×(7)2+10×(7)+7
p(7)=147+70+7=2240
Hence, (x7) is not a factor of p(x).

So, (x+1) is the factor of the polynomial p(x)=3x2+10x+7.

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