Question

(x+1) is a factor of p(x)=3x³+2x²+7x+8,Examine the validity of the given statement.

Answer 1

Hi ,

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By factor theorem :

If ( x - a ) is a factor of polynomial p( x )

then p( a ) = 0
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Here ,

It's given that ( x + 1 ) is a factor of

p( x ) = 3x³ + 2x² + 7x + 8

We have to show that p( - 1 ) = 0

p( - 1 ) = 3(-1 )³ + 2( -1 )² + 7( -1 ) + 8

= -3 + 2 - 7 + 8

= -10 + 10

= 0

Therefore ,

( x + 1 ) is a factor of p( x )

I hope this helps you.

: )

Answer 2

Given, p(x) = 3x³ + 2x² + 7 x + 8

For (x + 1) to be a factor of p(x),

the condition: p(–1) = 0; should be satisfied.

p(–1) = 3(–1)³ + 2(–1)² + 7(–1) + 8

= 3(–1) + 2(1) + 7(–1) + 8

= –3 + 2 – 7 + 8

= 0
Thus, (x + 1) is a factor of the given polynomial.

 therefore, the given statement is valid.