Question

(x+2) is a factor of f(x)=x3+px+6.find the value of p​

Answer 1

Answer:

(x+2) is a factor of f(x)=x3+px+6.

then, x= -2.

so,   f(x)=3x+px+6=0

f(-2)=3(-2)+p(-2)+6=0

f(-2)=-6-2p+6=0

f(-2)=-2p=0

f(x)=p=0/2

f(x)=p=0

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Answer 2

Concept

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Given

Given that (x + 2) is a factor of f(x) = x³ + px + 6.

Find

We have to find the value of p.

Solution

Since (x + 2) is a factor of f(x), we can say x = - 2 is a solution of the equation of f(x) = 0.

Now, f(- 2) = 0

i.e. (- 2)³ + p * (- 2) + 6 = 0

i.e. - 8 - 2p + 6 = 0

i.e. - 2 = 2p

i.e. p = - 1.

Hence, the value of p is - 1.

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