Question

Find the value of a if x-a is a factor of x³-a²x+x+2

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Answer 1

Answer:

-2

Step-by-step explanation:

Let p(x) = x³ - a²x + x + 2 be the given polynomial. By factor theorem , ( x - a ) is a factor of p(x) of p(a) = 0.

Now,

p(a)=0

=> a³ - a² × a + a + 2 = 0

=> a³ - a³ + a + 2 = 0

=> a + 2 = 0

=> a = -2

Hence, (x-a) is a factor of the given polynomial, if a = -2.

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Answer 2

Answer:

I consider the function,

F(x)= x3−a2x+x+2

Given x-a is a factor of F.

Then we get x2+ax+1 as product and a+2 as remainder.

Then we get x2+ax+1 as product and a+2 as remainder.Since x-a is a factor of F, F must be divisible by x-a. This will happen if the remainder is zero

Then we get x2+ax+1 as product and a+2 as remainder.Since x-a is a factor of F, F must be divisible by x-a. This will happen if the remainder is zeroi.e if a+2=0

I.e if a=−2