Question

factorize using factor theorem : x^3-6x ^2+3x+10

Answer 1

Answer: The factors are

(x-1)(x-2)(x-5)

Step-by-step explanation:

I hope ut helps❤️

Answer 2

Given:

x^3-6x ^2+3x+10

To Find:

factorize using factor theorem

Solution:

Factor theorem states that if a polynomial is divided by a linear equation of the form x-a by putting the value of polynomial P(x) as P(a) then the value of  polynomial becomes zero,

Now using the same theory we will try to check if (x+1) is a factor of the given polynomial by putting P(-1), which goes as,

$P(x)=x^3-6x^2+3x+10\\P(-1)=-1-6-3+10\\P(-1)=0$

So x+1 is a factor of the given polynomial,

Now after taking x+1 common out of the given polynomial we have,

$P(x)=x^3-6x^2+3x+10\\P(x)=(x+1)(x^2-7x+10)$

Now factorizing the quadratic equation using the splitting method,

$P(x)=(x+1)(x^2-7x+10)\\P(x)=(x+1)(x^2-5x-2x+10)\\P(x)=(x+1)(x(x-5)-2(x-5))\\P(x)=(x+1)(x-2)(x-5)$

Hence, the factorization of the polynomial is (x+1)(x-2)(x-5).