Question

Find the factors of the polynomial given below (x^2 - 6x)^2 +12 (x^2 - 6x) +35​

Answer 1

Answer:

Step-by-step explanation:

The two zeroes of the polynomial is 2+

3​ ,2− 3

​

Therefore, (x−2+ 3​ )(x−2− 3 )=x 2 +4−4x−3

= x 2 −4x+1 is a factor of the given polynomial.

Using division algorithm, we get

x 4 −6x 3 −26x 2 +138x−35=(x 2 −4x+1)(x 2 −2x−35)

So, (x 2 −2x−35) is also a factor of the given polynomial.

x 2−2x−35

=x 2 −7x+5x−35

=x(x−7)+5(x−7)

=(x−7)(x+5)

Hence, 7 and −5are the other zeros of this polynomial.