Question

use factor theorem
factorine x3-10x2-53x-​

Answer 1

Answer:

Answer

x

3

−10x

2

−53x−42

let p(x)=x

3

−10x

2

−53x−42

let x=−1

p(−1)=(−1)

3

−10(−1)

2

−53(−1)−42

=−1−10+53−42

=0

Hence (x+1) is factor of polynomial

p(x)=x

3

+x

2

−11x

2

−42x−11x−42

⇒x

2

(x+1)−11x(x+1)−42(x+1)

⇒(x+1)(x

2

−11x−42)

x

2

−11x−42=x

2

−14x+3x−42

=x(x−14)+3(x−14)

=(x+3)(x−14)

∴p(x)=(x+1)(x+3)(x−14)