Question

(c) Factorise: X^3 - 5x² - X + 5.
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Answer 1

Answer:

Factorise x^3-5x^2- x+5

f(1)= 1-5-1+5 =0

(x-1) is a factor

f(-1)= (-1)^3-5(-1)^2 --(-1) +5 =—-1- 5+1+5 =0

( x+1) is a factor

f(5)= (5 )^3--(5) 5^2 --( 5 ) +5= 125 -1 25—-5+5 =0

( x-- 5) is a factor

Factors of the given problem is( x+1)(x-1) (x-5)

Answer 2

Answer:

$\huge{\bf{\underline{\red{Solution :}}}}$

Given:-

X³ - 5x² - X + 5.

According to Question:-

$\Rightarrow$Group the first two terms and the last two terms.

(x³ - 5x²) + x - 5

$\Rightarrow$Factor out the greatest common factor from each group.

x²(x - 5) + 1 (x - 5)

$\Rightarrow$Factor the polynomial by factoring out the greatest common factor, x − 5.

(x - 5) ( x² + 1)

$\huge{\bf{\underline{\red{ final Answer :}}}}$

(x - 5) ( x² + 1)