Question

using the remainder and factor theorem factorise the following pilynomial:
${x}^{3} + 10 {x}^{2} - 37x + 26$

Answer 1

Heya user ,
Here is your answer !!

Polynomial : x^3 + 10x^2 - 37x + 26

If f(x) = 1 , then -
( 1 )^3 + 10 × ( 1 )^2 - 37 × 1 + 26
= 1 + 10 - 37 + 26
= 0

So , x = 1
=> ( x - 1 ) is a factor of the polynomial .

Hence , dividing the term by ( x - 1 ) , we get : x^2 + 11x - 26 .

[ Note : See the division in the attachment ]

Now ,
x^2 + 11x - 26
= x^2 + 13x - 2x - 26
= x ( x + 13 ) - 2 ( x + 13 )
= ( x - 2 ) ( x + 13 )

So the factorisation of x^3 + 10x^2 - 37x + 26 is :
( x - 1 ) ( x - 2 ) ( x + 13 ) ........ [Answer]

Hope it helps you !!