Question

Q. Using the Remainder and Factor Theorem , factorise
x 3 + 10 x 2 - 37 x + 26

Answer 1

Answer:

Step-by-step explanation:

If (x-1)=0

x=1

f(x)=x^3+10x^2-37x+26

f(1)=1^3+10(1)^2-37(1)+26

=1+10-37+26

=37-37

=0

∵(x-1) is a factor

    1    1   10   -37   26

         0   1       11   -26

         1    11    -26    0

$x^{2} +11x-26=0$

(x-1)($x^{2} +11x-26$)

(x-1)($x^{2} +13x-2x-26$)

(x-1)(x(x+13)-2(x+13))

(x-1)(x+13)(x-2)