Question

Factorise using factor theorem:
x^3 + 2x^2 – 13x + 10​

Answer 1

Step-by-step explanation:

x³+2x²-13x+10

if x=1,

1³+2×1²-13×1+10

=1+2-13+10

=13-13=0

so, (x-1) is a factor

x³+2x²-13x+10

x³-x²+3x²-3x-10x+10

x²(x-1)+3x(x-1)-10(x-1)

(x-1)(x²+3x-10)

(x-1) (x²+5x-2x-10)

(x-1)[x(x+5)-2(x+5)]

(x-1)(x-2)(x+5)