Question

factories :x cube-x square-17x-15​

Answer 1

Answer:

(x+1)(x+3)(x-5)

Step-by-step explanation:

x^3-x^2-17x-15

Let us think, f(x)=x^3-x^2-17x-15

if we put x=-1,

f(-1)=(-1)^3-(-1)^2-17(-1)-15

= -1-1+17-15 = 0

x= -1

then, x+1=0

then it is a factor of f(x)

using vanishing method,

x^3-x^2-17x-15

=x^3+x^2-2x^2-2x-15x-15

=x^2(x+1)-2x(x+1)-15(x+1)

=(x+1)(x^2-2x-15)

=(x+1)(x^2-5x+3x-15)

=(x+1){x(x-5)+3(x-5)}

=(x+1)(x-5)(x+3)

=(x+1)(x+3)(x-5)