find the x and y intercepts of P(x)=1x^3−10x^2−11x

Answer 1

y intercept = 0 or the origin, the point (0,0)

the y intercept is the y value when x=0, P(0) = 1(0^3) -10(0^2 -11(0) = 0-0-0= 0

x intercept is the x value when y = 0

it's not easy to solve a cubic equation, except in a problem like this where the x factors out

x = 0 or the origin is one x intercept, same as the y intercept

then you're left with a quadratic factor

x^2 -10x -11 = 0

which factors into

(x-11)(x+1) = 0

set each factor =0 and solve for x

x= -1 or 11 are two more x intercepts or the points (-1,0) and (11,0)