Use the drawing tool(s) to form the correct answer on the provided number line.Consider the given function.f(x) = x^3 - 2x^2 - 11x + 12Use the remainder theorem to find the x-intercepts of the function, and plot their x-values on the number line.

Answer: x= 1, x= 4, and x= -3Step-by-step explanation:Use the possible combinations of factors of the constant term of the polynomial to find a first root. Try 1, -1, 2, -2, 3, -3, etc.Notice in particular that x = 1 is a root (makes f(1) = 0):[tex]f(1)=x^3-2*1^2-11*1+12=1-2-11+12=13-13=0[/tex]So we know that x=1 is a root, and therefore, the binomial (x-1) must divide the original polynomial exactly.As we perform the division, we find that the remainder of it is zero (perfect division) and the quotient is: [tex]x^2-x-12[/tex]This is now a quadratic expression for which we can find its factor form:[tex]x^2-x-12=x^2-4x+3x-12=x(x-4)+3(x-4)=(x-4)*(x+3)[/tex]From the factors we just found, we conclude that x intercepts (zeroes) of the original polynomial are those x-values for which each of the factors: (x-1), (x-4) and (x+3) give zero. That is, the values x= 1, x= 4, and x= -3. (these are the roots of the polynomial.Mark these values on the number line as requested.