Question

Find all the common zeroes of the polynomials x^3+5x^2-9x-45 and x^3+8x^2+15x

Plz do it step by step. . Like all the divisions and plz divide it in a befitting manner

Answer 1

Find all the common zeroes of the polynomials x^3+5x^2-9x-45 and x^3+8x^2+15x

Let us factor each expression.
x^3+5x^2-9x-45 can be factored nby groupimg 1st 2 terms and 2nd 2 terms and taking out common factors
x^3+5x^2-9x-45 = x^2 (x+5) -9(x+5)= (x^2-9)(x+5) factor further using a^2-b^2=(a-b)(a+b)
=> x^3+5x^2-9x-45 = (x-3)(x+3)(x+5)

x^3+8x^2+15x = x(x^2+8x+15) = x(x+3)(x+5)

Comparing factors we see that (x+3)(x+5) are common factors
Hence common roots are x = -3 and x = -5 Answer