Answer:
[tex]2x^3+3x^2-32x+15=(x+5)(2x-1)(x-3)[/tex]
Step-by-step explanation:
If "-5" is a zero of the function, then we know that the binomial (x+5) divides perfectly our cubic expression.
By using division of polynomials we find that :
[tex]f(x) = (x+5)*(2x^2-7x+3)[/tex]
and now we proceed to factor out the trinomial :
[tex]2x^2-7x+3 = 2x^2-6x-x+3 =\\2x(x-3)-(x-3)= (2x-1)(x-3)[/tex]
Therefore the full factorization is:
[tex]2x^3+3x^2-32x+15=(x+5)(2x-1)(x-3)[/tex]
