Question

homework 5: polynomials
multiply.
$(x - 4)(x + 5)(x - 2) =$

Explanation:

Step1: Multiply first two binomials

Use FOIL method: $(a+b)(c+d)=ac+ad+bc+bd$
$$(x-4)(x+5) = x^2 +5x -4x -20 = x^2 +x -20$$

Step2: Multiply result by third binomial

Distribute each term: $(x^2+x-20)(x-2)$
$$x^2(x-2) + x(x-2) -20(x-2) = x^3 -2x^2 +x^2 -2x -20x +40$$

Step3: Combine like terms

Simplify the polynomial
$$x^3 + (-2x^2+x^2) + (-2x-20x) +40 = x^3 -x^2 -22x +40$$

Answer:

$x^3 - x^2 - 22x + 40$