Question

expand the expression to a polynomial in standard form:
$(x + 1)(2x - 5)(x - 3)$

Explanation:

Step1: Multiply first two factors

Multiply \((x + 1)\) and \((2x - 5)\) using distributive property (FOIL method).
\((x + 1)(2x - 5)=x(2x - 5)+1(2x - 5)=2x^{2}-5x + 2x - 5=2x^{2}-3x - 5\)

Step2: Multiply result with third factor

Now multiply \((2x^{2}-3x - 5)\) with \((x - 3)\)
\((2x^{2}-3x - 5)(x - 3)=2x^{2}(x - 3)-3x(x - 3)-5(x - 3)\)
\(=2x^{3}-6x^{2}-3x^{2}+9x - 5x + 15\)

Step3: Combine like terms

Combine the like terms:
\(2x^{3}+(-6x^{2}-3x^{2})+(9x - 5x)+15=2x^{3}-9x^{2}+4x + 15\)

Answer:

\(2x^{3}-9x^{2}+4x + 15\)