the variables a, b, and c represent polynomials where a = x + 1, b = x² + 2x - 1, and c = 2x. what is ab + c…

the variables a, b, and c represent polynomials where a = x + 1, b = x² + 2x - 1, and c = 2x. what is ab + c in simplest form?\n○ x³ + 3x - 1\n○ x³ + 4x - 1\n○ x³ + 3x² + 3x - 1\n○ x³ + 2x² - x + 1

the variables a, b, and c represent polynomials where a = x + 1, b = x² + 2x - 1, and c = 2x. what is ab + c in simplest form?\n○ x³ + 3x - 1\n○ x³ + 4x - 1\n○ x³ + 3x² + 3x - 1\n○ x³ + 2x² - x + 1

Answer

Explanation:

Step1: Calculate (AB)

Multiply (A=x + 1) and (B=x^{2}+2x - 1) using distributive property. ((x + 1)(x^{2}+2x - 1)=x(x^{2}+2x - 1)+1\times(x^{2}+2x - 1)) (=x^{3}+2x^{2}-x+x^{2}+2x - 1) (=x^{3}+(2x^{2}+x^{2})+( - x+2x)-1=x^{3}+3x^{2}+x - 1)

Step2: Calculate (AB + C)

Add (C = 2x) to (AB=x^{3}+3x^{2}+x - 1). (x^{3}+3x^{2}+x - 1+2x=x^{3}+3x^{2}+(x + 2x)-1=x^{3}+3x^{2}+3x - 1)

Answer:

(x^{3}+3x^{2}+3x - 1) (the third option)