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?\no x³ + 3x - 1\no x³ + 4x - 1\no x³ + 3x² + 3x - 1\no x³ + 2x² - x + 1
Answer
Explanation:
Step1: Calculate AB
Multiply A and B: [ \begin{align*} AB&=(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 \end{align*} ]
Step2: Calculate AB + C
Add C = 2x to AB: [ \begin{align*} AB + C&=(x^{3}+3x^{2}+x - 1)+2x\ &=x^{3}+3x^{2}+(x + 2x)-1\ &=x^{3}+3x^{2}+3x - 1 \end{align*} ]
Answer:
C. (x^{3}+3x^{2}+3x - 1)