Question

1. consider the polynomials a(x) = 2x + 3 and b(x) = x - 1. what is c(x) = a(x) · b(x)?

a. (2x^2 + 5x - 3)
b. (2x^2 - x - 3)
c. (2x^2 + x - 3)
d. (2x^2 - 2x - 3)

Explanation:

Step1: Recall the distributive property (FOIL method)

To multiply two binomials \((a + b)(c + d)=ac + ad + bc + bd\). Here, \(A(x)=2x + 3\) and \(B(x)=x - 1\), so we apply the FOIL method:
\((2x + 3)(x - 1)=2x\times x+2x\times(- 1)+3\times x + 3\times(-1)\)

Step2: Simplify each term

Calculate each product:
\(2x\times x = 2x^{2}\), \(2x\times(-1)=-2x\), \(3\times x = 3x\), \(3\times(-1)=-3\)

Step3: Combine like terms

Combine the linear terms: \(-2x + 3x=x\)
So the product is \(2x^{2}+x - 3\)

Answer:

C. \(2x^{2}+x - 3\)