The variables cap A , cap b , and cap c represent polynomials where cap A is equal to x plus 1 , cap b is equal to x squared plus 2 x minus 1 , and cap c is equal to 2 x What is cap A cap b plus cap c in simplest form?
Answer
A
x cubed plus 4 x minus 1
B
x cubed plus 2 x squared minus x plus 1
C
x cubed plus 3 x squared plus 3 x minus 1
D
x cubed plus 3 x minus 1
Explanation
Substitute the polynomials into A·b + c: (x + 1)(x² + 2x − 1) + 2x. Expanding the product gives x³ + 3x² + x − 1; adding 2x gives x³ + 3x² + 3x − 1. This matches choice D, “x cubed plus 3 x squared plus 3 x minus 1.”
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