Question

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?

x3 3x − 1
x3 4x − 1
x3 3x2 3x − 1
x3 2x2 − x 1

Answer 1

If you would like to write a * b + c in simplest form, you can do this using the following steps:

a = x + 1
b = x^2 + 2x - 1
c = 2x
a * b + c = (x + 1) * (x^2 + 2x - 1) + 2x = x^3 + 2x^2 - x + x^2 + 2x - 1 + 2x = x^3 + 3x^2 + 3x - 1

The correct result would be x^3 + 3x^2 + 3x - 1.

Answer 2

This are expression that has a leading degree of 3 and above. The sum of ab and c in its simplest form is expressed as:  x³ + 3x² + 3x -1

Polynomial expressions

This are expression that has a leading degree of 3 and above.

Given the following parameters

• a = x + 1
• b = x² + 2x - 1
• c = 2x

Required

• ab + c

Take the product of a and b

ab = (x+1)( x² + 2x - 1)

ab = x³ +2x² - x +x² + 2x -1

ab = x³ + 3x² + x -1

Take the sum of ab and c

ab + c =  x³ + 3x² + x -1  + 2x

ab +c =  x³ + 3x² + 3x -1

Hence the sum of ab and c in its simplest form is expressed as:  x³ + 3x² + 3x -1

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