Question

What is the sum of the polynomials 6a²-17a-9 and -5a²+8a-2?

A) a²-9a-11
B) a²-25a-7
C) 11a²-9a-11
D) 11a²-25a-7

Answer 1

Choice A) a² - 9a - 11.

Explanation:

Separate the terms by the power of the variable,
`a`.

Terms with power 2 on
`a`:

• First equation: 6a²;
• Second equation: -5a².

Terms with power 1 on
`a`:

• First equation: -17a;
• Second equation: 8a.

Terms with power 0 on
`a`, which are also known as constant terms:

• First equation:
  `-9`;
• Second equation:
  `-2`.

Apply the distributive property of multiplication in reverse. In other words, factor out terms with the same power and add the coefficients.

Terms with power 2 on
`a`:

`6a^(2) + (-5a^(2)) = (6 + (-5))a^(2) = a^(2)`.

Terms with power 1 on
`a`:

`-17 a + 8a = ((-17) + 8)a = -9a`.

Constant terms:

`(-9) + (-2) = -11`.

Add the sum of the individual terms to find the sum of the two polynomials:

`a^(2) + (- 9a) +(- 11) = a^(2)-9a -11`.