Question

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

Answer 1

Answer:

Choice A) a² - 9a - 11.

Step-by-step 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:

$a^{2} + (- 9a) +(- 11) = a^{2}-9a -11$.