Adding/ Subtracting Polynomials

Question

Use the following polynomials to determine the sum or difference:

f(x) = 3x^2 g(x) = 5x^4 - 2x^3 h(x) = -3x^6 + 2x^4 - 3x^2

1) f(x) + g(x): 2) g(x) + h(x): 3) h(x) - g(x):

Answer 1

Hello Jacqueline G.,

In each part, you want to combine like terms (terms are added or subtracted). Like terms will have the same exponent of x. So 3 x ^ 2 and 2 x ^ 3 are NOT like terms because the exponent of x is different. But 5 x ^ 4 and 2 x ^ 4 are like terms because the exponent of x is the same.

I'll show you one. See if you can do the other two.

In part 2), you would have 5x ^ 4 - 2x ^ 3 + -3x ^ 6 + 2x ^ 4 - 3x ^ 2.

The only like terms are 5x ^ 4 and + 2x ^ 4 which adds to 7x ^ 4. The other 3 terms will stay as they are.

It is nice to put the terms with the exponents in decreasing order.

So the answer to 2) is -3 x ^ 6 + 7 x ^ 4 - 2 x ^ 3 - 3 x ^ 2.

After you do parts 1) and 3), you can submit the answers to be checked by an expert.

Answer 2

1. 5x⁴-2x³+3x²
2. -3x⁶+7x⁴-2x³+3x²
3. -3x⁶-3x⁴+2x³-3x²

^{Basically, you are just adding and subtracting polynomials with the same power.}