i need help with Polynomial Add and Subtract questions

Question

i need to add these (6x2+2x)+(5x−3x2+4) but i need help doing it.

Answer 1

So the trick to adding/substracting polynomials, is "collect' the like powers of the independent variable (in this case "x").

So we have

1. polynomial 1 --> P₁(x) = 6x² + 2x
2. polynomial 2 --> P₂(x) = 5x - 3x² + 4

In the first polynomial, we have a term which is related to x² and a term related to x

In the second polynomial, we have a term related to x², a term related to x, and a constant term (something related to x⁰)

So let's deal with the x² term first...

6x² - 3x² leaves us with 3x²

Dealing with the linear term (x) next...

2x + 5x = 7x

Lastly, dealing with the constant terms...

4

Therefore, the final polynomial (the sum of P₁(x) + P₂(x)) is 3x² + 7x + 4

Answer 2

(6x² + 2x) + (5x − 3x² + 4)

Here is the strategy.

1) Apply any exponents to groups. For instance, (a + b)² = (a + b)(a + b) = a² + 2ab + b². We don't have any of those kind of exponents here.

2) Remove parentheses but, while doing this, distribute any multiplier to EACH term inside the parentheses. For instance, if there was subtraction, you would multiply each term by (–1). We don't have that here, so you can simply drop the parentheses to get: 6x² + 2x + 5x − 3x² + 4

3) Next, you identify like or similar terms. For instance, x² terms are similar but different from x terms. Doing this, we get: 3x² + 7x + 4

We are done!!!!