Match the polynomial on the left with the corresponding polynomial on the right.

1. Add: [tex](-4x^2 - 3x + 6) + (6x^2 - 2x + 1)[/tex]
2. Find the opposite of: [tex]2x^2 + x - 7[/tex]
3. Subtract: [tex](-4x^2 + 2x - 1) - (-2x^2 + 3x + 6)[/tex]

A. [tex]-2x^2 - x - 7[/tex]
B. [tex]-2x^2 - x + 7[/tex]
C. [tex]-2x^2 - 5x + 7[/tex]
D. [tex]2x^2 - x + 7[/tex]
E. [tex]2x^2 - 5x + 7[/tex]



Answer :

Sure, let's address each step-by-step and match the polynomials.

1. Add the polynomials: [tex]\( \left(-4x^2 - 3x + 6\right) + \left(6x^2 - 2x + 1\right) \)[/tex]

We need to add the corresponding coefficients:

[tex]\[ -4x^2 + 6x^2 = 2x^2 \][/tex]
[tex]\[ -3x - 2x = -5x \][/tex]
[tex]\[ 6 + 1 = 7 \][/tex]

So the result is:

[tex]\[ 2x^2 - 5x + 7 \][/tex]

Match: [tex]\( 2x^2 - 5x + 7 \)[/tex]

2. Find the opposite of: [tex]\( 2x^2 + x - 7 \)[/tex]

The opposite polynomial means changing the sign of each term:

[tex]\[ -2x^2 - x + 7 \][/tex]

Match: [tex]\( -2x^2 - x + 7 \)[/tex]

3. Subtract the polynomials: [tex]\( \left(-4x^2 + 2x - 1\right) - \left(-2x^2 + 3x + 6\right) \)[/tex]

First, distribute the negative sign to the second polynomial:

[tex]\[ -(-2x^2 + 3x + 6) = 2x^2 - 3x - 6 \][/tex]

Now, add this to the first polynomial:

[tex]\[ (-4x^2 + 2x - 1) + (2x^2 - 3x - 6) \][/tex]

Combine the like terms:

[tex]\[ -4x^2 + 2x^2 = -2x^2 \][/tex]
[tex]\[ 2x - 3x = -1x \][/tex]
[tex]\[ -1 - 6 = -7 \][/tex]

So, the result is:

[tex]\[ -2x^2 - x - 7 \][/tex]

Match: [tex]\( -2x^2 - x - 7 \)[/tex]

Grouping the results and available options:

- [tex]\( 2x^2 - 5x + 7 \)[/tex] matches [tex]\( 2 x^2 - 5 x+7 \)[/tex]
- [tex]\( -2x^2 - x + 7 \)[/tex] matches [tex]\( -2 x^2-x+7 \)[/tex]
- [tex]\( -2x^2 - x - 7 \)[/tex] matches [tex]\( -2 x^2-x-7 \)[/tex]