Questions: Match the polynomial on the left with the corresponding polynomial on the right. Add: (-4 x^2-3 x+6)+(6 x^2-2 x+1) Find the opposite of: 2 x^2+x-7 Subtract: (-4 x^2+2 x-1)-(-2 x^2+3 x+6). -2 x^2-x-7 -2 x^2-x+7 -2 x^2-5 x+7 2 x^2-x+7 2 x^2-5 x+7

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

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

-2 x^2-x-7
-2 x^2-x+7
-2 x^2-5 x+7
2 x^2-x+7
2 x^2-5 x+7

Transcript text: Match the polynomial on the left with the corresponding polynomial on the right. Add: $\left(-4 x^{2}-3 x+6\right)+\left(6 x^{2}-2 x+1\right)$ Find the opposite of: $2 x^{2}+x-7$ Subtract: $\left(-4 x^{2}+2 x-1\right)-\left(-2 x^{2}+3 x+6\right)$. \[ \begin{array}{l} -2 x^{2}-x-7 \\ -2 x^{2}-x+7 \\ -2 x^{2}-5 x+7 \\ 2 x^{2}-x+7 \\ 2 x^{2}-5 x+7 \end{array} \]

Solution

Solution Steps

Step 1: Add the polynomials $\left(-4 x^{2}-3 x+6\right)$ and $\left(6 x^{2}-2 x+1\right)$

Combine like terms: \[ (-4x^2 + 6x^2) + (-3x - 2x) + (6 + 1) = 2x^2 - 5x + 7 \]

Step 2: Find the opposite of $2 x^{2}+x-7$

Multiply each term by $-1$: \[ -(2x^2 + x - 7) = -2x^2 - x + 7 \]

Step 3: Subtract the polynomials $\left(-4 x^{2}+2 x-1\right)$ and $\left(-2 x^{2}+3 x+6\right)$

Distribute the negative sign and combine like terms: \[ (-4x^2 + 2x - 1) - (-2x^2 + 3x + 6) = -4x^2 + 2x - 1 + 2x^2 - 3x - 6 \] \[ = (-4x^2 + 2x^2) + (2x - 3x) + (-1 - 6) = -2x^2 - x - 7 \]

The remaining questions are left unanswered as per the guidelines.