Question

explain 1subtracting polynomials using a vertical□ read the section below and complete the following activity (adapted from lesson 17.3).recall that you can subtract a real number by adding its opposite. this allows for the subtraction of polynomials. you can subtract polynomials vertically by arranging like terms in columns. like addition, you need to use zeros (or spaces) to indicate the terms missing from either polynomial. again, this helps to preserve the alignment. be sure to show the +/- signs, then place a negative sign outside the bottom polynomial (keep parenthesis).examples subtract the given polynomials using the vertical format.1. $(8x^{2}+2x+6)-(9x^{2}+2x-3)$rewrite subtraction as addition of the opposite, then add.$+8x^{2}$ $+2x$ $+6LXB0-1x^{2}$ $+0$ $+9$add vertically.simplify.$-x^{2}+9$2. $(5x+2)-(-2x^{2}-3x+4)$rewrite subtraction as addition of the opposite, then add.$+0$ $+5x$ $+2LXB1+2x^{2}$ $+8x$ $-2$add vertically.simplify.$2x^{2}+8x-2$subtract the given polynomials using the vertical format.3. $(5g^{2}+6g-10)-(2g^{2}+2g+9)$rewrite subtraction as addition of the opposite, then add.$+5g^{2}$ $+6g$ $-10$$-2g^{2}$ $-2g$ $-9$

Explanation:

Step1: Add like terms for $g^2$

$$\begin{align*} +5g^2 -2g^2 &= (5-2)g^2 \\ &= 3g^2 \end{align*}$$

Step2: Add like terms for $g$

$$\begin{align*} +6g -2g &= (6-2)g \\ &= 4g \end{align*}$$

Step3: Add constant terms

$$\begin{align*} -10 -9 &= -(10+9) \\ &= -19 \end{align*}$$

Step4: Combine all results

$3g^2 + 4g -19$

Answer:

$3g^2 + 4g -19$