Question

name: jayla smith block: 2nd date: jan 9, 2026
adding and subtracting polynomials
steps in adding polynomials.

1. arrange polynomials in column. make sure like terms are aligned.
2. add the coefficients observing the rule for adding integers.
3. bring down the variable and exponents.

example:
simplify the expression
(5x²−7x + 3) + (3x² + 5x −1).
solution:
+ 5x²−7x + 3
3x² + 5x −1
8x²−2x + 2
steps in subtracting polynomials.

1. arrange polynomials in column. make sure like terms are aligned.
2. change the sign of the subtrahend to its opposite sign.
3. proceed to addition rule for the coefficients.
4. bring down the variable and exponents.

example:
simplify the expression
(-8x² + 7x +2) - (4x² - 5x + 9).
solution:
+ -8x² + 7x + 2
-4x² + 5x - 9
-12x² +12x - 7
solve each of the following.

1. (2x²−2x + 1) + (x² +x +3)
2. (-2x² + 3x - 2) + (3x² +2x - 3)
3. (-2m −9) + (5m + 1)
4. (10x² + 7x + 1) + (4x² −5)

Explanation:

Problem 1: \((2x^2 - 2x + 1) + (x^2 + x + 3)\)

Step 1: Arrange like terms

Arrange the polynomials vertically to align like terms:
\[

$$\begin{align*} &2x^2 - 2x + 1\\ +&x^2 + x + 3\\ \end{align*}$$

\]

Step 2: Add coefficients of like terms

• For \(x^2\) terms: \(2x^2 + x^2 = (2 + 1)x^2 = 3x^2\)
• For \(x\) terms: \(-2x + x = (-2 + 1)x = -x\)
• For constant terms: \(1 + 3 = 4\)

Step 3: Combine results

Combine the results of each like - term addition: \(3x^2 - x + 4\)

Step 1: Arrange like terms

Arrange the polynomials vertically to align like terms:
\[

$$\begin{align*} &-2x^2 + 3x - 2\\ +&3x^2 + 2x - 3\\ \end{align*}$$

\]

Step 2: Add coefficients of like terms

• For \(x^2\) terms: \(-2x^2+3x^2=(-2 + 3)x^2=x^2\)
• For \(x\) terms: \(3x + 2x=(3 + 2)x = 5x\)
• For constant terms: \(-2-3=-5\)

Step 3: Combine results

Combine the results of each like - term addition: \(x^2+5x - 5\)

Step 1: Arrange like terms

Arrange the polynomials vertically to align like terms:
\[

$$\begin{align*} &-2m-9\\ +&5m + 1\\ \end{align*}$$

\]

Step 2: Add coefficients of like terms

• For \(m\) terms: \(-2m+5m=(-2 + 5)m = 3m\)
• For constant terms: \(-9 + 1=-8\)

Step 3: Combine results

Combine the results of each like - term addition: \(3m-8\)

Answer:

\(3x^2 - x + 4\)

Problem 2: \((-2x^2 + 3x - 2) + (3x^2 + 2x - 3)\)