Adding and Subtracting Polynomials

Selasa, 20 Juni 2023

You can use algebra tiles like the ones below to model polynomials.

A model of the polynomial 2x² + 3x + 1 is shown below.

Red tiles are used to represent –1, –x, and –x². The model of the polynomial –x² – 2x – 3 is shown below.

Once you know how to model polynomials using algebra tiles, you can use algebra tiles to add and subtract polynomials.

You can add polynomials by grouping the like terms together and then finding their sum.

 

Example

Find each sum.

 

1.    (4x – 3) + (2x + 5)

 

Alternative Solutions:

 

Method 1

Group the like terms together.

 

Method 2

Add in column form.

 

2.    (x² + 2x – 5) + (3x² – x + 4)

 

Alternative Solutions:

 

(x² + 2x – 5) + (3x² – x + 4) = (x² + 3x²) + (2x – x) + (–5 + 4)

                                             = (1 + 3) x² + (2 – 1) x + (–5 + 4)

                                             = 4x² + 1x – 1 or 4x² + x – 1

 

Check your answer by adding in column form.

 

3.     (2x² + 5xy + 3y²) + (8x² – 7y²)

 

Alternative Solutions:

 

Recall that you can subtract an integer by adding its additive inverse or opposite.

Similarly, you can subtract a polynomial by adding its additive inverse. To find the additive inverse of a polynomial, replace each term with its additive inverse.

Example

Find each difference.

 

4.    (6x + 5) – (3x + 1)

 

Alternative Solutions:

 

Method 1

Find the additive inverse of 3x + 1. Then group the like terms together and add.

The additive inverse of 3x + 1 is – (3x + 1) or –3x – 1.

 

Method 2

Arrange like terms in column form.

 

5.    (2y² – 3y + 5) – (y² + 2y + 8)

Alternative Solutions:

 

 

The additive inverse of y² + 2y + 8 is (y² + 2y + 8) or –y² – 2y – 8.

 

(2y² – 3y + 5) – (y² + 2y + 8) = (2y² – 3y + 5) + (–y² – 2y – 8)

 = (2y² – 1y²) + (–3y – 2y) + (5 – 8)

 = (2 – 1)y² + (–3 – 2)y + (5 – 8)

 = 1y² + (–5y) + (–3) or y² – 5y – 3

 

To check the answer, add y² – 5y – 3 and y² + 2y + 8. The sum should be
2y² – 3y + 5.

 

6.    (3x² + 5) – (4x + 2x² + 3)

Alternative Solutions:

 

Reorder the terms of the second polynomial so that the powers of x are in descending order.
–4x + 2x² + 3 = 2x² – 4x + 3

Then arrange like terms in column form.

 

Polynomials can be used to represent measures of geometric figures.

 

Example

Geometry Link

 

7.     The perimeter of triangle ABC is 7x + 2y. Find the measure of the third side of the triangle.

 

Alternative Solutions:

 

 

 

Sumber

Labels: Mathematician

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