5-1 Pt II - Add/Subtract Polynomials

5-1 Pt II - Add/Subtract Polynomials

You'll want to have your notes and a pencil handy.

Let's Take a Mental Field Trip Back To Grade School

How did you add two numbers like this?

Like this, right?

The place values are lined up so we are adding ones digit to ones digit, tens digit to tens digit, and so forth.

So it turns out that you already know how to add polynomials.

We're just going to combine like terms.

Let's look at an example:

 $\left(3x^2+7+x\right)\ +\ \left(14x^3+2+x^2-x\right)$  

First Method - Add Vertically

First write both polynomials in standard form. Then line up the like terms above one another. Then add.

Second Method - Add Horizontally

Re-write the two polynomials as a sum. Combine the like terms. Write the answer in standard form.

Now you try:

Multiple Choice

Add the polynomials:

 $\left(15x^2-3x+11\right)\ +\ \left(2x^3-x^2+6x+1\right)$  

•  $17x^2-3x+12$  

•  $2x^3+16x^2-9x^{ }+10$  

•  $2x^3+14x^2+3x+12$  

•  $17x^3-x^2+3x+12$  

Multiple Choice

Another one. Add the polynomials:

 $\left(x^2-3x+4\right)\ +\ \left(x^3+3x-4\right)$  

•  $x^3+x^2+6x+8$  

•  $x^3+x^2-6x-8$  

•  $0$  

•  $x^3+x^2$  

Good work so far.

Now let's add a hook.

To subtract polynomials

• Recall the Subtraction Rule: to subtract, add the opposite. So when we think

   $5-3$  , the math that's happening is  $5+\left(-3\right)$  

• So we will change the sign on every term in the second polynomial, then add as we did previously.

Subtract the polynomials (we'll do this together):

 $\left(5x^3+12+6x^{2\ }\right)-\left(15x^2+3x-2\right)$  

First, put both polynomials in standard form

 $\left(5x^3+6x^2+12\right)-\left(15x^2+3x+2\right)$  

Next:

• Change from subtraction to addition

• Change the sign of every term in the second polynomial

• Line up like terms

• Add

Solution:

 $5x^3-9x^2-3x+10$  

You try:

Multiple Choice

Subtract the polynomials:

 $\left(x^2-3x+7\right)-\left(6x^2+4x+12\right)$  

•  $7x^2-7x-5$  

•  $-5x^2-7x-5$  

•  $-5x^2+7x+5$  

•  $-4x^2-22x$  

After the break we'll get a chance to practice some on your own