Warm-up Nov. 15

Lovely quiz day! Remember that you only have 15 minutes. Good

luck!HW #5: red text pg. 149 #s 15, 18, & 31 - 51 (1st column) use pp. 9 & 10

Notes #3: Combining Polynomials

HW #5: red text pg. 149 #s 15, 18, & 31 - 51 (1st column) use pp. 9 & 10

• Monomials - a number, a variable, or a product of a number and one or more variables.

4x, 20x2yw3, -3, a2b3, and 3yz are all monomials.

• Polynomials – one or more monomials added or subtracted

4x + 6x2, 20xy - 4, and 3a2 - 5a + 4 are all polynomials.

Vocabulary

Binomial: a polynomial with two terms, such as ex1. 3x + 4 ex2. 5m2 + 6m

Trinomial: a polynomial with three terms, such as ex3. 5c2 + 4c – 1 ex4. -12xy + 3y + 9

Constant: any term that doesn’t have a variable in it.

Like terms: terms with the same base

1st term 2nd term constant

1st term 2nd term 3rd term constant

How do you remember the names? Think

cycles!There are special names for polynomials with 1, 2 or 3 terms:

3xy2

Monomial(1 term)

5x – 1 Binomial(2 terms)

3x + 5y2 – 3

Trinomial(3 terms)bicycle

tricycle

Monocycleor

Unicycle

Like TermsLike Terms refers to monomials that have

the same variable(s) but may have different coefficients. The variables in the

terms must have the same powers.Which terms are like? 3a2b, 4ab2, 3ab, -5ab2

4ab2 and -5ab2 are like.

Even though the others have the same variables, the exponents are not the same.

3a2b = 3aab, which is different from 4ab2 = 4abb.

Add: (x2 + 3x + 1) + (4x2 + 5)

Add the coefficients of like terms, do not change the powers of the variables:

Adding Polynomials

4x2 + 5

Example

1:

x2 + 3x + 1

5x2 + 3x + 6

Adding PolynomialsEx. 2 Add these polynomials:

(2a2 + 3ab + 4b2) + (7a2+ ab – 2b2)

2a2 + 3ab + 4b2

7a2 + ab – 2b2

9a2 + 4ab + 2b2

3.) Add: (12a3 – 12a – 3) + (14a3 + 16a + 4)

26a3 + 4a + 1

12a3 – 12a – 3 14a3 + 16a + 4+

Subtract: (3x2 + 2x + 7) – (x2 + x + 4)

Subtracting Polynomials

When subtracting polynomials, Change the signs of the second polynomial.

Remember to place a 1 in front of a variable without a coefficient.

1st polynomial 2nd polynomial

Example

4:

3x2 + 2x + 7 1x2 + 1x + 42x2 + x + 3

5.) Subtract: (5x2 – 4) – (2x2 + 3)

Steps:1. Line up the like

terms together. 2. Change the signs

of the second polynomial.

3. Combine like terms

1st polynomial 2nd polynomial

5x2 – 4 -2x2 – 3

3x2 – 7

6.) Subtract: (-4x2 – 3x + 6) – (3x2 + 4x – 3)

Change the signs of the 2nd poly

-7x2 – 7x + 9

-4x2 – 3x + 6-3x2 – 4x + 3

Subtract (3b2 + 5b + 2) from (8b2 + 4b – 6).

8b2 + 4b – 6 -3b2 – 5b – 25b2 – b – 8

Exit Question