** Like terms :**

Like terms are term with exactly the same variables

raised to the exactly the same powers. Any constants in

an expression are considered like terms. Terms that are

not like terms are called unlike terms.

Like Terms |
Unlike Terms |

2x, 3x, -4x
Same variables, each
with a power of 1. |
2x, 2x^{2}
Different powers |

3, 5, -1
Constants |
3, 3x, 3x^{2}
Different powers |

5x^{2}, -x^{2}
Same variables and
same powers |
5x^{2}, 5y^{2}
Different variables |

** Combining like terms :**

Combining like terms is to add or subtract like terms.

Combine like terms containing variables by combining

their coefficients and keeping the same variables with the

same exponents

Example: 3x^{2} – 8x^{2} = -5x^{2}

Example: 5x + 2x = 7x

Example:

3x^{2} + 5x + 2 + x^{2} – x - 3

=3x^{2} + x^{2} + 5x-x + 2-3

= 4x^{2} + 4x - 1

**POLYNOMIALS**

A Polynomial is a term or sum of terms in which all variables

have whole number exponents .

Example: 2, 3x + 1, ½ x^{2} + 4x + 1,

Not polynomials:

Monomial : Has one term (such as 5x^{2}, -6x, 29)

Binomial: Has two unlike terms (such as 2x – 1, x^{2} + 4x)

Trinomial : Has three unlike terms (such as ½ x^{2} + 4x + 1)

The degree of a polynomial is the highest exponent among all

the terms. If the polynomial is a constant, the degree is 0.

The polynomial 3x^{3} + 5

is a binomial with degree 3.

What type of polynomial is -2x^{2} + x - 3?

What degree is it?

Evaluate this polynomial for x = 3.

Example 4 p. 414 The polynomial -16t^{2} + 28t + 8

gives the height (in feet) of an object t seconds after it has

been thrown straight upward. Find the height of the object

in 1 second.

The value of the polynomial when t=1 is the height of the

object after 1 second.

Height after 1

Example 5: Graph y = 2x^{2
}

This is not a linear equation because it is degree 2.

This is a parabola.

The coefficient of x^{2} tells us how “fat” or “skinny” the

parabola is. If the coefficient is positive , the parabola is

pointing up. If the coefficient is negative , the parabola is

pointing down.

Since there is no constant added to this equation . The yintercept

is (0,0). When x=0, y=0.

Therefore this parabola is pointing up with it’s y-intercept at

(0,0)