Recall that a monomial is a number, a variable, or a productof numbers andvariables. A
Consider the expression .
The expression is the sum of three monomials, therefore it isa polynomial. Since there are three monomials, the polynomial isa trinomial.
The degree of is 2, the degree of 5 is 0, and thedegree of 7x is 1. The greatest degree is 2, so the degree of thepolynomial is 2.
## Adding and Subtracting PolynomialsTo add polynomials, you can group like terms and then findtheir sum, or youcan write them in column form and then add. Tosubtract a polynomial, add its additive inverse, which is theopposite of each term in the polynomial.
Find each sum or difference.
Arrange like terms in column form and add. Follow the rulesfor adding signed numbers.
Find the additive inverse of - x + 2y. Then group the liketerms and add. The additive inverse of - x + 2y is x - 2y. (12x + 7y ) - (- x + 2y ) = (12x + 7y ) + (+ x - 2y ) = (12x + x) + (7y - 2y) = 13x + 5y
## Multiplying a Polynomial by a MonomialUse the distributive property to multiply a polynomial by amonomial. Youmay find it easier to multiply a polynomial by amonomial if you combine alllike terms in the polynomial beforeyou multiply.
Find
Combine like terms in the polynomial and then multiply usingthe distributive property.
## Multiplying PolynomialsUse the distributive property to multiply polynomials. If youare multiplying two binomials, you can use a shortcut called theFOIL method. To multiply two binomials, find the sum of the products of
Find (2x + 3)(4x - 1). |