Ch 4.2: Adding, Subtracting, and Multiplying Polynomials

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Presentation transcript:

Ch 4.2: Adding, Subtracting, and Multiplying Polynomials Essential Questions:

What is a Polynomial Function? A monomial is a number, a variable, or the product of a number and one or more variables with whole number exponents. A polynomial is a monomial or a sum of monomials. A polynomial function is in standard form when its terms are written in descending order of exponents from left to right.

EX 1: Adding and Subtracting Polynomials Subtract 2x³ + 6x² − x + 1 from 8x³ − 3x² − 2x + 9 Add 9z³ + 3z² − 2z + 1 To −5z² + z − 4

You Try!

EX 2: Multiplying Polynomials Multiply −x² + 2x + 4 and x − 3 Multiply x − 1, x + 4, and x + 5

You Try! (2x² − 3x + 5)(x − 2) b) 7x³ (5x² + 3x + 1) c) (x+1)(x+1)(x+1) d) (x-1)³ e) (a+b)³

What is Pascal’s Triangle? When you arrange the coefficients of the variables in the expansion of (a + b) 𝑛 , you will see a special pattern called Pascal’s Triangle. Pascal’s Triangle is named after French mathematician Blaise Pascal (1623−1662). In Pascal’s Triangle, the first and last numbers in each row are 1. Every number other than 1 is the sum of the closest two numbers in the row directly above it. The numbers in Pascal’s Triangle are the same numbers that are the coefficients of binomial expansions, as shown in the first six rows.

EX 3: Using Pascal’s triangle for a quick expansion a) (𝑥+4) 5 b) (6m + 2)³

You Try! Use Pascal’s Triangle to Expand a) (𝑥+3) 6 b) (2y + 1)³