Multiply polynomials, identifying factors, degrees, and number of real roots. Identify features of a polynomial in standard form.
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There are several strategies for multiplying polynomials. Ensure that students understand that all methods are ways to organize distribution of each term in one polynomial over all terms in the other polynomial.
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What is the product of these pairs of polynomials written in standard form?
$${ (x-1)(3x^2-2x+5)}$$
$${(x^2+y^2 )(x^3-2x+4)}$$
Explain how $${f(x)∙g(x)}$$ results in the function $${ {h(x)}}$$, both algebraically and graphically.
$${f(x)=(x-2)^2}$$
$${g(x)=x^2-5x+4}$$
$${h(x)}$$
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Find the product of $${(x-1)(x^3+4x^2+4x-1)}$$.
What is the end behavior of the resultant polynomial? How can you use the degrees of the polynomial factors to check the reasonability of your solution?
Algebra II > Module 1 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..