Divide polynomials by binomials to determine linear factors.
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In this lesson, students will focus on long division and not be introduced to synthetic division. For more information about reasoning for this, see the Algebra Progressions for the Common Core, page 9. Lane Walker also provides some additional reasoning on the topic. She addresses the topic again in this post.
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Find the product.
$${(x-3)(x^2-2x+3)}$$
Once we find the product, how would we work backwards to get both factors again?
What is the other factor you would multiply $${x-2}$$ by to get the polynomial $${x^4-4x^2-5x+10}$$?
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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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One factor of the polynomial $${2x^4+2x^3+3x+3}$$ is $${(x+1)}$$. What is the other factor?
How can you confirm that $${x+1}$$ is indeed a factor of $${2x^4+2x^3+3x+3}$$ through the long division?