Questions and Answers
What is a trinomial?
What is a binomial?
What is a factor?
An integer that divides evenly into another; a polynomial that divides evenly into another; the process of writing a polynomial as a product of prime factors.
What is the middle term of the product of (x + 5)(x + 2)?
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What is the middle term of the product of (x - 4)(x - 3)?
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What is the product of (n - 8)(n + 2)?
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What is the product of (-a + 3)(a + 4)?
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Factor y^2 + 5y + 6.
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Factor completely x^2 + 13x + 36.
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Factor completely a^2 - a - 20.
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Factor completely x^2 - 5x - 14.
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Factor p^2 + 18p + 32.
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Factor completely b^2 + 12b + 32.
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Factor x^2 + 29x - 30.
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A certain rectangle has an area of x^2 + 7x + 12. What are the length and width of the rectangle?
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Study Notes
Key Definitions
- Trinomial: A polynomial consisting of three terms.
- Binomial: A polynomial composed of two terms.
- Factor: An integer or polynomial that divides another evenly; also refers to the process of expressing a polynomial as a product of its prime factors.
Middle Terms of Products
- The middle term of the product of (x + 5)(x + 2) is 7x.
- The middle term of the product of (x - 4)(x - 3) is -7x.
Products of Binomials
- The product of (n - 8)(n + 2) results in n² - 6n - 16.
- The product of (-a + 3)(a + 4) gives -a² - a + 12.
Factoring Trinomials
- y² + 5y + 6 factors to (y + 2)(y + 3).
- x² + 13x + 36 factors completely to (x + 4)(x + 9).
- a² - a - 20 can be factored as (a - 5)(a + 4).
- x² - 5x - 14 factors into (x + 2)(x - 7).
- p² + 18p + 32 breaks down to (p + 2)(p + 16).
- b² + 12b + 32 can be expressed as (b + 4)(b + 8).
- x² + 29x - 30 factors to (x - 1)(x + 30).
Application to Geometry
- For a rectangle with an area given by x² + 7x + 12, factor the trinomial to determine its dimensions: Length (l) is (x + 4) and Width (w) is (x + 3).
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Description
Test your knowledge of key concepts in factoring trinomials with this flashcard quiz. Learn definitions of important terms such as trinomial and binomial, and practice identifying middle terms in polynomial products. Perfect for Algebra I students looking to strengthen their understanding of polynomials.
