Algebra 1 Unit 9.2 Pre-test worksheet
Factor a common factor: The word factor is the opposite of the word distribute. When factoring out a
common factor you write the number and/or variable that ALL of the terms are divisible by on the outside of
parentheses. The expression inside the parentheses is what remains in each term after that common factor is
divided out. You can CHECK your result by distributing and comparing to the original expression.
Examples:
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Factor a Trinomial: First factor out any common factors. Then find the two binomials that multiply to result in
the simplified trinomial after the two middle terms were combined. Students often use the “diamond”
method with a generic rectangle to figure out what the constants are in the two binomials.
Leading coefficient is 1 and all signs are positive (All signs in the binomials will be +):
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Leading coefficient is 1 and all signs are negative (One sign, the bigger number, is negative):
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Leading coefficient is 1 and only the middle term is negative (Both signs will be negative):
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Leading coefficient is 1 and only the last term is negative (One sign, the smaller number, is negative):
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Algebra 1 Unit 9.2 Pre-test worksheet
Leading coefficient is NOT 1:
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Difference of perfect squares: (Remember the pattern! Remember to factor out any common factors first.)
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SOLVE a Quadratic Equation: Quadratic equations usually have TWO solutions. Follow the steps below to
solve any equations with an x2 in it.
1st Get all the terms on one side of the equation
2nd Factor the quadratic
3rd Set each of the binomials equal to zero and solve
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Algebra 1 Unit 9.2 Pre-test worksheet
Examples:
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Word Problems with Quadratics
1) The area of a rectangle is 105 square inches. The length is 1 more than twice the width. Find the length
and the width.
2) A picture has a height that is 3/4 its width. It is to be enlarged to have an area of 108 square cm. What
will be the dimensions of the enlargement?
3) Mary wants her garden to be 2 feet longer than the width. She has enough compost to cover an area
120 square feet with two inches of compost. What should the dimensions of her garden be in order to
use all the compost?
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