These 24 problems cover the factoring skills in Common Core A-SSE.A.2 and A-SSE.B.3a: the greatest common factor, trinomials, the difference of squares, perfect squares, grouping, and using factors to find zeros.
The problems begin with simple GCF and trinomial factoring and grow harder. The last six are word problems with areas, projectile height and number puzzles.
Problem 1: GCF of a binomial
Factor out the greatest common factor: \(6 x^{2} + 9 x\).
Problem 2: GCF with powers
Factor \(12 a^{3} – 20 a^{2}\).
Problem 3: GCF of a trinomial
Factor \(8 x^{3} + 12 x^{2} – 16 x\).
Problem 4: Factor x² + bx + c
Factor \(x^{2} + 8 x + 15\). The area model shows the first and last cells.
Problem 5: Both numbers negative
Factor \(x^{2} – 9 x + 20\).
Problem 6: Opposite signs
Factor \(x^{2} + 2 x – 35\).
Problem 7: Larger negative number
Factor \(x^{2} – 3 x – 28\).
Problem 8: Difference of squares
Factor \(x^{2} – 49\).
Problem 9: Difference of squares with a coefficient
Factor \(25 x^{2} – 16\).
Problem 10: Perfect square trinomial
Factor \(x^{2} + 12 x + 36\).
Problem 11: Perfect square with a coefficient
Factor \(4 x^{2} – 20 x + 25\).
Problem 12: Factor ax² + bx + c
Factor \(2 x^{2} + 7 x + 3\).
Problem 13: ax² + bx + c, negative middle
Factor \(3 x^{2} – 10 x + 8\).
Problem 14: ax² + bx + c, negative constant
Factor \(6 x^{2} + x – 15\).
Problem 15: Factor by grouping
Factor \(x^{3} + 4 x^{2} + 3 x + 12\) by grouping.
Problem 16: GCF then difference of squares
Factor \(2 x^{2} – 32\) completely.
Problem 17: GCF then perfect square
Factor \(3 x^{3} + 18 x^{2} + 27 x\) completely.
Problem 18: Zeros of a quadratic
Solve \(x^{2}-5x-14=0\) by factoring. The graph of \(y=x^{2}-5x-14\) is shown.
Problem 19: Zeros with a leading coefficient
Find the zeros of \(2x^{2}+x-6\).
Problem 20: Dimensions of a rectangle
The area of Sofia’s rectangular patio is \(x^{2}+9x+14\) square feet. Factor the area to find expressions for its length and width. If the width is 5 feet, find the length and the area.
Problem 21: When does the ball land?
Diego throws a ball upward from a platform. Its height in feet after \(t\) seconds is \(h=-16t^{2}+64t+80\). Factor the expression and find when the ball hits the ground (\(h=0\)).
Problem 22: Consecutive integers
The product of two consecutive positive integers is 156. Write an equation, solve it by factoring and find the integers.
Problem 23: Is it factored completely?
Mei factors \(4x^{2}-36\) as \((2x-6)(2x+6)\). Explain why this is not complete and write the complete factorization.
Problem 24: Banner dimensions
A banner for the Little League banquet has area \(6x^{2}+13x+6\) square inches. Find binomials for its length and width.
See every chapter on the Algebra 1 math page.