Why does x^2 - 5x + 6 = 0 have two answer boxes to fill?
x^2 - 5x + 6 = 0 has two solutions, not one. Once the quadratic is factored, a product equal to zero tells you exactly where they hide.
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1 lesson for “Solving quadratics by factoring”
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Which pair of numbers factors x^2 + 7x + 12?
A trinomial like x^2 + 7x + 12 hides a pair of numbers. Find the pair, and the factored form falls into place.
Try this lessonWhat is x when x^2 - 2x - 4 = 0?
Not every quadratic factors over the integers. The quadratic formula works for all of them, and it only asks you for three careful numbers.
Try this lessonWhat do you add to make x^2 + 6x a perfect square?
A perfect square like (x + 3)^2 is easy to solve. Completing the square builds one on purpose, right in the middle of an equation.
Try this lessonWhat is the greatest common factor of 12x^3 and 18x^2?
When every term of a polynomial shares a factor, you can write the whole thing as a product. The tricky part is knowing exactly how much to pull out.
Try this lessonWhere do the cross products come from?
Tess solved 6/10 = 30/x by computing 6 * 30 / 10 and got 18. The cross products were paired wrong.
Try this lessonHow does y = 2x + 1 help you solve x + y = 10?
Two equations with two unknowns feel harder than one. Substitution turns the pair into a single equation with one letter.
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