What 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.
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2 lessons for “Factoring out the greatest common factor”
Why does 18/24 turn into 3/4?
The fraction looks different and describes the same amount. The rule that allows this is the same rule that makes adding fractions possible at all.
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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^2 - 9)/(x^2 + 5x + 6) in lowest terms?
A fraction like this simplifies only after you factor the top and the bottom. Cancellation happens between factors, never between single terms.
Try this lessonWhy 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.
Try this lessonWhy is x^2 - 36 not (x - 6)(x - 6)?
x^2 - 36 looks like an ordinary binomial, but it carries a special pattern. A difference of two squares always factors into a sum times a difference.
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 lessonWhy does 10% growth beat adding 10 each year?
Adding the same amount each year is linear. Multiplying by the same number each year is exponential, and the difference grows fast.
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