Back in May, I began a series of posts about factoring polynomials. \u00a0To refresh the topic, you can check here,<\/a> here, <\/a> and here<\/a>.<\/p>\n Factoring polynomials is a make-or-break skill for high school students taking academic math. It encompasses about five techniques, of which easy trinomial factoring is probably the best known. Let’s have a quick look:<\/p>\n Example 1: Factor x2<\/span><\/sup> -3x -28<\/strong><\/p>\n Solution: Since the coefficient of x2<\/span><\/sup> is 1 (which we know because there is no number written in front of it), we can use the easy trinomial method.<\/p>\n Step 1: Write (x \u00a0 \u00a0 \u00a0)(x \u00a0 \u00a0 )<\/p>\n Step 2: After the x’s, write the numbers that will multiply to give -28, but add to give -3.<\/p>\n You have to do some mental math: 7×4=28, but one of the numbers has to be negative to give -28. The numbers must be -7 and +4, since -7+4=-3.<\/p>\n (x -7)(x +4)<\/p>\n The answer is (x – 7)(x + 4). You can verify using the foil <\/a>method:<\/p>\n First: x*x=x2<\/span><\/sup><\/p>\n Outer: x*4=4x<\/p>\n Inner: -7*x=-7x<\/p>\n Last: -7*4=-28 (remember: negative times positive gives negative)<\/p>\n Now, line up the four terms we just obtained:<\/p>\n x2<\/span><\/sup> +4x -7x -28<\/p>\n We can combine the like terms: 4x – 7x = -3x<\/p>\n Finally we get<\/p>\n x2<\/span><\/sup> -3x -28.<\/p>\n If you foil out your answer and get back the original trinomial, you know it’s right.<\/p>\n Example 2: Factor x2<\/span><\/sup> + 5x + 4<\/strong><\/p>\n Solution: The numbers that multiply to give 4 but add to give 5 are 1 and 4: 1*4=4, 1+4=5.<\/p>\n Therefore, the answer is (x + 4)(x + 1)<\/p>\n Example 3: Factor x2<\/span><\/sup> -10x + 16<\/strong><\/p>\n Solution: The numbers that multiply to give 16 but add to give -10 are -8 and -2 (recall that negative times negative gives positive): -8*-2=16, -8+-2=-10<\/p>\n The answer is (x – 8)(x – 2)<\/p>\n Example 4: Factor x2<\/span><\/sup> +5x – 14<\/strong><\/p>\n The answer is (x + 7)(x – 2)<\/p>\n Good luck with this method. Most people like it once they get used to it:)<\/p>\n