Factoring means breaking a number or expression into a product. \u00a0For instance, we’ll factor 45:<\/p>\n
45=9×5<\/p>\n
In earlier posts I’ve mentioned prime factorization:<\/a><\/p>\n 45=3x3x5<\/p>\n Now we’ll look at factorization of polynomials using common factor. Solution: With the common factor method, we look for the expression that divides into all the terms, then write it out front. What remains in the brackets is each term divided by the common factor.<\/p>\n In this case we notice that 2x2<\/span><\/sup> divides into all the terms. Therefore, we “take it out front”. Actually, we take out -2x2<\/span><\/sup> because whenever the lead term is negative, you take out the negative with the common factor. Inside the brackets we write each term divided by -2x2<\/span><\/sup>:<\/p>\n -2x2<\/span><\/sup>(x4<\/span><\/sup> -4x3<\/span><\/sup>+6)<\/p>\n Common factoring doesn’t have to be as complicated as the example above. \u00a0Consider the following:<\/p>\n 3x – 15 factors to 3(x – 5)<\/p>\n Working with polynomials, factoring is constantly used. \u00a0There are at least five factoring techniques, of which common factor is the first. \u00a0I’ll discuss the other techniques in future posts:)<\/p>\n
\nExample: factor -2x6<\/span><\/sup> + 8x5<\/span><\/sup>-12x2<\/span><\/sup><\/p>\n