What I learned this week in Math 10 is to factor trinomials easily. It seems more difficult, but trinomials that can be factored if we find and use the pattern, it is similar to simplify polynomials. I could find the pattern of factoring other trinomials. It is not different to find and divide trinomials by the greatest common factor (GCF) on trinomials from simplifying polynomials.

Factoring with Common Factor: find greatest common factor and divide the trinomial by GCF.

Example: 3x2 + 6x + 9 = 3(x2 + 2x + 3)

Factoring the square binomials: the terms in binomials are perfect squares.

Example: 9x2 – 4 = (3x + 2)(3x – 2)

BUT, it is impossible => 9x2 + 4

Factoring simple trinomials: find the factors of last term and add them, and find a pair which is become a number of middle term (coefficient of x)

Example: x2 + 4x +3 = (x+3)(x+1)

Factoring UGLY trinomials:

The most important term in the trinomial in the picture is the first term that is the coefficient of x2 and the term that is just a number. After he coefficient of x2 and the last numbers are multiplied, we can find the factors of the multiplied number. (1, 24), (2, 12), (3, 8), and (4, 6). The numbers are added by their pair (1+24 = 25), (2+12 = 14), (3+8 = 11), and (4+6 = 10) and we can find the middle term (the coefficient of x, 11) 3+8 = 11. Factors of 6 are (1, 6) and (2, 3). Factors of 4 are (1, 4) and (2, 2). 1×3 (= 3) + 4×2 (= 8) = 11.

So, 6x2 + 11x + 4 = (3x + 4)(2x+1)