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Finding Factors. Factorizing algebraic expressions is a way of turning a sum of terms into a product of smaller ones. The product is a multiplication of the factors. Sometimes it helps to look at a simpler case before venturing into the abstract.
Grade 10 Mathematics 1. Identify whether the following expressions are monomial, binomial, trinomial or polynomial: a) b) c) d) e) ) ( f) g) h) i) j) 2. Multiply out and then simplify the following: )a) )( ( ( b) )
Factoring Trinomials (a > 1) Date_____ Period____ Factor each completely. 1) 3 p2 − 2p − 5 2) 2n2 + 3n − 9 3) 3n2 − 8n + 4 4) 5n2 + 19 n + 12 5) 2v ... n2 − 27 n − 6 10) 5x2 − 18 x + 9 11) 4n2 − 15 n − 25 12) 4x2 − 35 x + 49 13) 4n2 − 17 n + 4 14) 6x2 + 7x − 49
Factoring Trinomials (a = 1) Date_____ Period____ Factor each completely. 1) b2 + 8b + 7 2) n2 − 11 n + 10 3) m2 + m − 90 4) n2 + 4n − 12 5) n2 − 10 n + 9 6) b2 + 16 b + 64 7) m2 + 2m − 24 8) x2 − 4x + 24 9) k2 − 13 k + 40 10) a2 + 11 a + 18 11) n2 − n − 56 12) n2 − 5n + 6-1-
If the leading coefficient of a trinomial is negative, then it is a best practice to factor that negative factor out before attempting to factor the trinomial. Factoring trinomials of the form \(ax^{2}+bx+c\) takes lots of practice and patience.
Factoring using Quadratic Trinomials when a = 1 Example: Factor the trinomial. x2 + 6x + 8 factored form: _____ Factor the following trinomials. a. Factor x2 + 4x – 32 b. Factor x2 – 3x – 18 c. Factor x2 – 36 d. Factor 2x2 + 16x + 24
L2-3 Factoring trinomials III. Factoring trinomials – examples The basic steps are reproduced below so you do not have to flip pages back and forth. The basic steps for factoring trinomials with the form ax2 + bx + c, are: 1) Multiply a·c to produce the number. 2) List the factors of the number. 3) Find two factors of the number that add up to b
