Factoring

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Section 4.3: Solve by Factoring Vocabulary ? Monomial: OA 4?ct&in j?W ? Binomial: cuij e'ICS 1uX i-ewis Trinomial: CLAA Cc(.1 tJ9 :!2i *ermS *Some binomials and trinomials will have a Greatest Common Factor (GCF) that we will factor ou7 when factoring ? Solutions to a Quadratic Equation: X-'zef1 (O*5 so W )(-V 0 Greatest Common Factoring Ex1: Factor 3x2 +9x QCF? Ex 2: Factor 4x + 6 .. 3x(*-s x+3) Factoring a Trinomial with a leading coefficient of 1 (iejjx2 + bx + c) -Iind luy 'f&r&c -mc** Ex 3: Factor X2 - 9x+ 20 C, (x-5 I X-4 ) Ex 5: Factor x2 - 3x ?18 (-)(x+3) (14-C oxILt Ex4: Factor x2_3x+93 a tb :: -3 - 01 rj -.t - - - - Special Factoring Patterns ? Difference of Perfect Squares: a2 - - b)(a + b) Ex 6: Factor x2 - 9 xX 3

Simple Algebra Factoring

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Factoring Equations

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x^2+2x-15=(x+5)(x-3)

Algebra 1 Notes Con.t

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Factoring Trinomials

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(Back to the Intermediate Algebra Homepage) (Back to the GRE Math Help Page) (Back to the THEA Math Help Page) -------------------------------------------------------------------------------- Intermediate Algebra Tutorial 28: Factoring Trinomials Learning Objectives After completing this tutorial, you should be able to: Factor a trinomial of the form . Factor a trinomial of the form . Factor using substitution. Indicate if a polynomial is a prime polynomial. Introduction

Factoring Trinomials

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Guide to Factoring 1) Factor out the GCF (always factoring out at least a ?1 if needed). 2) Factor the remaining polynomial based on the number of terms: two terms Difference of two squares ? a2 ? b2 If so, factor it as (a+ b)(a ? b) OR Difference or sum of two cubes A3 + B3 = (A + B)(A2 ? AB + B2) A3 ? B3 = (A ? B)(A2 + AB + B2) three terms Perfect Square Trinomial ? a2 + 2ab + b2 or a2 ? 2ab + b2 If so, factor it as (a + b)2 if the middle term in positive and (a? b)2 if the middle term is negative. Trinomial ? x2 + bx + c (no coefficient on the leading term) If so, find two numbers with product = c and sum = b Factor the trinomial as (x + ?)(x + ?), putting those two numbers in for the ??s. Trinomial ? ax2 + bx + c (coefficient on the leading term)

factor_pairs

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? Pairs of Factors List ALL the pairs of factors of the given number Ex) Ex) 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 6 1 6 2 3 18 1 18 2 9 3 6 8 10 12 16 18 20 24 28 32 36 40 42 48 56 72 80 100 144

Steps for Factoring Polynomials

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1. Pull out greatest common factor or GCF [This is a very important step that is often skipped] Ex: or 2. Look at number of terms a. 2 Terms: If there are two terms (binomial), then check to see if it is i. A difference of squares: Ex: ii. A difference of cubes Ex: iii. A sum of cubes Ex: If there are two terms and the expression is none of the above, it is prime! b. 3 Terms: If there are three terms (trinomial), then factor into two binomials thinking of the FOIL method in reverse. Find factors of c that add up to b. Start by identifying the factors of c. The sign before c determines whether signs are the same or different in the 2 binomials that are produced, .