steps for factoring quadratic expressions

steps for factoring quadratic expressions

1. 5.fcatoring complex trinomials

   • A complex trinomial is in the form y=ax^2+bx+c,a≠1 Step 1. Factor out the greatest common factor if necessary and determine the appropirate method of factoring. Step 2. Determine two numbers the multiply to 'a.c' and add to 'b' Step 3. decompose the middle term using the numbers from step 2 . Step 4. factor out the greatest common factor of the first two terms and the last two terms. Step 5. factor out the common binomial factor 3x^2-7x-6=3x^2+2-9x-6=x(3x+2)-3(3x+2)=(3x+2)(x-3) TRIAL AND ERROR METHOD FOE COMPLEX TRINOMIALS Step1. find two factors of 3, say 3 and1. Write these as shown. Step 2. find the two factors of -6, say -2 and 3. Step3. multiply the numbers in the diagonal. Step4. Add these together. Step5. Now use the numbers 3 and 2 to write the binomial (3x-2). The numbers 1 and 3 will make up the second binomial (x-3). Notice that the 3 and 1 each have an x so that their product is 3x*, which is the first term of the trinomial , therefor, the answer is (3x+2)(x-3) 3/1×2/

2. 1.Factoring out the greatest common factor

   • (GCF) a factor is a number that evenly divides into another and the greatest variable factor that divides evenly into all terms- the variable needs to be in all terms (x*) - wrighting the GCF in the front bracket the remaining divided terms =3x^2 ((6x^4)/(3x^2 ) +(12x^2 y)/(3x^2 )+(3x^2 y^2)/(3x^2 )) Expanding: going from left to right. Factoring: going from right to left. Step 1. Determine the GCF. Step 2. divide all terms by the GCF.

3. 2.Difference of squares factoring

   • Step 1. determine if the expanded from is a difference of squares, three things must be true 1, expression must be a binommial (two terms) 2, both terms must be perfect squares 3, there must be a subtraction between terms. Step 2. factor using the square roots of each term remeber that in the factored form, both brackets have the same terms with opposite signs. a^2-b^2 =(√(a^2 )+√(b^2 )) (√(a^2 )-√(b^2 )) 9x^2-49=(3x+7)(3x-7)

4. 3.Perfect squares trinomials

   • Expanded form= The first term is the square of the first term in the binomial. The last term is the square of the second term in the binomial. The middle terms are the same with the same signs. Simplified form= You can see the middle term is double the product of the two terms of the binomials. Step 1. determine if the expanded form is a perfect square expression. Two things must be true. 1, The first and last term must be perfect squares. 2, The middle term must be double the product of the roots of the other terms. 2(√(4x^2 ))(√36) = 2(2x)(6)=24x Step 2. factoring using the square roots of each term rember that in the factored form, both brackets have the same terms the sign in the bracket should match the sign of the middle term in expanded form. a^2-2ab+b^2=(√(a^2 )- √(b^2 ))

5. 4.Factoring simple trinomials

   • Y=ax^2+bx+c,a=1 Step 1. factor out the greatest common factor in nessacery and determine the apropriate method of factoring Step 2. determine two numbers the multiply to c' and add the b' Step 3. Write the numbers from step 2 in the binomials with thte appropriate varuables x*+7-18 The numbers that multiply to -18 and add to 7 are 9 and -2 = x*+7z-18=(x+9)(x-2)