8.8: FACTORING BY GROUPING:
description
Transcript of 8.8: FACTORING BY GROUPING:
8.8: FACTORING BY GROUPING:
Higher Degree Polynomials: Polynomials with a degree higher than 2.
FACTORING ax2 + bx + c Procedure:
1) Always look for the GCF of all the terms2) Factor the remaining terms – pay close attention to the value of coefficient a and follow the proper steps.
3) Re-write the original polynomial as a product of the polynomials that cannot be factored any further.
GOAL:
FACTORING: By Grouping
Ex: What is the FACTORED form of:
3n3-12n2+2n-8?
SOLUTION: To factor a polynomial by grouping we group terms that have a GCF:
Look at GCF of each: 3n3-12n2
Now take the GCF of the two:
Factored form : (n-4)(3n2+2)
3n3-12n2+2n-8 3n3-12n2+2n-8
3n2(n-4) 2n-8 2(n-4)
3n2 (n-4) +2 (n-4)
YOU TRY IT:
Ex: What is the FACTORED form of:
8t3+20t+14t2+35?
SOLUTION: To factor a polynomial by grouping we group terms that have a GCF:
Look at GCF of each: 8t3+14t2
Now take the GCF of the two:
Factored form : (4t+7)(2t2+5)
8t3+14t2+20t+35 8t3+14t2+20t+35
2t2(4t+7) 20t+35 5(4t+7)
2t2 (4t+7) +5(4t+7)
YOU TRY IT:
Ex: What is the FACTORED form of:
4q4-8q3+12q2-24q?
SOLUTION: Before we group, we must again go back to the first step of factoring:
1) Factor what is in common? 4q4-8q3+12q2-24q?
4q(q3-2q2+3q-6)
SOLUTION: To factor a polynomial by grouping we group terms that have a GCF:
Look at GCF of each: q3-2q2
Now take the GCF of the two:
Factored form : 4q (q-2) (q2+3)
4q(q3-2q2+3q-6) 4q(q3-2q2+3q-6)
q2(q-2) 3q-6 3(q-2)
q2 (q-2) +3(q-2)
REAL-WORLD:
The area of a square rug is given by 4x2-100.What are the possible dimensions of the rug?
SOLUTION: To factor a difference of two squares with a coefficient ≠ 1 we still follow the factoring procedure:
4x2-100ax2+c a= +1 c =-25 Look at the factors of a and c:
a : (1)(1) c: (-5)(5)We now see that the factored form is:
4(x-5)(x+5)
4(x2-25)
NOW SOLVE THIS:
VIDEOS: FactoringQuadratics
Factoring by Grouping:
Factoring by Grouping:http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/factoring-trinomials-with-a-non-1-leading-coefficient-by-grouping
http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/ex2-factoring-quad
VIDEOS: FactoringQuadratics
Factoring by Grouping:
Factoring by Grouping:
http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/factoring-trinomials-by-grouping-5
http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/factoring-trinomials-by-grouping-6
CLASSWORK:
Page 514-516:
Problems: 1, 2, 3, 9, 13, 16, 22, 27, 30, 32, 37, 45.