This is a free lesson from our course in Algebra I
This lesson explains how to solve an equation using factoring by grouping. There are a few simple
concepts to keep in mind while factoring a polynomial:
• when trying to factor a polynomial, first try to identify the GCF and divide every term of the polynomial by GCF. For example,
8x^{3} + 4x^{2} + 2x can be simplified
into 2x(4x^{2} + 2x + 1). Factor by grouping, is simply defined as the grouping of terms
with common factors before factoring a polynomial.
(More text below video...)
(Continued from above) A polynomial is a mathematical
expression that is formed by variables and constants. The construction of such variables
and constants is done by using operations of addition, subtraction, multiplication
and nonnegative whole number exponents
• in cases where there are four terms with no GCF, you should try factoring by grouping.
First group the first two terms together and then the last two terms together and
factor out a GCF from each seperate binomial, followed by factoring out the common binomial.
• in cases where there is no constant term in the polynomial, first factor out the
variable and then factor the expression in the parenthesis into a product of binomials.
E.g. 9a^{3} – 15a^{2} + 3ba – 5b
Solution: 9a^{3} – 15a^{2} + 3ba – 5b
= (9a^{3} – 15a^{2}) + (3ba – 5b)
= 3a^{2}(3a – 5) + b(3a – 5)
= (3a – 5)(3a^{2} + b)
The explanation provided by our instructor in the video above will help you understand
these concepts in an easier manner.
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