polynomials is a key skill in algebra. It's all about breaking down complex expressions into simpler parts. This makes solving equations and simplifying expressions much easier.
Learning to factor helps you understand the structure of polynomials. You'll use techniques like finding common factors, grouping terms, and working with special patterns. These skills are crucial for more advanced math topics.
Factoring Polynomials
Greatest common factor identification
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Largest factor that divides all terms in an algebraic expression without a remainder
Found by listing factors of coefficients, identifying the largest number that is a factor of all coefficients
List variables appearing in every term, find the lowest for each
is the product of the GCF of coefficients and common variables raised to their lowest exponents
Essential for simplifying expressions and solving equations by factoring
Factoring out common factors
Rewriting a as a product of factors by dividing each term by the GCF
Steps: identify GCF of all terms, divide each term by GCF, write factored expression as product of GCF and quotient
Example: 10x3+15x2 factored is 5x2(2x+3) because 5x2 is the GCF
Useful for simplifying complex polynomials and solving equations by factoring
Techniques for polynomial factoring
: grouping terms, factoring out common factors
Example: ax+ay+bx+by=a(x+y)+b(x+y)=(a+b)(x+y)
Factoring trinomials using trial and error or decomposition
Sum/: a3±b3=(a±b)(a2∓ab+b2)
Example: x2+5x+6=(x+2)(x+3)
Factoring four-term polynomials by grouping or substitution