why do you factor in math 3u 4 24uv 3 3u u 3 2v 3 3u u 2v u 2 2uv 4v 2 That is as far as I can go Example z 3 z 2 9z 9 Try factoring the first two and second two separately z 2 z 1 9 z 1 Wow z 1 is on both so let us use that z 2
It is called Factoring because we find the factors a factor is something we multiply by Example x 4 and x 1 are factors of x2 3x 4 Let us expand x 4 and x 1 to be sure x 4 x 1 x x 1 4 x 1 x2 x 4x 4 x2 3x 4 Yes x 4 and x 1 are definitely factors of x2 3x 4 Why is this a quadratic equation x 2 2 x 3 0 This is a product of two expressions that is equal to zero Note that any x value that makes either x 1 or x 3 zero will make their product zero x 1 x 3 0 x 1 0 x 3 0 x 1 x 3
why do you factor in math
why do you factor in math
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First off all numbers have factors even if it is the number times 1 So if you have x 2 6x 5 5 is prime but 5 1 5 and 5 1 6 so you can factor x 5 x 1 You also have to remember that factoring does not work for all quadratic equations Why are we interested in factoring polynomials Just as factoring integers turned out to be very useful for a variety of applications so is polynomial factorization Specifically polynomial factorization is very useful in solving quadratic equations and
Factoring is a complementary operation to the distributive property it is a way to unpack the multiplication done by applying the distributive property Reorganizing polynomials by factoring allows us to find solutions for certain types of polynomials Typically there are many ways to factor a number For example 60 6 10 60 2 30 F a c t o r i z a t i o n s o f 60 60 4 3 5 Recall that a prime number is defined as a natural number with exactly two natural number factors 1 and itself
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Factoring is a complementary operation to the distributive property it is a way to unpack the multiplication done by applying the distributive property Reorganizing polynomials by factoring allows us to find solutions for certain types of polynomials Factoring out a greatest common factor essentially undoes the distributive multiplication that often occurs in mathematical expressions This factor may be monomial or polynomial but in these examples we will explore monomial common factors
This is because factoring gives us an equation in the form of a product of expressions that we can set equal to 0 If the product of two or more expressions is equal to 0 as is the case when we factor polynomials at least one of the expressions must equal 0 How to factor Factoring in the context of algebra usually refers to breaking an expression such as a polynomial down into a product of factors that cannot be reduced further It is the algebraic equivalent to prime factorization where an integer is broken down into a product of prime numbers Factoring algebraic expressions can be
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why do you factor in math - Practice Questions FAQs What is Factorisation in Mathematics Factorisation of an algebraic expression means writing the given expression as a product of its factors These factors can be numbers variables or an algebraic expression To the factor a number means to break it up into numbers that can be multiplied to get the original