factoring equal to zero X 2 1 sum product pattern a b a b 3 a b 10 x 2 3 x 10 x a x b 10 3 a 2 b 5 the factored expression is x 2 x 5 The complete solution of the equation would go as follows x 2 3 x 10 0 x 2 x 5 0 Factor x 2 0 x 5 0 x 2 x 5
Factoring Method Set the equation equal to zero that is get all the nonzero terms on one side of the equal sign and 0 on the other ax 2 bx c 0 Factor the quadratic expression 0 By the zero factor property at least one of the factors must be zero so set each of the factors equal to 0 and solve for the variable Set each factor equal to zero and solve to find the displaystyle x text x intercepts Example 2 Finding the x Intercepts of a Polynomial Function by Factoring Find the x intercepts of displaystyle f left x right x 6 3 x 4 2 x 2 f x x6 3x4 2x2
factoring equal to zero
factoring equal to zero
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How To Solve Quadratic Equations By Factoring Not Equal Zero Tessshebaylo
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How To Solve Quadratics By Factoring equal To Zero YouTube
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Setting your quadratic equation equal to zero so that you can factor out GCF and solve YouTube Brian McLogan 1 44M subscribers Subscribed 215 30K views 8 years ago Solve Quadratic Sal solves the equation s 2 2s 35 0 by factoring the expression on the left as s 5 s 7 and finding the s values that make each factor equal to zero Created by Sal Khan and Monterey Institute for Technology and Education
So p x x 2 2x 5 1 2x 5 works well then factoring out common factor and setting p x 0 gives x 2 1 2x 5 0 From there note first is difference of perfect squares and can be factored then you use zero product rule to find the three x intercepts What we need to do is simply set each factor equal to zero and solve each equation for latex x latex The answers are latex x 7 latex and latex x 2 latex You may back substitute these values of latex x latex to the original equation to verify if
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General guidelines for factoring polynomials Step 1 Check for common factors If the terms have common factors then factor out the greatest common factor GCF Step 2 Determine the number of terms in the polynomial Factor four term polynomials by grouping either GCF of pairs or binomial square then difference of Steps for Solving an Equation by Factoring write the equation as a polynomial and set it equal to zero factor the polynomial review the Steps for Factoring if needed use Zero Factor Theorem to solve Example 1 Solve the quadratic equation 15 2 2 13 for and enter exact answers only no decimal approximations
The Zero Factor Principle tells me that at least one of the factors must be equal to zero Since at least one of the factors must be zero then I can set each of the factors equal to zero x 3 0 or x 4 0 This gives me simple linear equations and they re easy to solve x 3 or x 4 Rule Zero Product Rule If ab 0 then either a 0 or b 0 or both In other words if the product of two things is zero then one of those two things must be zero because the only way to multiply something and get zero is to multiply it by zero
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factoring equal to zero - Example Solve x 2 16 0 Since we factored this equation in example 2 above we can rewrite the above equation as x 4 x 4 0 We then know that at least one of the terms x 4 or x 4 must equal 0 for the statement to be true and can solve for x in either case x 4 0 x 4 x 4 0 x 4