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Solving Equations by Factoring>
Solving Equations by Factoring 1Solving Equations by Factoring 1
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Question 1 of 4
1. Question
Solve for `x`:`x^2-6x+5=0`Hint
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The cross method is a factorisation method used for quadratics.Since the equation is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`x^2``-6``x+``5``=0`To factorise, we need to find two numbers that add to `-6` and multiply to `5``-5` and `-1` fit both conditions`-5 + (-1)` `=` `-6` `-5 xx -1` `=` `5` 
Read across to get the factors.`(x-5)(x-1)=0`Solve for each value of `x`.`x-5` `=` `0` `x-5` `+5` `=` `0` `+5` `x` `=` `5` `x-1` `=` `0` `x-1` `+1` `=` `0` `+1` `x` `=` `1` `x=1, 5` -
Question 2 of 4
2. Question
Solve for `x`:`2x^2-3x+1=0`Hint
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The cross method is a factorisation method used for quadratics.Since the equation is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`2``x^2``-3``x``+1``=0`Find two numbers that multiply to `2` on the left side and multiply to `1` on the right side. Also, when cross multiplied they should add to the middle term (`-3x`).`2` and `1` fit the condition for the left side and two `-1`’s fit the condition for the right side`2 xx 1` `=` `2` `-1 xx -1` `=` `1` `(2x xx -1) + (x xx -1)` `=` `-3x` 
Read across to get the factors.`(2x-1)(x-1)=0`Solve for each value of `x`.`2x-1` `=` `0` `2x-1` `+1` `=` `0` `+1` `2x` `=` `1` `x` `=` `1/2` `x-1` `=` `0` `x-1` `+1` `=` `0` `+1` `x` `=` `1` `x=1/2, 1` -
Question 3 of 4
3. Question
Solve for `x`:`3x^2+2x-21=0`Hint
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The cross method is a factorisation method used for quadratics.Since the equation is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`3``x^2``+2``x``-21``=0`Find two numbers that multiply to `3` on the left side and multiply to `-21` on the right side. Also, the coefficients of `x` in the factors, when multiplied by the constants, should add to `2x`.`3` and `1` fit the condition for the left side and `-7` and `3` fit the condition for the right side`3 xx 1` `=` `3` `-7 xx 3` `=` `-21` `(3x xx 3) + (x xx -7)` `=` `2x` 
Read across to get the factors.`(3x-7)(x+3)=0`Solve for each value of `x`.`3x-7` `=` `0` `3x-7` `+7` `=` `0``+7` `3x` `=` `7` `x` `=` `7/3` `x` `=` `2 1/3` `x+3` `=` `0` `x+3` `-3` `=` `0` `-3` `x` `=` `-3` `x=2 1/3, -3` -
Question 4 of 4
4. Question
Solve for `x`:`-2x^2-11x-12=0`Hint
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Exceptional!
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The cross method is a factorisation method used for quadratics.Since the equation is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`-2``x^2``-11``x``-12``=0`Find two numbers that multiply to `-2` on the left side and multiply to `-12` on the right side. Also, the coefficients of `x` in the factors, when multiplied by the constants, should add to `-11x`.`-2` and `1` fit the condition for the left side and `-3` and `4` fit the condition for the right side`-2 xx 1` `=` `-2` `-3 xx 4` `=` `-12` `(-2x xx 4) + (x xx -3)` `=` `-11x` 
Read across to get the factors.`(-2x-3)(x+4)=0`Solve for each value of `x`.`-2x-3` `=` `0` `-2x-3` `+3` `=` `0``+3` `-2x` `=` `3` `x` `=` `-3/2` `x+4` `=` `0` `x+4` `-4` `=` `0` `-4` `x` `=` `-4` `x=-3/2, -4`
Quizzes
- Sum & Product of Roots 1
- Sum & Product of Roots 2
- Sum & Product of Roots 3
- Sum & Product of Roots 4
- Solving Equations by Factoring 1
- Solving Equations Using the Quadratic Formula
- Completing the Square 1
- Completing the Square 2
- Intro to Quadratic Functions (Parabolas) 1
- Intro to Quadratic Functions (Parabolas) 2
- Intro to Quadratic Functions (Parabolas) 3
- Graph Quadratic Functions in Standard Form 1
- Graph Quadratic Functions in Standard Form 2
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities 1
- Quadratic Inequalities 2
- Quadratics Word Problems 1
- Quadratics Word Problems 2
- Quadratic Identities
- Graphing Quadratics Using the Discriminant
- Positive and Negative Definite
- Applications of the Discriminant 1
- Applications of the Discriminant 2
- Solving Reducible Equations