Solving Quadratic Equations (Factoring)
Amaleen Gonzalez
Trevion Martin
A quadratic equation is an equation with the highest exponent of two. For example, x²+2x+5 is a quadratic expression. Factoring a quadratic equation is making it into two binomials, where you would use FOIL to return it to a quadratic equation. There are two ways to factor a quadratic equation. Each quadratic equation needs to be factored a different way.
One way to factor a quadratic equation is by using a perfect square. For example, x²+10x+25 has a perfect square of twenty-five. A square root of twenty-five is five. When you factor it, the equation becomes (x+5)². If the equation was x²-10x+25, you could still use the perfect square to factor. When factored, that equation becomes (x²-5)² because negative five times negative five equals twenty-five. You could also use the fact that twenty-five is a perfect square if the equation was x²-25. When factored, that equation becomes (x+5)(x-5).
The other way to factor a quadratic equation is by using Box Method. You use Box Method when the quadratic equation doesn’t have a perfect square or if the equation does have a perfect square but the coefficients don’t add up correctly. For example, x²+7x+10 needs to be factored using Box Method. Box Method is used by setting up a box with four equally smaller boxes inside.
The first term is put into the first box and the last term is put in the last box. Then you multiply the first and last term together, which in this case would give you 10x². Now you have to find two numbers that equal 10x² when multiplied and 7x when added.
____ · ____ = 10x² ____ · ____ = 7x
With these numbers plugged in, you find the GCF going down and across. You end up with (x+2)(x+5).
Amaleen Gonzalez
Trevion Martin
A quadratic equation is an equation with the highest exponent of two. For example, x²+2x+5 is a quadratic expression. Factoring a quadratic equation is making it into two binomials, where you would use FOIL to return it to a quadratic equation. There are two ways to factor a quadratic equation. Each quadratic equation needs to be factored a different way.
One way to factor a quadratic equation is by using a perfect square. For example, x²+10x+25 has a perfect square of twenty-five. A square root of twenty-five is five. When you factor it, the equation becomes (x+5)². If the equation was x²-10x+25, you could still use the perfect square to factor. When factored, that equation becomes (x²-5)² because negative five times negative five equals twenty-five. You could also use the fact that twenty-five is a perfect square if the equation was x²-25. When factored, that equation becomes (x+5)(x-5).
The other way to factor a quadratic equation is by using Box Method. You use Box Method when the quadratic equation doesn’t have a perfect square or if the equation does have a perfect square but the coefficients don’t add up correctly. For example, x²+7x+10 needs to be factored using Box Method. Box Method is used by setting up a box with four equally smaller boxes inside.
The first term is put into the first box and the last term is put in the last box. Then you multiply the first and last term together, which in this case would give you 10x². Now you have to find two numbers that equal 10x² when multiplied and 7x when added.
____ · ____ = 10x² ____ · ____ = 7x
You would find that 2x and 5x fit in. You put 2x and 5x into the remaining boxes.
With these numbers plugged in, you find the GCF going down and across. You end up with (x+2)(x+5).
Sometimes there is a perfect square, but you still need to use Box Method. For example, x²+10x+16. If you do not use Box Method, you’d think it was (x+4)², but this is equal to x²+8x+16. Using Box Method, you’d have the correct answer, which would be (x+2)(x+8).
Quadratic Problems
5) 1. 2x²-8x+24 =0 2. 7x²-21x-18 =0
3. 9x² +3x-22 =0 4. 14x² +100x-25=0
5. 12x² +14x+4=0 6. 22x² +5x-30 =0
7. X² + 2x-8=0 8.4x²-10x = 7
9. 2x²-3x+ 12 =15(x² +4) 10. 40x²-28x-36=0
Quadratic Equations Continued
As my partner has stated a quadratic equation is a equation with the highest exponent is 2. One way to making it into two binomials is to use box method or find the perfect square of a number. If you want to check your answer just FOIL the problem which is the opposite of box method. Box method is only used when you don’t have a perfect square. This is a non quadratic equations like 5x³-30x+20 because the highest exponent is 3.
5) 1. 2x²-8x+24 =0 2. 7x²-21x-18 =0
3. 9x² +3x-22 =0 4. 14x² +100x-25=0
5. 12x² +14x+4=0 6. 22x² +5x-30 =0
7. X² + 2x-8=0 8.4x²-10x = 7
9. 2x²-3x+ 12 =15(x² +4) 10. 40x²-28x-36=0
Quadratic Equations Continued
As my partner has stated a quadratic equation is a equation with the highest exponent is 2. One way to making it into two binomials is to use box method or find the perfect square of a number. If you want to check your answer just FOIL the problem which is the opposite of box method. Box method is only used when you don’t have a perfect square. This is a non quadratic equations like 5x³-30x+20 because the highest exponent is 3.
- Trevion
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