(Solved) How do I do these Factorising Quadratics Questions?

smithcherry

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11 years ago

How do I do these Factorising Quadratics Questions?

Example

Rearrange into the form "x² + bx + c = 0", then solve by factorising:

a) x² + 6x = 16

b) x² - 21 = 4x

c) x² = 11x

I just don't understand the method on how to work it out and how to write the answer.

Thank You For Your Help

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julie.t

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11 years ago

x^2+6x-16=0
(x+8)(x-2)=0
x=-8or2

x^2-4x-21=0
(x-7)(x+3)=0
x=-3or7

x^2-11x=0
x(x-11)=0
x=0or11

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smithgary

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11 years ago

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julibyrd

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11 years ago

First you have to put the equation in the correct form.
a) x^2+6x-16=0
Next you figure out the factors of 16. In this case the factors of 16 you would use are 8&2.
(x-8)(x+2) -8x2= -16 -8+2=6

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rjt6250

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11 years ago

You need to move everything over to the left side first, so you have to subtract the right side. Then you find a common factor or you can use the (x + a)(x + b) form (the signs in between the x variable and the constant can be either + or -; I chose + because it's more convenient, and a and b are numbers) to factor the equation.

The way I would factor with the (x + a)(x + b) form is to find what two numbers multiplied together would give you the third term (using a, the pairs for the number 16 are 4 x 4, 8 x 2, and 16 x 1). When you find all the pairs, you can either add or subtract the two numbers within the pair to find which pair would give you the constant for the second term (which is 6). Because the pair 8 x 2 would give you the number six if you subtract them (8 - 2), then this is what you're going to use. This also tells you that 8 is going to be positive, and 2 would be negative.

a) x² + 6x = 16
x² + 6x -16 = 0
(x + 8)(x - 2) = 0

b) x² - 21 = 4x
x² - 4x - 21 = 0
(x - 7)(x + 3)

c) x² = 11x
x² - 11x = 0
x(x - 11) = 0

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