We have been given a quadratic formula. we need to find the factors. the factors are multiplied by each other and gives rise to the quadratic formulax² - 4x - 5to find the factors we need to multiply x² by -5 = -5x²then the factors of 5x² should add up to -4x. possible factors of 5x² are 1x and 5x. to get a negative product one factor should be positive and other factor should be negative. the sum of the factors is -4x, then the larger factor should be negative. From 1x and 5x, larger factor is 5x therefore it should be -5x.sum of 1x and -5x is -4x.we write -4x in the quadratic formula as (1x - 5x)x² + 1x - 5x - 5taking the common factors outx (x + 1) - 5 (x + 1)(x-5) (x+1)therefore factors are (x -5) and (x + 1)answers are 1) and 4)

1.) (x-5) and 4.) (x+1). Factoring works as follows: x*x = x^2 and x*1=x and -5*x=-5x and -5*1=-5. So you then have, x^2+x+(-5x)+(-5), therefore, you get the original: x^2-4x-5. This is how factoring works. You could not have x-4 or x-3 for various reasons, including the fact that the only factors of 5 are 5 and 1.

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Ask: Which two numbers add up to -4 and multiply to -5?

-5 and 1

Rewrite the expression using the above

= (x - 5) and (x + 1)


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