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Please help asap! I don’t really understand

Please help asap! I don’t really understand-example-1
User Matvei
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Answer:

  1. x² +3x -8x -24
  2. (x² +3x) +(-8x -24)
  3. x(x +3) -8(x +3)
  4. (x +3)(x -8)

Explanation:

This is trying to help you understand a method of factoring trinomials.

The first step is to look at the linear term (-5x) and the constant term (-24) and identify the coefficients and their signs: -5 and -24.

The next step is to identify factors of -24 (the constant) that have a sum equal to -5 (the linear term coefficient). We can look at the ways that -24 can be factored:

-24 = 1(-24) = 2(-12) = 3(-8) = 4(-6)

The sums of these factor pairs are 1-24=-23, 2-12=-10, 3-8=-5, 4-6=-2. Of course, the pair we're looking for is +3 and -8.

The next step from here is to rewrite the linear term using these factors. (-5x=3x-8x) This is the first step of the sequence shown in the figure:

x² +3x -8x -24

The next step is to group these terms in pairs:

(x² +3x) +(-8x -24)

And then, to factor each pair using the distributive property:

x(x +3) -8(x +3)

Finally, finish the factoring, again using the distributive property:

(x +3)(x -8)

User Paul Lydon
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