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How do you factor 5x2 plus 10x 40?

Updated: 4/28/2022
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Wiki User

12y ago

Best Answer

Here are some steps to factor out the polynomial like this:

Factor out 5 to get:

5(x² + 2x - 8)

Here is how to work out the decomposition of the center value:

  1. Find two integers such that the product of these integers is -8 and the sum of these two integers is 2.
  2. We know that the factors of 8 are 1 and 8 and 2 and 4.
  3. Good thing that we obtain the pairs of factors. Now, we need to determine what type of signs we need to assign each factor of 8. Since the sum of two integers is 2, the only two values that work are -2 and 4. How? 4 - 2 = 2. That gives the sum of 2. Then, 4 * -2 = -8, which gives the product -8.

So we can rewrite the expression as:

5(x² + 4x - 2x - 8)

Factor by grouping, we have:

5(x(x + 4) - 2(x + 4))

Therefore, by collecting the terms and grouping the binomial (x + 4), we obtain:

5(x - 2)(x + 4)

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Wiki User

11y ago
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Wiki User

12y ago

If you mean:

5x2 + 10x + 40

Then the only factoring you can do is to divide it by five:

5(x2 + 2x + 8)

beyond which it can not be factored.

If on the other hand you mean:

5x2 + 10x - 40

Then you can factor it out as follows:

5x2 + 10x - 40

= 5(x2 + 2x - 8)

= 5(x2 - 2x + 4x - 8)

= 5(x(x - 2) + 4(x - 2))

= 5(x + 4)(x - 2)

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Luoyan

Lvl 7
3y ago

Here are some steps to factor out the polynomial like this:Factor out 5 to get:5(x² + 2x - 8)Here is how to work out the decomposition of the center value:Find two integers such that the product of these integers is -8 and the sum of these two integers is 2.We know that the factors of 8 are 1 and 8 and 2 and 4.Good thing that we obtain the pairs of factors. Now, we need to determine what type of signs we need to assign each factor of 8. Since the sum of two integers is 2, the only two values that work are -2 and 4. How? 4 - 2 = 2. That gives the sum of 2. Then, 4 * -2 = -8, which gives the product -8.So we can rewrite the expression as:5(x² + 4x - 2x - 8)Factor by grouping, we have:5(x(x + 4) - 2(x + 4))Therefore, by collecting the terms and grouping the binomial (x + 4), we obtain:5(x - 2)(x + 4)

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Anonymous

Lvl 1
3y ago

Denise begans playing with her dog at 8:25 and finished with him at 8:53 how long did she play with him ?

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