How do you factor 5x2 plus 10x 40?

Answer 1

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)

Answer 2

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)

Answer 3

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)

Answer 4

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