# How do you factor : `F(x) = 2x^2 - 9x - 5` ?

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`F(x) = 2x^2 - 9x -5`

To factor this, apply ac method.

To do so, multiply the coefficient of x^2 (a) and the constant (c).

`a*c = 2*(-5)=-10`

Then, determine the two numbers that will have a product of -10 and a sum of -9. (Take note that -9 is the coefficient of x.)

`-10 * 1 =-10`

`-10 + 1 = -9`

Thus, the pair factor of -10 that satisfiy the condition above is -10 and 1.

Use the pair factor to re-write the middle term.

`F(x) =2x^2 -9x -5`

`F(x)=2x^2 -10x + x - 5`

Then, group the terms into two.

`F(x) =(2x^2 - 10x) + (x - 5)`

Factor the GCF of each group.

For the first group, its GCF is 2x.

While the second group has no GCF.

`F(x) =2x(x-5) + (x - 5)`

And factor out the GCF of the two groups which is (x-5).

`F(x) = (x - 5)(2x +1)` **Thus the factor form of `F(x) = 2x^2 - 9x-5` is `F(X) = (x-5)(2x+1)` .**

**QUESTION:-**

**How do you factor : ?**

**SOLUTION:-**

`f(x)=2x^2-9x-5`

Now we have use the factorization method, so for that we have to find the values that when simplified gives the middle number. Like this;

`f(x)=2x^2-10x+x-5`

When we will simplify the middle value, we will get the same number that is -9x, hence this is the base of the factorization method.

`f(x)=2x(x-5)+1(x-5)`

Taking the two values:

`f(x)=2x+1, f(x)=x-5`

Hence the solution set for f(x) is: {(2x+1),(x-5)}

Hence Solved!

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First, you have to know what two things multiply to make 2x^2. X times x gives you x squared and 2 times 1 gives you the two. That means 2x and x are your first factors.

2x^2-9x-5

(2x )(x )

Next, you have to know what will multiply to give you a negative 5, but also add to give you a negative 9. 4 and 5 are the factors that work, but don't forget the signs.

(2x+1)(x-5)

You can factor that back out to check your work.

`f(x) = 2x^2 - 9x- 5`

When you have to factor a complicated equation, look at the signs. There are two minus (or negative) signs. The "bx" should be found through addition and the "c" should be found through multiplication.

To have a negative value of "bx," you must add one positive number with a greater negative number. To have a negative value for "c," you must multiply a positive number with a negative number.

First set up the general form of a factored equation:

`f(x) = (x+-n)(x+-m)`

The two in front of the polynomial can only be factored into 2 and 1.

`f(x) = (2x+-n)(x+-m)`

Look at "c" again. "2m" and "n" must multiply to be 5. The only numbers that do so are 5 and 1. You must either divide 5 or 1 in half and the greater number must be negative.

Therefore, the equation can be factored to:

`f(x) = (2x + 1)(x - 5)`

a=2 b=9 c=-5

multiply `axxc`

`2xx-5=-10 `

numbers that multiply to -10 and minus to 9 are -10 and 1

`2x^2-10x+1x-5 `

factor

`(2x^2-10x)+(1x-5) `

`2x(x-5)+1(x-5) `

(2x+1)(x-5)

x=(-1)/2 x=5

`2x^2 - 9x - 5`

`(2x +a )(x + b)`

`axxb = -5`

`2b + a = -9`

`(2x + 1)(x - 5)`

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