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...

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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)` .

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