Question

Factor: a) 4x^2-13x+9

Answer 1

A.
`x = (9)/(4)`

B.
`x = 1`

Explanation:

I don't know if you know this method. I'll explain.

1. Rewrite the same expression, but multiplied and divided by the same number that has the squared variable.

`4((4x^2-13x+9)/(4))`

2. Take this expression to the expression
`x^(2) +bx+c`, you can do this by grouping. (4)(
`4x^(2)`) can be grouped as
`(4x)^2` ; since what we want is to keep the (4x) in parenthesis, we don't multiply by 13. leaving it like 13(4x). Finally, we multiply 4 * 9 = 36. The denominator remains. Leaving the expression like:

`((4x)^2-13(4x)+36)/(4)`

So you see, we now have the expression
`x^2+bx+c`

`x^(2) =(4x)^(2)`

`bx = -13(4x)`

`c = 36`

3. Solve the expression by making 2 parenthesis, extracting (4x) and putting it into both of them like so.

(4x) (4x)

The sign in the first parenthesis is going to be the same as the second number; in this case, negative.

(4x -) (4x)

The sign in the second parenthesis is going to be the multiplication of the second and third signs in front of the numbers. In this case (-) (+) = -

(4x -) (4x -)

Next, we have to find a number that multiplied by another number be equal to ''c'' and added up or substracted (depending on the signs) be equal to ''b''. In this case, since we have the same signs in both parenthesis, we must only find a number which multiplied by another number be equal to 36 and substracted by that number be equal to 13. These two numbers are: 9 and 4 because 9 * 4 = 36 and - 9 + (-4) = -13

Remember that everything is being divided by 4 in this problem.

`((4x-9)(4x-4))/(4)`

4. Factor. If you have done everything correctly, the factor number will be the same as the one in the denominator. In this case, it's 4.

`(4x-4)` is factorable. Their common factor number is 4. If you do not remember how to factor, it's basically dividing by a common number or variable.

`(4x)/(4) = x`

`(4)/(4) = 1`

The factor number is put outside the parenthesis, leaving this expression like:

`4(((4x-9)(x-1))/(4))`

So you see, now we cancel out the 4 outside the parenthesis and the one in the denominator. Leaving the expression like:

`(4x-9)(x-1)`

5. Equal both expressions to 0 (NOTE: If you're not required to do this, the answer is both parenthesis above)

4x - 9 = 0

4x = 9

x =
`(9)/(4)`

AND

x - 1 = 0

x = 1