Factoring quadratics

Question

I need help with factoring quadratics

1. 25x^2+15x+2
2. x^2+3x-28
3. x^2+9x+18
4. 26x^2=19x+3

Answer 1

The first 3 are in are in the Standard Form for a quadratic that being

ax² + bx + c

This is typically factored by unFOILing, Completing the Square or using the Quadratic Equation.

If you have multiplied polynomials you've probably used FOIL

A standard form quadratic always has 2 for the highest exponent

so your factors will consist of x times x

Sometimes your a term will also have factors

Your c term will have factors as well

The middle term is the sum of the a times c factors

For example let try the first one

1. 25x^2+15x+2

Factors of x² = x times x

Factors of a = factors of 25 they are 1, 25, 5 we also know that 25 is a perfect square

Factors of c = factors of 2 they are 1 and 2

We need to use and set up the factors above so that they multiply to a = 25, c = 2 and at the same time add to b= 15

1. 25x^2+15x+2

(5x + 1)(5x + 2)

You can use FOIL to check this

The fourth one is not quite in the form yet of a standard quadratic so we need to get it there correct format by moving everything over to one side of the equal sign

1. 26x^2=19x+3
2. 26² - 19x - 3 = 0

Now we just repeat the process from above

Factors of x² = x times x

Factors of a = factors of 26 = 1 , 26, 13, and 2

Factors of c = factors of -3 = -3, 1 and -1, 3

We need to use and set up the factors above so that they multiply to a = 26, c = -3 and at the same time add to b= -19; this is not quite obvious and I would suggest using the quadratic formula instead remember to solve for both roots and you can check this by graphing question 4 at Desmos.com I got x intercepts at x = 0.864 and x = -0.134 give it a try. You can also lookup Completing the Square on your own

Answer 2

As far as I know there is no easy way to factor trinomials except to practice.

In the first one 25 can only factor as 5x5 and 2 can only factor as 2x1.

The answer then is easy,

In the second one the only factors of 28 which differ by 3 are 7 and 4.

In the 3rd one the obvious factors of 18 are 6 and 3.

I'm not sure what is wanted in the 4th one,