# Math Help - What's the "best" Way of Solving Trinomial with leading coefficient that's not one?

1. ## What's the "best" Way of Solving Trinomial with leading coefficient that's not one?

By best I mean best for you. I posted this thread to find out different ways people use. I know what I've been taught is popular according to my teacher.

My way is:
Example:

3a^2+10a+7

write the first and last numbers. The middle number "10a" is what we will divide into two numbers.

3a^2+ ______+_______+7

Multiple 3 by 7= 21.

Our goal is similar to a normal trinomial without a leading coefficient more than one now. We need to find a number that when multiplied is 21 and added 10. Eventually, the numbers 3 and 7 will come up. Better to go in chronological order for those who do not know.

3a^2+3a+7a+7

Now use grouping method.

3a(a+1) 7(a+1)

Take the numbers 3a and 7... put them in (3a+7)

(a+1) (a+1) is similar to doing it with (3a+7)

=(3a+7) (a+1)

This is how I do it. It might not make sense for you, but it does for me.

2. ## Re: What's the "best" Way of Solving Trinomial with leading coefficient that's not on

Originally Posted by xivivx
By best I mean best for you. I posted this thread to find out different ways people use. I know what I've been taught is popular according to my teacher.

My way is:
Example:

3a^2+10a+7

write the first and last numbers. The middle number "10a" is what we will divide into two numbers.

3a^2+ ______+_______+7

Multiple 3 by 7= 21.

Our goal is similar to a normal trinomial without a leading coefficient more than one now. We need to find a number that when multiplied is 21 and added 10. Eventually, the numbers 3 and 7 will come up. Better to go in chronological order for those who do not know.

3a^2+3a+7a+7

Now use grouping method.

3a(a+1) 7(a+1)

Take the numbers 3a and 7... put them in (3a+7)

(a+1) (a+1) is similar to doing it with (3a+7)

=(3a+7) (a+1)

This is how I do it. It might not make sense for you, but it does for me.

The method you described above called: Vieta's Formulas -- from Wolfram MathWorld

3. ## Re: What's the "best" Way of Solving Trinomial with leading coefficient that's not on

I've tried my method on 40 problems. I , however, got stuck at this one:

3x^2-15x+16

Why can't I solve this with the Vieta formula?

Can you try and do it ?

4. ## Re: What's the "best" Way of Solving Trinomial with leading coefficient that's not on

Originally Posted by xivivx
I've tried my method on 40 problems. I , however, got stuck at this one:

3x^2-15x+16

Why can't I solve this with the Vieta formula?

Can you try and do it ?

If \alpha and \beta are the two roots of the above equation, then:

$\alpha+\beta=5$

and,

$\alpha \cdot \beta=\frac{16}{3}$

solve that system of equations, and you will get your roots.

5. ## Re: What's the "best" Way of Solving Trinomial with leading coefficient that's not on

I can't find it. I think this darn thing is a prime. Try to find it -.-

6. ## Re: What's the "best" Way of Solving Trinomial with leading coefficient that's not on

Originally Posted by Also sprach Zarathustra
$\alpha+\beta=5$ and,
$\alpha \cdot \beta=\frac{16}{3}$

solve that system of equations, and you will get your roots.
That simply leads back to the original equation!

Try the quadratic formula: b^2 - 4ac = 33 ; get my drift?