one more to check please?
Factor completely. Remember to look first for a common factor and to check by multiplying. If a polynomial is prime, state this.
2a^2 + 28a + 98 = 2 (a^2 + 14a + 49)

Question

one more to check please?
Factor completely. Remember to look first for a common factor and to check by multiplying. If a polynomial is prime, state this.
2a^2 + 28a + 98 = 2 (a^2 + 14a + 49)

hero · Answer

Have you already tried factoring it yet?

anonymous · Answer

yes. the original equation was 2a^2 + 28a + 98 and what i came up with was 2 (a^2 + 14a + 49)

hero · Answer

Which means that you have to continue by factoring the polynomial a^2 + 14a + 49

anonymous · Answer

how do i factor it further?

campbell_st · Answer

now you need to find the factors of 49 that add to 14

then it will be written as 

2(a + factor 1)(a + factor 2)

anonymous · Answer

i am sorry i am a little lost. :/

campbell_st · Answer

a factor is a number that divides evenly into another... 

in this question a^2 = a x a     so the factors of a^2 are a and a

e.g the factors of 8  are 1x 8, 2x4

anonymous · Answer

so in this case it would be 1, 7, & 1x49?

hero · Answer

Basically the polynomial a^2 + 14a + 49 has the form ax^2 + bx + c. Anytime a polynomial has this form and you're asked to factor it, the first thing you'll want to do is find two numbers that multiply to get ac, but add to get b. 

In this case, you want to find two numbers that multiply to get 49, but add to get 14. Can you figure out what those two numbers are? @beatlesgirl

anonymous · Answer

isn't it just 7*7?

hero · Answer

Yes and also 7 + 7 = 14, so you know you've found the right numbers. The next thing you'll want to do is split the middle term by using those two numbers you've found. So basically, when you split the middle term of the polynomial a^2 + 14a + 49, you'll end up with a^2 + 7a + 7a + 49. Notice that 7a + 7a = 14a .

hero · Answer

So far, in our attempt to factor the polynomial, we have accomplished the first step

0. a^2 + 14a + 49
1. a^2 + 7a + 7a + 49
2. 
3. 
4. 
5. 
6. 

There are several other steps involved with factoring this completely: 
2. The next step would be to do what is called factor by grouping. Meaning, you factor the first two terms a^2 + 7a. Then you would factor the last two terms 7a + 49. When you do this properly, you'll end up with a binomial that is the same for both the first two terms and the last two terms. 

Factoring the first two terms we get a^2 + 7a = a(a + 7)
Factoring the last two terms we get 7a + 49 = 7(a+7)

So when we put this all together we will have accomplished the second step: 

0. a^2 + 14a + 49
1. a^2 + 7a + 7a + 49
2. a(a+7) + 7(a+7)

Let me know if you understand this.

anonymous · Answer

vaguely I think I do.

hero · Answer

Okay, well, I will continue and in the end, you might get it.

anonymous · Answer

i sure appreciate it all, thank you!

hero · Answer

The third step involves using the distributive property. Recall that the distributive property is ab + ac = a(b+c). 

In our case, a = (a+7), b = a, and c = 7 <--- I know that might be confusing, but bare with me. 

What happens is, since (a+7) is common, we can factor it out, so a(a+7) + 7(a+7) becomes
(a+7)(a+7). So we have completed our third step: 

0. a^2 + 14a + 49
1. a^2 + 7a + 7a + 49
2. a(a+7) + 7(a+7)
3. (a+7)(a+7)

And actually, since we don't need to set this equal to zero to solve for a, we are actually done factoring. However, usually, when we have a binomial multiplied by itself, we can express it as a binomial square: 

4. (a+7)^2

I hope you're still with me.

hero · Answer

So the continuity of steps to get from the problem to the solution is: 

0. a^2 + 14a + 49
1. a^2 + 7a + 7a + 49
2. a(a+7) + 7(a+7)
3. (a+7)(a+7)
4. (a+7)^2

anonymous · Answer

i am. i am saving this lesson if you dont mind so in case i get confused i can return to it.

hero · Answer

Now, earlier you factored out 2 from the polynomial 2a^2 + 28a + 98 to get 
2(a^2 + 14a + 49). Since we have completely factored the a^2 + 14a +49 part, we can replace it with it's factored expression: 

5. 2(a+7)^2

And that is the way the final answer should be expressed.

hero · Answer

And to express the final answer more clearly, you could write: 

6. 2a^2 + 28a + 98 = 2(a+7)^2

anonymous · Answer

thank you so much! you have helped me more than you know. i would like to save this so that i may return to it in the future to help walk through it.

hero · Answer

It will be saved automatically. You'll be able to access every question you've ever asked on this site by clicking on your own username and going to your profile.

anonymous · Answer

perfect! thank you so so so much!!