Question

factor 4x^2 + 49

Answer 1

What squared = 49?
Or in other words what times itself = 49?

Answer 2

7

Answer 3

This equation isn't factorable.

Answer 4

oh ok thxs

Answer 5

how can you prove it's not factorable @ErinOfTime ?

Answer 6

If it was a difference of two squares, it could be factored. (i.e. 4x^2 - 49, which would have an answer of (2x-7)(2x+7).) Since there's a plus sign, it can't be done.

Answer 7

would you happen to know that part in the quadratic formula that tells if the expression is factorable or not?

Answer 8

Personally, I think using quadratic formula in doing factorization is a kind of .... cheating.
I think this expression cannot be factored unless you use complex number.

Answer 9

but im interested to learn it hehe..ive seen a lot of questions abt it

Answer 10

Well you can factor the difference of two squares (ex. 4x^2-49), because there's a subtraction sign. With the subtraction sign there, the middle terms get cancelled out, leaving you with just the 4x^2 and the negative 49. If it was 4x^2+49, it can't be factored because however you try to factor it, you're going to end up with a middle term. So the way to tell right off the bat is if it has a subtraction sign, it can be factored. If there's an addition sign, it can't. Is that what you were asking?

Answer 11

It can be factored like this:
4x^2 + 49
= (2x - 7i)(2x+7i)
But I think this is not the asker wants. So, we would say it cannot be factored.

Answer 12

@ErinOfTime nahh i was just asking the formula lol...but yeah it cant be factored

Answer 13

is this one not factorable also x^2-8x+16

Answer 14

The answer is (x-4)^2

Answer 15

thxs

Answer 16

@ErinOfTime It's better to guide the asker instead of giving the answer. It's against our Code of Conduct.

Answer 17

oh. sorry, this is literally the first few hours i've ever been on this site

Answer 18

@annej When you ask a new question, please close the current question and start a new one. Thanks.

Answer 19

oh ok
srry

Answer 20

\[x ^{2}-8x+16\]
1. Since you have an x^2, put two open parentheses with an x in both:
(x___)(x___)

2. Now figure out what signs you need. Since the 16 is positive and the 8x is negative, you need both numbers to be negative. Adding two negatives, the sum stays a negative. Multiplying two negatives gives you a positive:
(x-__)(x-__)

3. Figure out what multiplies to 16 and adds to 8. Experiment with different number combinations until you find the correct numbers. In this case, it would both be a 4:
(x-4)(x-4)