Question

Can someone please help me with these questions? :)
1. Factor: x2 - 100
2. Factor: 81x2 - 49
3. Factor: x2 + 20x + 100
4. Solve the equation: x2 - 12x = -36

Answer 1

What part of factoring is giving you a hard time?

Answer 2

Everything. Lol.

Answer 3

1 and 2 are difference of squares
\[a^2-b^2=(a+b)(a-b)\]

Answer 4

1) (x-10)(x+10)

Answer 5

do you see the second one?

Answer 6

for the third problem, think of two numbers that when multiplied togeether equal a hundred and that when added together equal 20

Answer 7

Do you understand what a factor is?

Answer 8

Kind of. I was absent on the day that they were teaching all this stuff, so I'm kind of confused.

Answer 9

factoring is the opposite of distributing, think of it as multiplying and dividing.

when you're distributing, you're multiplying whatever is in the equation by whatever is outside of the equation, so for example

x(5+7+3x) = distribute the x
(5x+7x+3x^2) right?
when you're factoring, you're taking out whatever is in common with all of three terms. in this case, each of the terms has an x in common, so you can take it out (or divide each term by x)
x(5+7+3x) right?

Answer 10

Oh, okay. I kind of understand what you're saying itzmashy.

Answer 11

What if they have nothing in common though? Can you do one of the problems of mine above for me? So I can see what you're talking about.

Answer 12

the same thing for when you're trying to multiply two polynomials together. are you familiar with FOIL?

if you multiply (x-2)(x-3), you have to FOIL it to get x^2-5x+6, right?

so when you have an equation like x^2+20x+100, you look at the last term (100) and the second term (20x), and you think two polynomials were multiplied to get this in the form of:

(x+__)(x+__)
now i have to figure out what two terms, when multiplied together equal a hundred, and when added together equal 20?

try thinking of the multiples of 100

Answer 13

how did you get the 5 and six?

Answer 14

because -2 + -3 = 5, and 2x3=6

Answer 15

oops sorry -2+ -3 = -5

Answer 16

Well, how do I factor the problem 81x2 - 49? I don't have a lot of time and I'm really confused and frustrated.

Answer 17

i got the five and six by using FOIL (first term, outside term, inside term, last term) i can type it out but it may be get kind of confusing haha

(x-2)(x-3) will be first term times inside, outside = x(x)+x(-3)
then last term, times inside, outside so -2(x)+ (-2)(-3)
when you put it all together you get x^2-3x+ (-2x)+6, you can combine like terms to get
x*2-5x+6

doe that make sense?

i know it can be frustrating, but if you try to understand it now, then it'll be a lot easier for you when you have to learn more difficult things, and this way,when your'e tested on it, you'll get it ^.^

Answer 18

Many classifications, including polynomials and intgers, are capable of being broken down into the parts that when multiplied equal it. For example the number for consists of the prime factors 2 and 2 because when multiplied they equal two. A simple example of factoring a polynomial is presented in:

\[2x^2 + 2\]

If you think about the polynomial all terms are divisible by 2. Knowing this allows us to factor out the 2 into the product of the two.

\[2(x^2 + 1)\]

The concept can be extended to strictly polynomials such as your first question. If we look at the equation, think of what two polynomials whose product would be this equation.

\[x^2 - 100\]

The x square is a dead give away. It lets us know that the first term of the polynomials has to be x.

\[(x - ?)(x + ?)\]

We can then extend that principal to the 100 term. 100 is a perfect square and is the product of 10. We have to remember that the signs are important. In my above equation I use a negative and positive sign. If you insert 10 into the equation and foil them out you will see how the signs cancel one another out so we are left with a binomial.

\[(x - 10)(x + 10)\]
\[x2 + 10x - 10x - 100\]

Answer 19

the 81x^2-49 is also a difference of squares, but it's kind of complicated.. try to think of two numbers that when multiplied together equal 81, and then two other numbers that when multiplied together will equal -49

since its a negative, and there is no middle term, that means that, when you're foiling, the middle term will get cancelled out because one will be positive one will be negative

Answer 20

use the formula that precal gave you for it, a2−b2=(a+b)(a−b)