Exponents? I will answer your question if you leave it!?

Question

a.) (4x)^3=

b.) x^2+6x+9=

c.)2x^2-20x-25=

Thanks

Answer 1

Yeah, if it is equal to zero you need to factor it all.

b. would be

x^2+3x+3x+9

x(x+3) + 3(x+3)

(x+3) (X+3)

So x = -3... right? I forgot it all after two years!

Answer 2

a)  (4x)^3 Whenever you have an exponent outside of a parentheses, you can always "distribute" it-- give it to both values (4 and x), and so you will have (4^3)(x^3). 4^3= 4*4*4= 64. So it = 64x^3.

b) This is a polynomial (a chain of different x^whatever # (x^0=1, x^1=x, x^2= x^2) being added/subtracted ). In particular, it is a trinomial (3 terms), and it can be factored like so:

First, put the terms in order of greatest exponent to least (already done). You need x^2 to be in front, with 6x following, and 9 last.

Make two sets of parentheses : (         )(          )

Since you don't have any number in front of x^2, you can just put one x in the first slot of each parentheses:

(x       )(x          )      (This multiplied together will give you x^2 first when you do FOIL to distribute)

Look at the last sign of the polynomial. It is a +. This means both signs in the parentheses will be the same. Look at the sign towards the front. It is also a +. So you will have two +'s:

(x+       )(x+      ).

Now look at the last number (9) and the middle number (6). You will need to find two numbers multiplied together that equal 9, that also add together to equal six. This is a bit tricky! Think of the multiples of 9 first: 3*3, 9*1.   3+3=6, while 9+1=10, so 3 and 3 must be our numbers!

(x+3)(x+3)

Another way to look at this polynomial is to remember that whenever the first term and last term are both squares (x*x=x^2) and (3*3=9), and the middle is 2* the square root of 9 (3), then you can just write (x+3)(x+3), or (x+3)^2.

c) This is also a trinomial, but the x^2 has a number in front of it. This makes it a little bit harder.

The way I solve these is to put one x in the front of each parentheses like last time, but put a 2 in front of each. (2x      )(2x     ). Notice that when you multiply these for the First in FOIL, you would get 4x^2. But we will fix that issue later after we have put all our numbers and signs in. Just wait! :)

Take a look at the signs. The one towards the end is a - . This means the two signs we put in our (  )(  ) will be different, or + and -. So we don't need to look at the sign in front.

Now we have (2x+    )(2x-     ).

Ok--this is different from the last one. You now need to multiply the 1st term by the last term (2*-25=-50), and this is the number you will use as a "temporary last term" for the next step. Like in problem b, you need to now find what*what=-50 that will also add up to -20.

Try all the multiples.....none of them work!! :( But that's ok! We didn't come this far for nothing!

You need to know this process: when you can't factor a trinomial, you must use the quadratic formula.

[-b +/- sqrt(b^2-4ac)]/2a

This means -B plus or minus the square root of everything in parentheses: (B squared minus 4 times A times C)  ALL over 2 times A.

Remember to do 4ac first before you subtract from b^2.

When you plug a, b, and c (first, second, and last) into this equation, you get:

5 +/- [5*sqrt(6)]/2

Sorry about the computer notation! I know its confusing! But I'm sure there are examples online that don't look so ugly written out!

P.S.: sqrt means take the square root of whatever is in the parentheses. The brackets mean keep all that together and put it all over 2. The * means multiply. And +/- is a symbol for either + or -! So you basically have two answers (one with a plus in it, and one with a minus in it) But math people like to shorten things, so they put them together.

d) Sorry, I don't want to write it all out again! But you take the same steps as in problem c. This is because you line up the x's from greatest to least (put 3x^2 out front), and you see there is a number (3) in front of x^2. And once again you find out you can't factor it. Awesome, right! :D So you use the quadratic equation, and get this:

1 +/- [2*sqrt(6)]/2.

Sorry if you only needed the answers and already knew this stuff, but just were confused. I wanted to make sure you understood! This is a hard concept that you will get better with over time. Remember: You can only fail if you quit! So keep at it! Rock on!