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these are the choices 4, multiplicity 1; -7, multiplicity 3; 7, multiplicity 3 -7, multiplicity 3; 7, multiplicity 2 4, multiplicity 1; 7, multiplicity 1; -7, multiplicity 1 -7, multiplicity 2; 7, multiplicity 3 can someone help me please
do you mean ?\[f(x) = 4(x + 7)^2(x - 7)^3\]
you should put in ^ to show exponents. I assume this is f(x) = 4(x + 7)^2(x - 7)^3 \[ f(x) = 4(x + 7)^2(x - 7)^3 \]
what happens if you erase the x and put in 7 in its place in (x-7) what number do you get ?
yes. they use the word "multiplicity" so look for an answer that says 7 multiplicity 3
-7, multiplicity 3; 7, multiplicity 2 so would this be the answer
it is easy to get confused. 4(x + 7)^2(x - 7)^3 we did (x-7) . what x makes that zero?
what do you mean by that like its the second x the one that says in (x-7) and if x is 7 it will equal 0 right ?
(x-7) is zero when x=7 and multiplicity 3 because we have (x-7)^3
you picked *** 7, multiplicity 2 so would this be the answer***
it would be -7, multiplicity 2; 7, multiplicity 3
thanks btw can you help me with one more
i need help understanding either the triangle or the theorem to answer this question Expand the following using either the Binomial Theorem or Pascal’s Triangle. You must show your work for credit. (x - 5)5
like you dont have to tell me the answer more like help me understand how to get there
please use the ^ otherwise it looks like (x-5) times 5 you mean \( (x-5)^5 \) first, write it like this: \( (x + (-5) )^5 \)
next, we start with this pattern \[ (a+b)^5 = a b + a b + a b + ...\] make the exponent of the a in the first term 5, and the exponent on b 0 (the exponents will *always* add up to 5) the next a will have an exponent of 4 (and the b will have 1) can you write out the a b pattern for (a+b)^5 ?
so it will be (5+0)^5= (4)(1).....
no. I am trying to say that \[ (a+b)^5 = a^5 b^0 + a^4 b^1 + ... \] (there are also numbers we have to put in, but first we need to learn how to write down this pattern) can you finish writing out the full pattern ?
would the next one be like a^3b^2
yes keep going
you mean a^2 b^3 (remember the exponents add up to 5) or the a goes down, the one on b goes up
ya sorry thats what i ment
keep going, we need all the terms
yes. so we have (so far) \[ (a+b)^5 = a^5 b^0 + a^4 b^1 + a^3b^2+a^2b^3 + a^1 b^4 +a^0 b^5\] now we have to put in coefficients (numbers) in front of each term. we use Pascal's triangle to find these numbers.
start by writing this pattern |dw:1437687651177:dw|
next we add a new row by adding 1 on each side, and adding the two numbers in the row above it. Like this |dw:1437687710434:dw|
now we keep adding rows until we get to a row with 6 entries... that will be the row we will use. |dw:1437687767682:dw|
can you find the next row ?
i seen it before but how does it help for the problem
and we add those to our pattern \[ (a+b)^5 = 1a^5 b^0 +5 a^4 b^1 + 10a^3b^2+10a^2b^3 + 5a^1 b^4 +1a^0 b^5 \]
we can simplify that a little... a^0 and b^0 are both 1. And we can leave off a coefficient of 1. so the pattern can be \[ (a+b)^5 = a^5 +5 a^4 b + 10a^3b^2+10a^2b^3 + 5a b^4 +b^5 \]
now we can tackle your problem \[ (x + (-5) )^5 \] every where you see a in the pattern , replace it with x and replace b with (-5) can you do that ?
i changed everyhthing
they probably want you to multiply out the (-5) to each exponent
the first two terms should be \[ x^5 - 25x^4 ...\]
sorry im writing everything on a piece of paper
+250x^3 is the next one right
-1250x^2 is next one
last -3125 is ok but redo 5*x*(-5)^4
yes. so put it together for the final answer.
thats the answer right
thank you so much