Question

Please someone helps with 1,2,3,4 much appreciated!

Answer 1

Answer:

2)

-5 has multiplicty 2,

2 has multiplicity 3

there is a multiplicity of 3 for x=3/2

degree is 8

3)

Zeroes: -9 and 1

Step-by-step explanation:

Number 2 is in a really easy  form to answer.  First though on a calculator or some website that lets you graph (desmos and geobra are excellent choices) try graphing (x-2)(x+3) and find its zeroes.  You'll find -3 and 2 are the zeroes, and when you have a function made of terms like (x+a) all being multiplied you can find zeroes like that.  Also keep in mind that if you have one that looks like (x+a) then -a is the zero and (x-a) makes a the zero.

Multiplicity then is basically the exponent on the outside of these (x+a) terms.  (x+a)^2 has multiplicity 2 and (x-b)^3 has multiplicity 3.  Super simple.  If you try graphing something like (x-1)(x+2)^2(x-3)^3(x+5)^4 you will see that the line crosses the x axis at x=1 and 3 while it just touches it at x=-2 and -5.  They are all zeroes, multiplicity just shows if the line crosses or just touches.  They cross at odd multiplicities and touch on evens.

Now!  Let's look at your problem.

4(x+5)^2(x-2)^3(2x-3)^3

There are three zeroes.  -5 has multiplicty 2, 2 has multiplicity 3 and (2x-3) represents 3/2 as a 0 because (2(3/2)-3)=0.  Which is how you determine zeroes.  Anyway, there is a multiplicity of 3 for x=3/2

Degree is the highest exponent on a variable.  You could expand it all out, or, in this form, if you add all the exponents you get the degree.  This only works in this form.  So the exponents are 2,3 and 3 so add 2+3+3=8 o the degree is 8.

3 I think you should use the relation for a lot of quadratics.

For an eqaution that looks like ax^2 + bx + c you want to find two numbers x and y where x + y = b and x * y = a * c

So starting with a * c that gets us 9.  Now what are the factors of 9  1*9, -1*-9, 3*3 and -3*-3  Now do any add up to get b, which is 10?  of course!   9 and 1.  So now that we have 9 and 1  When you have your numbers you can safely turn the function into this (x+9)(x+1)  Try expanding it and check it's the same thing.  Sometimes this doesn't work though and you will learn other methods.  Anyway, going back to number 2 we find zeroes by the values in the parenthesis so the zeroes are -9 and -1

Finally 4 you just need to know how to do polynomial long division.    How okay are you at it?