Hellpppppp Please

Question

(x-4)² (x-9)

 

I have to put this polynomial in standard form :) Help please

Answer 1

Hello Rebecca,

I will try to give you an explanation for how to multiply polynomials.

 

 (x-4)^2 (x-9) 

= (x-4)(x-4)(x-9)

You can do the multiplication in any order.  Just for fun let's do (x-4)(x-9) first.  What you should remember is that multiplication for polynomials is distributive.

 

The distributive law says that a(b+c) = a*b+a*c.  You can also apply it to (a+b)(c+d) by distributing twice, first a then b: (a+b)(c+d) = a(c+d) +b(c+d) = ac+ad + bc + bd.

 

What this means is that (x-4)(x-9) = x(x-9) - 4(x-9)  notice that I get x and -4 from (x-4).

 

Now x(x-9) also requires the distributive property: you do: x(x-9) = x*x - x*9 = x^2-9x

Likewise for 4(x-9) you get: 4(x-9) = 4*x - 4*9=4x-36.  Now recall that these are meant to go together:

x^2-9x - [4x-36] = x^2-9x -4x + 36 = x^2-13x+36

 

Now we need to multiply (x-4)(x^2 - 13x +36).

 

Again break it up into parts: x(x^2-13x+36) - 4(x^2 - 13x +36)

And again first distribute the x: x(x^2 - 13x +36) = x^3-13x^2+36x 

Then distribute the 4: 4(x^2 - 13x +36) = 4x^2 -52x +144

And finally put them together:

x^3-13x^2+36x - [4x^2 - 52x +144]

= x^3-13x^2+36x -4x^2+52x - 144

= x^3 -17x^2 +88x -144

 
The FOIL method is a mnemonic for remembering that this is what you are doing when you multiply polynomials:

(a+b)(c+d) =

a(c+d) + b(c+d) =

ac + ad + bc + bd

First Outside Inside Last 

 

I hope this helps in understanding the FOIL method.  Remember that you could use the same strategy for numbers since they also follow the distributive law: 4(3+4) = 4*3+4*4 = 12 + 16 = 4(7)= 28, and perhaps a little harder; 12*12 = (10+2) * (10+2) = 10(10+2) + 2(10+2) = 100 + 20 +20 + 4 = 144.

 

If you have any questions, please feel free to ask!  

Sincerely,

Jose

The FOIL method is a mnemonic for remembering that this is what you are doing when you multiply polynomials:(a+b)

Answer 2

1. expand it to (x-4)((x-4)   (x-9)

=                 (x² -8x + 16)(x-9)

2. multiply these together giving

=                  x³ -8x² +16x

                         -9x² +72x -144

                    -----------------------

=                  x³ -17x² +88x -144

Answer 3

To multiply (x-4)²(x-9) first you need to know...

(x-4)² means (x-4)(x-4)

Now you have (x-4)(x-4)(x-9)

You can multiply any two of these binomials (2-term polynomial). Let's use the FOIL method. (FIRST terms, OUTER terms, INNER terms, LAST terms)

Note: Here is how you FOIL in case you didn't know. You can only use this method with two binomials.

(a+b)(c+d) =

ac + ad + bc + bd

First Outer Inner Last 

F x(x) = x²

O x(-4) = -4x

I (-4)(x) = -4x

L (-4)(-4) = +16

Combine -4x + -4x since these are like terms which = -8x

= x² -8x +16

Now take this answer and multiply it by the remaining binomial (x-9) by distributing the x to each term of the trinomial and then distributing -9 to each term of the trinomial.

 

(x-9)(x²-8x+16)

x • x²= x³

x • -8x = -8x²

x • 16 = +16x

-9 • x² = -9x²

-9 • -8x = +72x

-9 • 16 = -144

Now multiply by (x-9):

 

Put them together x³ - 8x² + 16x - 9x² + 72x - 144 and combine like terms. The x² terms are in bold and the x terms are underlined. These are the terms you combine.

Your final answer is x³ -17x² +88x -144. This polynomial is in standard form since the exponents are written in decreasing order.

 

Answer 4

(x-4)²(x-9)

 

Multiply out the squared factor first (FOIL):

 

(x²-8x+16)(x-9)

 

Now multiply by (x-9):

 

x³ - 8x² + 16x - 9x² + 72x - 144

 

Now combine like terms and arrange from highest degree (power) to lowest.