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a sum of several terms produces a polynomial

i dont get what you mean

look at this http://www.mathsisfun.com/algebra/polynomials.html

here it is ax^3+bx^2+cx+d

so is 5 a and -6.3 b?

nope

how do i determine a an

and b

x=5 and y=-6.3

using the graph u should find a, b, c and d

how so?

is it the right graph?

yes

x intercepts here are 2 and -2

as you can see from the graph another 2 points through which it passes are
(0,-2) and (0,2)

this one has a zero at \(-2\) and a zero at \(2\) with multiplicity 2

sorry i mean (2,0) and (-2,0)

making it
\[a(x+2)(a-2)^2\] and your last job is to find \(a\)

so -6.3=(5+2)(a-2)^2?

no, you need to solve for \(a\)

replace \(x\) by \(5\) not by \(a\)

\[ -6.3=a(5+2)(5-2)^2\]

\[-6.3=7\times 9 a\] etc

so a=-0.1

??

-6.3 / 63 = - 0.1 yes

so ax^3+bx^2+cx+d
how do i fit all this into this format

expand
-0.1(x +2)(x - 2)^2

-0.1x^3 + 0.2x^2 + 0.4x - 0.8???

yes

one last one

oh ok

i meant -4

so we can write
a(x+4)(x - 2)(x- 0)^2
or ax^2(x+4)(x-2)

can you continue from here?

you now need to use x = 5 y = -202.5

ive got 675 for a

-202.5 = 25a * 9 * 3
= -202.5 / (25*27)

cant be 675

-0.3?

oh ok

so you need to expand
-0.3 x^2(x + 4\)(x - 2)

thanks

yw