polynomial

[Anonymous No.5128134]

Just one quick question that has been pestering me for a while, how do you know where the function begins if you are given an equation of a polynomial? Under or over the x-axis ?

the example is p(x)=-(x+3)(x+1)^2(x-1)^3(x-4)^2

[Anonymous No.5128141]

look at the sign of the highest power

[Anonymous No.5128145]

>>5128141
Ok, i'm a little bit confused

[Anonymous No.5128147]

>>5128134
What do you mean by "begin"...just plug in x=0?

[Anonymous No.5128148]

Do you mean what it does as x tends to negative infinity?

Expand the polynomial out, or at least find the leading coefficient.

If the leading coefficient is positive and the degree is even, it will 'begin' above the x-axis, and if it is negative and the degree is even it will begin below the x-axis

If the leading coefficient is positive and the degree is odd, it will 'begin' below the x-axis, and if it is negative and the degree is odd it will begin above the x-axis

[Anonymous No.5128157]

>>5128148
are you talking about degree of the first intersection with the x-axis or about degree of all intersections

[Anonymous No.5128160]

>>5128145

Well, do you know what a highest power is? And do you know what + and - signs are?

[Anonymous No.5128168]

>>5128157
he's talking about the degree of the polynomial

it really is very fucking simple, and to do with whether the coefficient of the largest power of x is +ve or -ve, and whether that power is even or odd.

[Anonymous No.5128170]

>>5128160
I'm not aware what a highest power is, for we didn't learn math in an english language

[Anonymous No.5128171]

Your example will be -x^8...

from which we conclude it starts negative and ends negative

[Anonymous No.5128172]

>>5128170
the highest power of x^3 +4x^2 - 2x +6 is x^3

[Anonymous No.5128176]

>>5128172
aha, so the degree of the highest power is the one i should be interested in?

[Anonymous No.5128178]

>>5128176
degree and sign

as x -> oo and x-> -oo you can ignore all lower powers of x

[Anonymous No.5128233]

>>5128178
is that the simbol for infinty?

Ok, just one last question. I have a polynomial p(x)=x^5-4x^3+3x, how do i find all of the intersections if the loose link(c) is equivalent to zero?

[Anonymous No.5128239]

>>5128233
x^5-4x^3+3x = 0
x(x^4-4x^2+3)=0
x(x^2-3)(x^2-1)=0
x(x-sqrt(3))(x+sqrt(3))(x-1)(x+1) = 0

etc

[Anonymous No.5128252]

>>5128233
<span class="math"> x^5-4x^3+3x=0[/spoiler]
<span class="math"> x(x-1)(x+1)(x^2-3)=0[/spoiler]
<span class="math"> x = 0 \vee x = 1 \vee x = -1 \vee x = \sqrt{3} \vee x = - \sqrt{3}[/spoiler]

[Anonymous No.5128444]

Thanks guys, i'm studying with my girlfriend and i forgot about this stuff