A REQUIREMENT FOR MATHEMATICS 10 1ST QUARTER

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* A Mathematical expression that contains one or more terms. It is in the form of ax^n where a is a real number and n is a positive integer.

* an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

* a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

axn + bxn-1 + . . . + rx + s = 0, where a, b, . . . , r and s are constants.

Solve the equation. x4-20x2+64=0Solution:

x4-20x2+64=0

(x2)2 – 20 (x2) +64=0

(x2-16)(x2-4)=0

x2- 16=0 x2- 4=0

x2= 16 x2=4

x= ±4 x= ± 2

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Solve the equation. x5+10x3+9x=0Solution:

x5+10x3+9x=0x(x4-10x2+9)=0

x((x2)2-10(x2)+9)=0

x((x2-9)(x2-1))=0

x=0; x2-9=0; x2-1=0x=0; x2=9; x2=1x=0; x= ±3 x= ±1

* Graphing the polynomials only need the information of completing the list of all zeroes (including multiplicity) for the polynomial

* an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

FIRST PROPERTY SECOND PROPERTY* There are no holes or breaks in the graph

and there are no sharp corners in the graph

* The graphs of polynomials will always be nice smooth curves.

* The “humps” where the graph changes direction from increasing to decreasing or decreasing to increasing are often called turning points

IF X=R IS A ZERO OF THE POLYNOMIAL P(X) WITH THE MULTIPLICITY K,

* If k is odd then the x-intercept corresponding to x=r will cross the x-axis

* If k is even then the x-intercept corresponding to x=r will only touch the x-axis and not actually cross it.

* Furthermore, if k>1 then the graph will flatten out at x=r

IF X=R IS A ZERO OF THE POLYNOMIAL P(X) WITH THE MULTIPLICITY K,

* If k is odd then the x-intercept corresponding to x=r will cross the x-axis

* If k is even then the x-intercept corresponding to x=r will only touch the x-axis and not actually cross it.

* Furthermore, if k>1 then the graph will flatten out at x=r

Graph the polynomial function:x3-2x2-3x

x F(x)

-3 -36

-2 -10

-1 0

0 0

1 -4

2 -6

3 0

4 20

* The degree of the polynomial is 3 and there would be 3 zeros for the functions.

* Make a table of values to find several points.

* Plot the points and draw a smooth continuous curve to connect the points

Graph the polynomial function:x2+x-12

x F(x)

-3 -6

-2 -10

-1 -12

0 -12

1 -10

2 -6

3 0

4 8

* Make a table of values to find several points.

* Plot the points and draw a smooth continuous curve to connect the points

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Aguilar, Jana Marie V. Ambrosio, Erica Jayne

Ecube, mia alexeneNavera, Erika Jane r.

Figueroa, Danniel