Question

Domain of function h , where h(x)2^x, is real number
a)find images of 0,2,-1 and 6
@ganeshie8

Answer 1

Do I need to substitute the given values to the function

Answer 2

Yes !

Answer 3

Okay

Answer 4

h(x) = 2^x

you just need to find h(0), h(2), h(-1), etc..

Answer 5

http://en.wikipedia.org/wiki/Image_(mathematics)

Answer 6

Understood
Another question
IF p(X)=2X^3+4X^2-X+3 AND q(X)=3X^2+X-1
FIND
A) P(x) times Q(x)

Answer 7

multiply

Answer 8

\[P(x) \times Q(x) = (2x^3+4x^2-x+3 )\times \color{red}{(3x^2+x-1 )}\]

Answer 9

I'm nt sure bout the factorisation part
Can u show me the first step.. I can do the rest

Answer 10

we need to distribute each term of one factor with the other factor

Answer 11

\[\large P(x) \times Q(x) = (2x^3+4x^2-x+3 )\times \color{red}{(3x^2+x-1 )}\]

\[\large = (2x^3+4x^2-x+3 )\times \color{red}{(3x^2)} \\ \large + (2x^3+4x^2-x+3 )\times \color{red}{(x)} \\ \large + (2x^3+4x^2-x+3 )\times \color{red}{(-1)} \]

Answer 12

Now, I undersatand the concept
Thanks a lot

Answer 13

understand*

Answer 14

good :) its going to be a bit lengthy - after multiplying, you need to group the like terms and simplify

Answer 15

Okay
Another Q:
Find quotient if x^3-4x^2+5x-2 can be divided by (x-2) exactly

Answer 16

this is a sample Q
Hang on

Answer 17

okie

Answer 18

the solution is
x^3-4x^2+5x-2=q(x) . (x-2)
They mention that q(x) is a polynomial of degree 2.. why?

Answer 19

whats the degree of polynomial on LEFT HAND side ?

Answer 20

3

Answer 21

what happens to its degree if you multiply the entire polynomial by \(x\) ?

Answer 22

It'll be 4.. I'm nt sure

Answer 23

Yes !

multiplying x^3 by x gives u x^4
so clearly the degree is 4

Answer 24

okay

Answer 25

Now look at the question you have asked earlier

Answer 26

x^3-4x^2+5x-2=q(x) . (x-2)


whats the degree of q(x) ?

Answer 27

Since the degree of LEFT SIDE polynomial is `3`,
the degree ofRIGHT SIDE polynomial must also equal `3`

Answer 28

Since `(x-2)` has degree `1` , the degree of q(x) has to be `2` so that when you multiply both you get a polynomial of degree 2+1 = 3

Answer 29

Understood

Answer 30

One more question
Using remainder theorem, find the remainder when polynomial P(x)=2x^3+7x^2-5x-4 is divided by (x+3)

Answer 31

do i jst need to find the x-intercept

Answer 32

As the question says, you need to divide and find the remainder

Answer 33

Nvm, I gt it
x+3=0
x=-3

Answer 34

Thank you Ganesh

Answer 35

http://www.mathsisfun.com/algebra/polynomials-remainder-factor.html

Answer 36

Using remainder theorem, find the remainder when polynomial P(x)=2x^3+7x^2-5x-4 is divided by (x+3)

Answer 37

x=-3

evaluate the polynomial at -3

P(-3) = ?

Answer 38

=2(-3)^3+7(-3)^2-5(-3)-4
=

Answer 39

20

Answer 40

Remainder is 20

Answer 41

Excellent !!

Answer 42

Alrite, thanks again
I'm done 4 nw... :)