# Algebra woes

• Jun 1st 2010, 02:38 PM
xirokx
Algebra woes
Hey guys,

I'm new and find your abode in great despair..

Im calling all maths guru...

Any chance the maths gurus can help me answer these questions and show me the working out for each of them?

They are like the last 4 questions I have(the hardest ones)

1 a. P(x) is a polynomial.
If P (a) =0
State the factor theorem.

b. Use the factor theorem to show that (x-2) is a factor of x3-x2-7x+2

c. Substitute x=2, x=3, and x=1 and x= -1 into the polynomial P(x)= x3-4x2+x+6

2 Express the quadratic x2-2x-3 in the form of (x+p)2+q where p and q are constants.

a. Hence or otherwise find the coordinates of the vertex of the parabola y= x2-2x-3.

b. Find the roots of x2-2x-3=0 and hence sketch the parabola y= x2-2x-3.

3b. Express the following quadratics in the completed square form and solve them.

i. X2-4x-3=0

ii. X2+6x+4=0
• Jun 1st 2010, 03:45 PM
pickslides
Quote:

Originally Posted by xirokx
1 a. P(x) is a polynomial.
If P (a) =0
State the factor theorem.

This is easy, just state the rule.

For $P(x)$, if $P(a) =0$ then $x-a$ is a factor

Quote:

Originally Posted by xirokx

b. Use the factor theorem to show that (x-2) is a factor of x3-x2-7x+2

Find P(2) if this equals zero you have shown it.

Quote:

Originally Posted by xirokx

c. Substitute x=2, x=3, and x=1 and x= -1 into the polynomial P(x)= x3-4x2+x+6

Find $P(2),P(3),P(1)$ and $P(-1)$

If any of these are zero then you have some factors.

Quote:

Originally Posted by xirokx

2 Express the quadratic x2-2x-3 in the form of (x+p)2+q where p and q are constants.

a. Hence or otherwise find the coordinates of the vertex of the parabola y= x2-2x-3.

b. Find the roots of x2-2x-3=0 and hence sketch the parabola y= x2-2x-3.

For this you need to complete the square, here's an example on how to do it.

http://www.mathhelpforum.com/math-he...-question.html

vertex will be $(-q,p)$ in what you find.
• Jun 1st 2010, 04:06 PM
xirokx
thanks,

A solution to the equation X2 -5x+2=0 lies between 4
and 5. Find this solution to two decimal place using
“trial and improvement” method

are you saying questions 2 and 3b are both "complete the square" type questions?

thanks
• Jun 1st 2010, 05:04 PM
pickslides
Quote:

Originally Posted by xirokx
are you saying questions 2 and 3b are both "complete the square" type questions?

thanks

Yep.

Quote:

Originally Posted by xirokx

A solution to the equation X2 -5x+2=0 lies between 4
and 5. Find this solution to two decimal place using
“trial and improvement” method

Find solution when x=4 and x=5, which is closer to zero?

Then concentrate on checking solutions on the interval (4,5) closer to that point. Make sense?