f(x)=2x^3+13x^2+13x-10
find the value of f(2),f(-2). state one of the factors of f(x). Factorise f(x) completely.
can someone fully explain this?
thanks
find the value of f(2),f(-2).
Compare this with f(x). This means subbing x=2 into the bracket.
"state one of the factors of f(x)"
If it is a factor of f(x), it will not have any remainder.
therefore, for eg. when u sub x=-2 into f(x),
f(x)=2x^3+13x^2+13x-10
f(-2)=2{(-2)^3} +13{(-2)^2}+13(-2)-10=Remainder=0
This means (x+2) is a factor of f(x)
...in your original response earlier today the bit i dont udnerstand is
f(x)=(x+2)(ax^2+bx+c)
"by synthetic mtd" and the little table that followed
then 2x^2+9x-5 = ans what part of the question does this answer?
thanks in advance
Umm..u see..
f(x)=(x+2)(ax^2+bx+c)
f(x)=(x+2)(2x^2+9x-5)
Do u see any resemblance??
Actually, when im doing the synthetic mtd, im actually finding the "ax^2+bx+c" which comprises of other factors of f(x) because
(2x^2+9x-5)=(2x-1)(x+5)
Therefore, f(x)=(x+2)(2x-1)(x+5)
As was stated before, since f(-2)=0, that makes x+2 a factor of .
Synthetic division works like this:
Since the dividend was degree 3, the quotient will be degree 2.Code:-2 |2 13 13 -10 | -4 -18 10 | --------------- 2 9 -5 0
Thus, the two factors so far are:
The trinomial has already been factored for you in Post #6
Take whatever is the result on the bottom and multiply it by the -2 in the corner. I'll try to explain this a bit in more detail.
You start with 2, and it goes straight down. Then multiply that 2 by the -2 in the corner and put it into the next column, so you get -4. 13 + (-4) = 9, so you write that on the bottom. Then multiply it by the -2 in the corner to get -18, and put that into the next column. 13 + (-18) = 5, and you put that on the bottom. Continue this, and you get your answer.
You really need to refer to the link I gave you. There are other links out there as well. Just google "synthetic division" and you'll find many examples and explanations.
The dividend is made up of the coefficients of the original cubic expression.
The divisor comes from (x - c) being a factor, so c is my divisor. Specifically, (x+2) is a factor, by using a divisor of -2, the remainder will be 0.
First, I bring down the leading coefficient (2).
Second, I multiply my divisor (-2) by (2) to get (-4)
Third, I add (13) and (-4) to get (9).
Fourth, I multiply (-2) times (9) to get (-18).
Fifth, I add (13) to (-18) to get (-5)
Sixth, I multiply (-2) times (-5) to get (-10)
Finally, I add (10) to (-10) to get a remainder of (0).
The explanation on the link is much better than this. Look there.