Need assistance.

[Rayz]

Can any one assist me with this questions?
A function of f is given by f(x) is = x³+4x²+x-6

a) show that (x+3) is the factor of f(x)
b) if f(-2)=0, factorise f(x) completely

 

[Dr.Peterson]

Can any one assist me with this questions?
A function of f is given by f(x) is = x³+4x²+x-6

a) show that (x+3) is the factor of f(x)
b) if f(-2)=0, factorise f(x) completely

(a) I would divide x³+4x²+x-6 by (x-3), either by synthetic or long division.

(b) What additional factor does the new information tell you to try? Do another division.

If you don't understand the connection, search for the factor theorem or remainder theorem.

 

[Harry_the_cat]

a) If (x -a) is a factor, then f(a)=0 and vice versa. So, if (x+3) is a factor then f(-3)=0

So, an alternative (and easier) way to Dr Peterson's method, is simply to show that f(-3)=0. Unless you like doing long division!

@Dr P .. I think you mean divide by (x+3) not (x-3).

@Rayz .. You need to learn about the factor theorem.

 

[Dr.Peterson]

So, an alternative (and easier) way to Dr Peterson's method, is simply to show that f(-3)=0. Unless you like doing long division!

... or unless you want the other factor, which they don't ask for, which would provide an alternative way to answer the second question.

Synthetic division is actually a shortcut to evaluate a polynomial (with fewer multiplications), so it can be considered a little easier, not harder -- once you are familiar with it, and if you aren't using a calculator.

But you're probably right about the intent of the problem.

@Dr P .. I think you mean divide by (x+3) not (x-3).

Yes, that was a typo. Oops.