Amath Question

PUrePLs SG

Find the value of a and b for which x^2 + 4x -1 is a factor of x^3 + ax^2 - 5x + b.

Anyone can help ? Thanks.

nightzip SG

Dont have paper with me, just some ideas.

If x^{2+4x-1 is a factor of the x}3+ax^{2-5x+b.

so we can factorize x}2+4x-1 term to obtain the two factors (x+/~~..)(x+/~~..)

Then since this two are factors of the x^{3 expression, we
use

f(..)= sub in the values of x for X}3 expressions = 0.

I think as you will have two factors, and two unknowns, should be able to solve.

Lee012lee SG

If the question is changed slightly, it will be a bit more fun.

Find the value of a and b for which x^2 + x + 4 is a factor of x^3 + ax^2 - 5x + b.

Mikethm SG

Find the value of a and b for which x^2 + 4x -1 is a factor of x^3 + ax^2 - 5x + b.

Anyone can help ? Thanks.

Let x^3 + ax^2 - 5x + b = (x^2+4x-1)(x-b)

Let x = 1

1+a-5+b = 4(1-b)

a+5b = 8 ------(1)

Let x = -1

-1 + a + 5 + b = -4(-1-b)

a-3b = 0----- (2)

Eqn (1) - (2)

8b = 8

b = 1

From (1)

a + 5 = 8

a = 3

nightzip SG

If the question is changed slightly, it will be a bit more fun.

Find the value of a and b for which x^2 + x + 4 is a factor of x^3 + ax^2 - 5x + b.

This is not difficult, just do long division x^3 expression divide by the x^2 expression. The remainder (x+_) term will be one of the factor already.

Lee012lee SG

This is not difficult, just do long division x^3 expression divide by the x^2 expression. The remainder (x+_) term will be one of the factor already.

The modified question is not difficult, it is just a bit more fun.

Using your earlier method, it will not be possible to solve the modified question.

Your suggestion of using the long division method to solve the modified question

also has the problem of not being able to divide due to the existence of a and b.

Mikethm has already shown the correct method to solve the modified question

ie the modified question can be solved by using the method used by Mikethm to

solve the original question.