Which binomial is a factor of x2 5x 4?

Answer 1

There are two ways you can solve this problem:

1) Factor

We will presume that the above polynomial can be easily factored into the form (x + a)*(x + b).

We want to find 'a' and 'b' such that:

i) a * b = 4

and

ii) a + b = 5.

If we presume that a and b must both be integers, that means that they must be factors of 4 in order to satisfy (i). The possible factorizations of 4 are:

-1, -4 : a + b = -5

-2, -2 : a + b = -4

2, 2 : a + b = 4

1, 4 : a + b = 5

You will notice that only a choice of 1,4 for our factors which satisfies (ii), a + b = 5. We therefore know that a = 1 and b = 4 (or vice versa, since order doesn't matter in this case.

So our two possible factors are:

(x + 1) and (x + 4).

2) Use the quadratic formula:

a = 1, b = 5, c = 4

(-b +- (b^2 - 4 * a * c)^(1/2)) / (2 * a)

(-5 +- (25 - 16)^(1/2))/2

(-5 +- sqrt(9)) / 2

(-5 + 3) / 2 or (-5 - 3) / 2

(-2 / 2) or (-8 / 2)

So your roots are:

-1 or -4

Plugging in -1 and -4 for x in the binomial equation:

(x + a) = 0 gives us:

-1 + a = 0

a = 1

and

-4 + a = 0

a = 4

Your possible factors are thus:

(x + 1) and (x + 4)