completely factor the polynomial x^2+2x-40

Question

I need to completely factor the polynomial. If it can't, I need to know if it is prime.

Answer 1

If the discriminant of the expression is not a perfect square, then it is not factorable.  In a quadratic equation, the discriminant is

 

b² - 4ac

 

where:

a = 1

b = 2

c = -40

 

Plugging this is, we get

 

2² - 4(1)(-40) = 4 + 160 = 164

 

164 is not a perfect square.  Therefore, you cannot factor the expression using integer values.   That is because taking the square-root of a number that is not a perfect square will only result in an irrational number.

 

Also, the term 2x in the polynomial has a coefficient of 2, which is prime.

Answer 2

You need to use quadratic formula since you won't be able to factor this out completely.

 

x = -b +/- sqrt(b² - 4ac) / 2a

 

Let a = 1, b = 2, and c = -40 be leading coefficients.  Then plug them in the quadratic formula.

 

x = -(2) +/- sqrt(2² - 4(1)(-40)) / 2(1) = -2 +/- sqrt(164) / 2 = -2 +/- 2*sqrt(41) / 2 = -1 +/- sqrt(41)

 

You will end up with 2 x-values:  -1 + 6.40 = 5.40 and -1 - 6.40 = -7.40

 

 

Answer 3

This polynomial is prime

 

You can use the "AC" method to factor polynomials in the form Ax² + Bx + C

 

Here A = 1 and C = -40

 

Find the product of AC, which is -40.

 

What are the factors of 40?

 

40 = 1 x 40

 

40 = 2 x 20

 

40 = 4 x 10

 

40 = 5 x 8

 

In order to use this method, we would need two factors of -40 that would combine to give us the coefficient of the x-term, which is 2.

 

None of the factors of -40 can combine to gives us 2.