We want to find the least common multiple of the given pair of polynomials.
x^2+3x-40 and x-8
To do so, we first need to find the prime factors of each expression. The degree of the second polynomial is 2 and the polynomial does not create a perfect square trinomial. Therefore, we can use the Quadratic Formula to help us factor. We will start by identifying the values of a, b and c in our polynomial.
x^2+3x-40 ⇔ 1x^2+ 3x+( -40)
Let's use the Quadratic Formula to factor our polynomial!
Knowing that x= - 3+132= 5 and x= - 3-132=-8 are the zeros of the trinomial, we can write the factored form of the quadratic expression.
(x- 5)(x-(-8)) ⇔ (x-5)(x+8)
The second expression is already written as a product of prime factors, so we can now write both expressions as the product of their prime factors.
x^2+3x-40 &= (x-5) (x+8)
x-8 &= (x-8)
Finally, we write the product of the prime factors, each raised to the greatest power that occurs in their expression.
(x-5) (x-8) (x+8)
