Exercise 15 Page 388

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!

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 3±sqrt(3^2-4( 1)( - 40))/2( 1)

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Simplify right-hand side

CalcPow

Calculate power

x=- 3±sqrt(9-4(1)(- 40))/2(1)

Multiply

Multiply

x=- 3±sqrt(9+160)/2

AddTerms

Add terms

x=- 3± sqrt(169)/2

CalcRoot

Calculate root

x=- 3 ± 13/2

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)