Exercise 16 Page 388

We want to find the least common multiple of the given pair of polynomials. x^2-2x-63 and x+7 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^2-2x-63 ⇔ 1x^2+( -2)x+( -63) Let's use the Quadratic Formula to factor our polynomial!

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( - 2)±sqrt(( - 2)^2-4( 1)( - 63))/2( 1)

▼

Simplify right-hand side

NegNeg

- (- a)=a

x=2±sqrt((- 2)^2-4(1)(- 63))/2(1)

CalcPow

Calculate power

x=2±sqrt(4-4(1)(- 63))/2(1)

Multiply

Multiply

x=2±sqrt(4+252)/2

AddTerms

Add terms

x=2± sqrt(256)/2

CalcRoot

Calculate root

x=2± 16/2

Knowing that x= 2+162= 9 and x= 2-162=-7 are the zeros of the trinomial, we can write the factored form of the quadratic expression. (x- 9)(x-(-7)) ⇔ (x-9)(x+7) 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^2-2x-63 &= (x-9) (x+7) x+7 &= (x+7) Finally, we write the product of the prime factors, each raised to the greatest power that occurs in their expression. (x-9) (x+7)