Question

Part A: Factor the expression 18x^2– 39x + 18 completely. Show your work for full credit (6 poionts)

Part B: How do you use multiplication of polynomials to verify the solution is correct? (4 points)

Answer 1

`(a)\`
`18x^2 - 39x + 18 = 3(3x -2)(2x - 3)`

(b) See Explanation

Explanation:

Given

`18x^2 - 39x + 18`

Solving (a): Factorize Completely

`18x^2 - 39x + 18`

Factor out the common term

`18x^2 - 39x + 18 = 3(6x^2 - 13x + 6)`

Expand

`18x^2 - 39x + 18 = 3(6x^2 - 9x -4x + 6)`

Factorize

`18x^2 - 39x + 18 = 3(3x(2x - 3) -2(2x - 3))`

Factor out 2x - 3

`18x^2 - 39x + 18 = 3(3x -2)(2x - 3)`

Solving (b): Verify the result

To do this, we simply multiply the terms of the polynomial

`3(3x -2)(2x - 3)`

`3(3x -2)(2x - 3) = (9x - 6)(2x - 3)`

Open brackets

`3(3x -2)(2x - 3) = 18x^2 - 27x - 12x + 18`

`3(3x -2)(2x - 3) = 18x^2 - 39x + 18`