Question

Please help Factor completely. Show your work (as much work as possible, including a ​list of factors if

needed) to receive full credit.

Answer 1

Explanation:

Using cross method

7.
`8x^2-6x-9\\`

4x 3

2x - 3

= (4x+3)(2x-3)

8.
`4x^2y-24xy+32\\`

= xy(4x-24+32)

= 4xy (x-4+8)

Answer 2

Explanation:

7) The given quadratic equation is expressed as

8x² - 6x - 9

We would apply completing the square method. We would equate it to zero and add 9 to the left hand side and the right hand side of the equation. It becomes

8x² - 6x = 9

Dividing the left hand side and the right hand side of the equation by 8, it becomes

x² - 6x/8 = 9/8

Adding square of half the coefficient of x to the left hand side and the right hand side of the equation, it becomes

x² - 6x/8 + (- 3/8)² = 9/8 + (- 3/8)²

(x - 3/8)² = 9/8 + 9/64

(x - 3/8)² = 81/64

Taking square root of the left hand side and the right hand side of the equation, it becomes

x - 3/8 = ±9/8

x = 3/8 ± 9/8

x = 3/8 + 9/8 or 3/8 - 9/8

x = 12/8 or x = - 6/8

x = 3/2 or x = - 3/4

The factors are

(x - 3/2)(x + 3/4)

8) 4x²y - 24xy + 32

4 is a common factor to all the terms, so

4[x²y - 6xy + 8]

Factorizing further, it becomes

4[xy(x - 6) + 8]