Answer:
Step-by-step 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]
