what are the step in changing this equation to factored form?
y= 1/3 x^2 - 7/3x = 8/3
Y = x^2- 7x - 8 = 0x^2/3 - 7x/3 = 8/3.
Multiply both sides by 3:
x^2 - 7x - 8 0
C = -8 = 1*(-8) = 2*(-4).
Choose the pair of factors whose sum=-7
Y = (x-8)(x+1) = 0.
Correction:
Y = x^2/3- 7x/3 = 8/3
Multiply both sides by 3:
x^2 - 7x = 8
x^2 - 7x - 8 = 0
C = 8 = 1*(-8) = 2*(-4).
Choose the pair of factors whose sum=-7.
Y = (X-8)(X+1) = 0.
To change the given equation into factored form, you need to follow these steps:
Step 1: Set the equation to zero by subtracting all the terms from both sides:
1/3 x^2 - 7/3x - 8/3 = 0
Step 2: Multiply the entire equation by 3 to eliminate the fractions:
x^2 - 7x - 8 = 0
Step 3: Split the middle term (-7x) into two terms whose coefficients multiply to give the product of the coefficients of the x^2 term (1) and the constant term (-8). In this case, the two terms are -8x and x since (-8) * (1) = -8 and (-8) + (1) = -7:
x^2 - 8x + x - 8 = 0
Step 4: Group the terms and factor by grouping:
(x^2 - 8x) + (x - 8) = 0
x(x - 8) + 1(x - 8) = 0
(x + 1)(x - 8) = 0
Thus, the factored form of the equation y = (1/3)x^2 - (7/3)x - (8/3) is (x + 1)(x - 8) = 0.