Step-by-step explanation:
Equation at the end of step 1
(3x2 - 38x) + 24 = 0
STEP2:Trying to factor by splitting the middle term
2.1 Factoring 3x2-38x+24
The first term is, 3x2 its coefficient is 3 .
The middle term is, -38x its coefficient is -38 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 3 • 24 = 72
Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is -38 .
-72 + -1 = -73 -36 + -2 = -38 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -2
3x2 - 36x - 2x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (x-12)
Add up the last 2 terms, pulling out common factors :
2 • (x-12)
Step-5 : Add up the four terms of step 4 :
(3x-2) • (x-12)
Which is the desired factorization
Equation at the end of step2:
(x - 12) • (3x - 2) = 0
STEP3:Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
3.2 Solve : x-12 = 0
Add 12 to both sides of the equation :
x = 12
Solving a Single Variable Equation:
Step-by-step explanation:
[tex]if \: (x + 12) = (3x + 2) \\ 12 - 2 = 3x - x \\ 2x = 10 \\ x = 5 \\ \\ \\ if(x + 12)(3x + 2) = 0 \\ x + 12 = 0 \: \: \: or \: \: \: 3x + 2 = 0 \\ x = - 12 \: \: \: or \: \: \: x = - \frac{2}{3} [/tex]
