Introduction to factoring:
In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Factorization (also factorization in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.
Example Problems for Factoring Fractional Exponents
Factoring fractional exponents example problem 1:
Factoring the given fractional expression `(1 / 3)` x^2 - `(11 / 3)` x - 144 = 0
Solution:
Given fractional expression is `(1 / 3)` x^2 - `(11 / 3)` x - 144 = 0
Multiply the given expression by 3 on both the sides, we get
x^2 - 11x - 432 = 0
Factorize the above equation, we get
x^2 - 27x + 16x - 432 = 0
Grouping the first two terms and second terms, we get
(x^2 - 27x) + (16x - 432) = 0
Take common terms, we get
x (x - 27) + 16 (x - 27) = 0
(x - 27) (x + 16) = 0
The factors of the given fractional expression is (x - 27) and (x + 16)
Answer:
The final answer is (x - 27) and (x + 16)
Factoring fractional exponents example problem 2:
Factoring the given fractional expression `(1 / 5)` x^2 - `(27 / 5)` x - 74 = 0
Solution:
Given fractional expression is `(1 / 5)` x^2 - `(27 / 5)`x - 74 = 0
Multiply the given expression by 5 on both the sides, we get
x^2 - 27x - 370 = 0
Factorize the above equation, we get
x^2 - 37x + 10x - 370 = 0
Grouping the first two terms and second terms, we get
(x^2 - 37x) + (10x - 370) = 0
Take common terms, we get
x (x - 37) + 10 (x - 37) = 0
(x - 37) (x + 10) = 0
The factors of the given fractional expression is (x - 37) and (x + 10)
Answer:
The final answer is (x - 37) and (x + 10)
Factoring fractional exponents example problem 3:
Factoring the given fractional expression `(1 / 7)`x^2 - `(12 / 7)`x + 5 = 0
Solution:
Given fractional expression is `(1 / 7)`x^2 - `(12 / 7)`x + 5 = 0
Multiply the given expression by 7 on both the sides, we get
x^2 - 12x + 35 = 0
Factorize the above equation, we get
x^2 - 7x - 5x + 35 = 0
Grouping the first two terms and second terms, we get
(x^2 - 7x) - (5x - 35) = 0
Take common terms, we get
x (x - 7) - 5 (x - 7) = 0
(x - 7) (x - 5) = 0
The factors of the given fractional expression is (x - 7) and (x - 5)
Answer:
The final answer is (x - 7) and (x - 5)
Between, if you have problem on these topics middle school math word problems, please browse expert math related websites for more help on easy math word problems.
Practice Problems for Factoring Fractional Exponents
Factoring fractional exponents practice problem 1:
Factoring the given fractional expression `(1 / 24)`x^2 + `(23 / 24)`x - 12 = 0
Answer:
The final answer is (x + 32) and (x - 9)
Factoring fractional exponents practice problem 2:
Factoring the given fractional expression `(10 / 7)`x^2 - `(59 / 7)`x + 7 = 0
Answer:
The final answer is (10x - 49) and (10x - 10)
In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Factorization (also factorization in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.
Example Problems for Factoring Fractional Exponents
Factoring fractional exponents example problem 1:
Factoring the given fractional expression `(1 / 3)` x^2 - `(11 / 3)` x - 144 = 0
Solution:
Given fractional expression is `(1 / 3)` x^2 - `(11 / 3)` x - 144 = 0
Multiply the given expression by 3 on both the sides, we get
x^2 - 11x - 432 = 0
Factorize the above equation, we get
x^2 - 27x + 16x - 432 = 0
Grouping the first two terms and second terms, we get
(x^2 - 27x) + (16x - 432) = 0
Take common terms, we get
x (x - 27) + 16 (x - 27) = 0
(x - 27) (x + 16) = 0
The factors of the given fractional expression is (x - 27) and (x + 16)
Answer:
The final answer is (x - 27) and (x + 16)
Factoring fractional exponents example problem 2:
Factoring the given fractional expression `(1 / 5)` x^2 - `(27 / 5)` x - 74 = 0
Solution:
Given fractional expression is `(1 / 5)` x^2 - `(27 / 5)`x - 74 = 0
Multiply the given expression by 5 on both the sides, we get
x^2 - 27x - 370 = 0
Factorize the above equation, we get
x^2 - 37x + 10x - 370 = 0
Grouping the first two terms and second terms, we get
(x^2 - 37x) + (10x - 370) = 0
Take common terms, we get
x (x - 37) + 10 (x - 37) = 0
(x - 37) (x + 10) = 0
The factors of the given fractional expression is (x - 37) and (x + 10)
Answer:
The final answer is (x - 37) and (x + 10)
Factoring fractional exponents example problem 3:
Factoring the given fractional expression `(1 / 7)`x^2 - `(12 / 7)`x + 5 = 0
Solution:
Given fractional expression is `(1 / 7)`x^2 - `(12 / 7)`x + 5 = 0
Multiply the given expression by 7 on both the sides, we get
x^2 - 12x + 35 = 0
Factorize the above equation, we get
x^2 - 7x - 5x + 35 = 0
Grouping the first two terms and second terms, we get
(x^2 - 7x) - (5x - 35) = 0
Take common terms, we get
x (x - 7) - 5 (x - 7) = 0
(x - 7) (x - 5) = 0
The factors of the given fractional expression is (x - 7) and (x - 5)
Answer:
The final answer is (x - 7) and (x - 5)
Between, if you have problem on these topics middle school math word problems, please browse expert math related websites for more help on easy math word problems.
Practice Problems for Factoring Fractional Exponents
Factoring fractional exponents practice problem 1:
Factoring the given fractional expression `(1 / 24)`x^2 + `(23 / 24)`x - 12 = 0
Answer:
The final answer is (x + 32) and (x - 9)
Factoring fractional exponents practice problem 2:
Factoring the given fractional expression `(10 / 7)`x^2 - `(59 / 7)`x + 7 = 0
Answer:
The final answer is (10x - 49) and (10x - 10)
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