The factors are (x-4) and x²+7
What is factorization?
'Factor' is a term used to express a number as a product of any two numbers. Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial or any algebraic expression. Thus, factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.
Factorization of Algebraic Expressions by Regrouping Terms
In some algebraic expressions, all the terms may not have a particular factor in common. Consider the algebraic expression 15x + y - xy - 15.
Step 1: Look for the terms with common factors. Only the first and last term has a common factor of 15. Similarly, the second and third term has a common factor y.
Step 2: Thus, the terms can be regrouped as 15x + y - xy - 15 = 15x - 15 + y - xy
Step 3: Take out common factors.15x - 15 - xy - y = 15(x -1) - y(x -1). Clearly, (a-1) is a common factor.
Step 4: Thus, the factorization of the given expression 15x - 15 - xy - y = (x -1) (15 -y)
Given:
x³ – 4x² + 7x – 28
Firstly,
(x-4) is a factor of x³ – 4x² + 7x – 28
Now, divide x³ – 4x² + 7x – 28 by (x-4) gives the quotient x²+7
Now factorize x²+7 gives x= ±√7i
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