The factors of the expression is 3x²(x+5)(x+5) .
Factors of a number are defined as the numbers which divide the given number completely.
For an algebraic expression the factors of the expression are smaller polynomials which divide the given expression completely.
Factors of algebraic expression can be calculated by the following methods:
The given polynomial is of the form:
3x⁴ + 30x³ + 75x²
Taking 3x² common from all the terms we get:
3x² (x² + 10x + 25)
Now we use middle- term factorization method to factor (x² + 10x + 25)
3x² (x² + 5x + 5x + 25)
or, ( 3x² ){x ( x + 5 ) + 5 ( x + 5 )}
or, 3x² (x + 5) (x + 5)
or, 3x² (x + 5)²
Hence the factors of the expressions are: 3x² (x + 5)²
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Factor completely: 3x⁴ + 30x³ + 75x²
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