Question

How do you factor $3{{x}^{2}}-15x$?

Answer 1

Hint: Find the factors of both the terms of the given expression separately. Then choose the greatest common factor from them. Take the greatest common factor out and leave the rest in multiplication form to obtain the required solution.

Complete step by step solution:
Factorization: A polynomial can be written as a product of two or more polynomials of degree less than or equal to that of it. Each polynomial involved in the product will be a factor of it. The process involved in breaking a polynomial into the product of its factors is known as the factorization of polynomials.
The expression we have $3{{x}^{2}}-15x$,
The factors of first term $3{{x}^{2}}=3\times x\times x$
The factors of first term $15x=3\times 5\times x$
So, the common factors of both the terms are $3\times x$
Hence, the greatest common factor of $3{{x}^{2}}$ and 15x is ‘3x’.
Taking the greatest common factor ‘3x’ out from the given expression, we get
$\Rightarrow 3x\left( x-5 \right)$
This is the required factorization of the given question.

Note: There is another method of factorization. First taking common ‘3’, we can apply the completing square method on the rest part i.e. $\left( {{x}^{2}}-5x \right)$. This can be done by applying the reverse of ${{\left( a+b \right)}^{2}}$ formula i.e. ${{\left( a \right)}^{2}}\pm 2\cdot a\cdot b+{{\left( b \right)}^{2}}$ and breaking the whole expression to two square terms. Then applying ${{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right)$ formula, we can get the required result.