Question

Factorize:
\[ax + bx = ?\]
\[3x.2 + 6x.6 = ?\]

Answer 1

Hint: Factorization of a polynomial consists of writing the polynomial as a product of two or more polynomials which have a degree smaller than the given polynomial or equal to the given polynomial. To factorize the given question, we will first take out the common term from them and then write them in the product form.

Complete step by step answer:
We have the first expression as;
\[ax + bx\]
We can see that \[x\]is common in both the terms. So, we will take \[x\] as common. So, we get;
\[ \Rightarrow ax + bx = x\left( {a + b} \right)\]
We can see that \[ax + bx\], is written as a product of two numbers. Hence, the factors of \[ax + bx\] are \[x,\left( {a + b} \right)\]. This means that if we divide \[ax + bx\] by any of \[x,\left( {a + b} \right)\], we will get zero as the remainder.
The second question is:
\[3x \times 2 + 6x \times 6\]
On multiplication it becomes;
\[ = 6x + 36x\]
Simply adding we get;
\[ = 42x\]
Hence, the factors are \[42{\text{ and }}x\].

Note:
One thing to note is that if a polynomial expression after factorization is expressed as a product of two expressions, then, if we divide the polynomial by one of them then the other will be the quotient and the remainder will be zero. For example, in the question above \[ax + bx = x\left( {a + b} \right)\], so if we divide \[ax + bx\] by \[x\], we get \[\left( {a + b} \right)\] as the quotient and vice-versa.