Question

How do you factor \[9 + 3y\]?

Answer 1

Hint: In this question we have to factor the given polynomial, this can be done by factoring the polynomial by taking out the common term, first write each term in the algebraic expression as a product of irreducible factors, and then take out the common factors and the rest of the expression is the required result.

Complete step by step solution:
The given expression is a polynomial which are algebraic expressions that are composed of two or more algebraic terms, the algebraic terms are constant, variables and exponents, there are different types of polynomials which are differentiated with the help of degree of the polynomial.
The polynomial of degree 1 is known as cubic polynomial. The given polynomial is a linear polynomial.
Given algebraic expression is \[9 + 3y\],
Now write each term as a product of factors,
1st term is 9 and so the factors of 9 are \[1 \times 3 \times 3\], and the factors for the 2nd term which is \[3y\]are \[1 \times 3 \times y\],
So, the given expression can be written as,
\[ \Rightarrow \left( {3 \times 3 + 3 \times y} \right)\],
Now taking out the common factor from the expression, we get,
\[ \Rightarrow 3\left( {3 + y} \right)\],
So, the factored form is \[3\left( {3 + y} \right)\].

Final Answer:
\[\therefore \]The factored form of the given algebraic expression \[9 + 3y\] will be equal to \[3\left( {3 + y} \right)\].

Note:
Factorization is a process which is necessary to simplify the algebraic expressions and is used to solve the higher degree equations. It is the inverse procedure of the multiplication of the polynomials. The algebraic expression is said to be in a factored form only when the whole expression is an indicated product. Factorisation of the algebraic expression can be also be done in another methods such as, factoring by grouping and factoring using identities and the commonly used identities are as follows,
\[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\],
\[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\],
\[\left( {a + b} \right)\left( {a - b} \right) = {a^2} - {b^2}\],
\[{a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\],
\[{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)\].