Question

The factor of $3x\left( {x - 4} \right) - 5\left( {x - 4} \right)$ is/are:
A. $\left( {3x + 5} \right)$
B. $\left( {3x - 5} \right)$
C. $\left( {x + 4} \right)$
D. $\left( {x - 4} \right)$

Answer 1

Hint: Here, first equate the given polynomial to 0. Take the expression common which is in both the terms of the polynomial. The factors that we get after taking common are the factors of the equation. There can be more than one factor for the given polynomial.

Complete step by step Answer:

The factorization of a polynomial simplifies the expression and is used in many algebraic expressions.
Factorization is the method in which we change the expression from a sum or difference of terms to a product of terms.
And the terms whose product is equal to the given polynomial are known as factors.
We can factorise the given expression $3x\left( {x - 4} \right) - 5\left( {x - 4} \right)$ further by taking the common term out and writing it in multiplication of the left terms.
We can see that $x - 4$ is a common term in both the terms of the equation.
When we take $x - 4$ common from the first term, only $3x$ will be left and when we will take $x - 4$ common from the second term, we will be left with $ - 5$
Hence, when we will take $x - 4$ common from the terms and we will get,
$\left( {x - 4} \right)\left( {3x - 5} \right)$
Now, we have expressed the polynomial as the product of two terms which are $x - 4$ and $3x - 5$
Here, if we multiply the two factors, we will again get the same polynomial back.
Hence, we can say that the terms $x - 4$ and $3x - 5$ are factors of the equation.
Therefore, $\left( {x - 4} \right)$ and $\left( {3x - 5} \right)$ are factors of $3x\left( {x - 4} \right) - 5\left( {x - 4} \right)$
Hence, options B and D are correct.

Note: When factors are multiplied with each other, they give back the same polynomial. If we have one of the factors of the polynomial, other factors can also be calculated by dividing the given polynomial with one of the factors and the quotient will give us the other factor of the polynomial.