Question

What is the factorisation of a quadratic polynomial?

Answer 1

Hint: In this problem, we can see about the factorization of a quadratic polynomial. We should know that in a quadratic equation, a polynomial that has a degree 2 is called a quadratic polynomial, which is also known as second-order polynomial. Here we can see how to factorize the quadratic polynomial with an example.

Complete step-by-step solution:
Here we can see about the factorization of a quadratic polynomial.
We know that in a quadratic equation, a polynomial that has a degree 2 is called a quadratic polynomial, which is also known as second-order polynomial.
We should also know that quadratic polynomial factorization is the reverse of multiplication, that is the separation of the given quadratic polynomials into two separate factors, which in turn multiplication gives the same equation itself.
We can now factor an example quadratic polynomial \[{{x}^{2}}-2x-15\].
We can now factorize the above quadratic polynomial.
We can write the above equation as,
\[\Rightarrow {{x}^{2}}+3x-5x-15\]
We can now separate the first two terms and last two terms, we get
\[\Rightarrow \left( {{x}^{2}}+3x \right)-\left( 5x+15 \right)\]
We can now take the common terms, we get
\[\Rightarrow x\left( x+3 \right)-5\left( x+3 \right)\]
We can now write it as,
 \[\Rightarrow \left( x+3 \right)\left( x-5 \right)\]
Therefore, the factorization of a quadratic polynomial is the separation of the equation into factors.

Note: We should remember the steps to factorize the given equation. We can separate the middle term as it should be the addition/subtraction which is equal to the middle term itself and the multiplication of the new middle terms should be equal to the constant term.