Question

How do you factor \[{x^2} - 9x - 10\]?

Answer 1

Hint: Quadratic factorization using splitting of middle term: In this method splitting of middle term into two factors.
Quadratic Factorization using Splitting of Middle Term which is \[x\] term is the sum of two factors and product equal to last term.
First, we will factor 10. So, we can write \[10 = 10 \times 1\]
Since, there is a subtraction sign in front of 10, we will use the factors of 10 and the subtraction sign to make as 9.

Complete step by step answer:
It is given that; \[{x^2} - 9x - 10\]
We have to factorize the term.
We will apply a middle term method.
First, we will factor 10. So, we can write \[10 = 10 \times 1\]
Since, there is a subtraction sign in front of 10, we will use the factors of 10 and the subtraction sign to make as 9.
So, we have,
\[ \Rightarrow {x^2} - 9x - 10\]
Simplifying we have,
\[ \Rightarrow {x^2} - (10 - 1)x - 10\]
Simplifying again we have,
\[ \Rightarrow {x^2} - 10x + x - 10\]
Now, we will take the common terms.
\[ \Rightarrow x(x - 10) - 1(x - 10)\]
Simplifying we have,
\[ \Rightarrow (x - 10)(x - 1)\]

Hence, the factors of \[{x^2} - 9x - 10\]is \[(x - 10)(x - 1)\]

Note: Quadratic Factorization using Splitting of Middle Term which is \[x\] term is the sum of two factors and product equal to last term.
To factor the form \[a{x^2} + bx + c\]
Find the product of 1st and last terms \[a \times c\]
Write the centre term using the sum of the two new factors including the proper signs.
Group the terms to form pairs – the first two terms and the last two terms.
Factor each pair by finding common factors.
Factor out the shared binomial parenthesis.