Question

Factorise \[x^{2} – 4x – 32\]

Answer 1

Hint: In this question, we need to factorise the given polynomial. Given expression is \[x^{2} – 4x – 32\] . Here we need to factorise the given expression and need to find the factors of the polynomial. Factorization is nothing but writing a whole number into smaller numbers of the same kind. By taking the common terms outside,we can factorize the given expression. We can also factorise the given polynomial by using quadratic formula.

Complete answer:
 Given, \[x^{2} – 4x – 32\]
Let us consider the given expression as \[f(x)\]
Thus, \[f\left( x \right) = \ x^{2} – 4x – 32\]
This can be factored by splitting the middle term of the expression.
By using sum-product pattern, we can write the middle term \[- 4x\] as \[4x – 8x\]
Thus , \[f\left( x \right) = \ x^{2} + 4x – 8x – 32\]
Now we need to take the common terms outside.
We can take \[x\] outside from the first two terms and \[- 8\ \] as common from the next two terms.
⇒ \[\ f(x)\ = x(x + 4)\ - 8(x + 4)\]
Here \[(x+4)\] is common,
Thus we get,
\[f(x) \ =(x+4) (x-8)\]
Thus the factors of \[x^{2} – 4x – 32\] are \[\left( x + 4 \right)\] and \[\left( x – 8 \right)\]
Final answer :
The factors of \[x^{2} – 4x – 32\] are \[(x + 4)\] and \[(x – 8)\].

Note:
In other words, factorization is known as the decomposition of the mathematical objects to the product of smaller objects. Matrices also possess the process of factorization.There are five methods in factorization. We can reduce any algebraic expressions into smaller objects where the equations are represented as the product of factors.