Question

factorization : x²+6√6x+48​

Answer 1

Answer:

$\large\boxed{\sf{(x + 2 \sqrt{6} )(x + 4 \sqrt{6} )}}$

Step-by-step explanation:

Given an expression such that,

${x}^{2} + 6 \sqrt{6} x + 48$

To factorise it,

By middle term splitting method, we will factorise this expression.

Now, splitting the middle term, we get,

$= {x}^{2} + 2 \sqrt{6} x + 4 \sqrt{6} x + 48$

Now, taking out the common terms, we get,

$= x(x + 2 \sqrt{6} ) + 4 \sqrt{6} (x + 2 \sqrt{6} ) \\ \\ = (x + 2 \sqrt{6} )(x + 4 \sqrt{6} )$

Hence, the required factors are (x+2√6)(x+4√6)

Answer 2

★ Answer :

→ x² + 6√6x + 48 = 0

Making factors

→ x² + 2√6x + 4√6x + 48 = 0

We can write 48 as (4√6) * (2√6)

→ x² + 2√6x + 4√6x + 4√6(2√6) = 0

→ x(x + 2√6) + 4√6(x + 2√6) = 0

→ (x + 2√6)(x + 4√6) = 0

→ x + 2√6 = 0

→ x = -2√6

Or

→ x + 4√6 = 0

→ x = -4√6

$\rule{200}{2}$

For factorising we have to follow these given below steps :

Let polynomial be ax² + bx + c = 0

• Firstly we will multiply a and c.
• Then we will make the factors of their product.
• The factors must be equal to b on adding or subtracting.
• Then, we will take common.