Question

factorise √3x^2+10x+8√3

Answer 1

$\sqrt{3} x {}^{2} + 10x + 8 \sqrt{3}$

$\sqrt{3} x {}^{2} + 6x + 4x + 8 \sqrt{3}$

$\sqrt{3} x(x + 2 \sqrt{3} ) + 4(x + 2 \sqrt{3} )$

$( \sqrt{3} x + 4)(x + 2 \sqrt{3} )$


Thanks

Answer 2

Concept:

Factorization is the method of breaking down a number or expression into its numbers and when we multiply those factors we get the original number or expression.

Given:

√3x² + 10x + 8√3

Find:

We are asked to factorize the given expression.

Solution:

We have,

√3x² + 10x + 8√3,

NOw,

To find the factor,

Use the middle-term splitting method,

i.e.

The factors of Product of coefficient of x² and the constant term should give the middle term i.e. 10x,

So,

NOw,

√3x² + 10x + 8√3

= √3x² + 12x - 2x + 8√3

Now,

Taking common,

i.e.

= √3x² + 12x - 2x + 8√3

= √3x(x + 4√3) - 2(x + 4√3)

NOw,

Again, Taking common,

i.e.

= (x + 4√3) (√3x - 2)

Hence, the factors of the given expression √3x² + 10x + 8√3 are  (x + 4√3) (√3x - 2).

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