Question

2√2x^2+9x+5√2 by splitting the middle term factor

Answer 1

$\textit{\large{\pink{\underline{\underline{Step by step Explanation:-}}}}}$

$\mathrm{2\sqrt{2}x^{2}+9x+5\sqrt{2}}$

$\mathrm{\implies{2\sqrt{2}x^{2}+4x+5x+5\sqrt{2}}}$

$\mathrm{\implies{2\sqrt{2}x(x+\sqrt{2})+5(x+\sqrt{2})}}$

$\mathrm{\implies{(x+\sqrt{2})(2\sqrt{2}x+5)}}$

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Answer 2

Factors of $\bf 2 \sqrt{2} {x}^{2} + 9x + 5 \sqrt{2}$ are $\bf \red{(2 \sqrt{2} x + 5)(x + \sqrt{2} )}$

Given:

• A quadratic polynomial
• $2 \sqrt{2} {x}^{2} + 9x + 5 \sqrt{2}$

To find:

Factorise the polynomial by splitting the middle term.

Solution:

The standard quadratic polynomial is written as

$\bf a {x}^{2} + bx + c \:$

where a≠0

Factors/split the b like that, multiplication of factors is equal to ac, and Sum/difference is equal to b.

Step 1:

Write coefficients of x², x and constant term.

a= 2√2

b=9

c=5√2

Step 2:

Split the middle term 9 as multiplication result to ac, ie 2√2(5√2)=10×2= 20

So,

9= 5+4

because 5×4= 20

Step 3:

Find the factors of polynomial.

$2 \sqrt{2} {x}^{2} + 4x + 5x + 5 \sqrt{2}$

or

$2 \sqrt{2} {x}^{2} + 2 \sqrt{2} \times \sqrt{2} x + 5x + 5 \sqrt{2}$

or

$2 \sqrt{2}x ( {x} + \sqrt{2} ) + 5(x + \sqrt{2} )$

or

$2 \sqrt{2} {x}^{2} + 9x + 5 \sqrt{2} = (2 \sqrt{2} x + 5)(x + \sqrt{2} )$

Thus,

Factors of quadratic polynomial is (2√2x+5)(x+√2).

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