Question

Factories
$5 \sqrt{5} {x}^{2} + 30x + 8 \sqrt{5}$
$8 {x}^{2} - 22x - 21$
fast please best answer brainliest​

Answer 1

Topic :-

• Factorisation

Given :-

• 5√5x² + 30x + 8√5
• 8x² - 22x - 21

To Find :-

Factors of given polynomials.

Solution :-

5√5x² + 30x + 8√5

Splitting 30x into 20x and 10x,

5√5x² + 20x + 10x + 8√5

Taking 5x as common from few terms,

5x(√5x + 4) + 10x + 8√5

Taking 2√5 as common from few terms,

5x(√5x + 4) + 2√5(√5x + 4)

Taking (√5x + 4) common,

(√5x + 4)(5x + 2√5)

Taking √5 as common from (5x + 2√5),

(√5)(√5x + 4)(√5x + 2)

----------------------------------------------

8x² - 22x - 21

Splitting -22x into -28x and 6x,

8x² - 28x + 6x - 21

Taking 4x as common from few terms,

4x(2x - 7) + 6x - 21

Taking 3 as common from few terms,

4x(2x - 7) + 3(2x - 7)

Taking (2x - 7) common,

(2x - 7)(4x + 3)

Answer :-

Respective factors of given polynomials are

• √5(√5x + 4)(√5x + 2)
• (2x - 7)(4x + 3)

Identities to Learn :-

a² + 2ab + b² = (a + b)²

a² - 2ab + b² = (a - b)²

a³ - b³ = (a - b)(a² + ab + b²)

a³ + b³ = (a + b)(a² - ab + b²)

a² - b² = (a + b)(a - b)

a⁴ + a² + 1 = (a² + 1 + a)(a² + 1 - a)