Question

4. The factors of x8 - x4 - 30 are-
x – x৭ – 30 ৰ উৎপাদক-
(a) (x4 - 6) and (717) (x - 5)
(b) (x4-6) and (75) (x + 5)
(c) (x4 + 6) and (TTC) (x - 5)
(d) (x4 + 6) and (717) (x + 5)​

Answer 1

Question :

The factors of x⁸ - x⁴ - 30 are :

Solution :

x⁸ - x⁴ - 30

> x⁸ - (6 - 5) x⁴ - 30

> x⁸ - 6x⁴ + 5x⁴ - 30

> x⁴( x⁴ - 6) + 5( x⁴ - 6)

> ( x⁴ + 5)(x⁴ -6)

The given options are wrong or there is a typing error.

Answer - The factors are (x⁴ + 5) and ( x⁴ - 6) .

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Additional Information -

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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Answer 2

Question :

⠀⠀⠀⠀⠀▪︎⠀⠀The Factors of x⁸ - x⁴ - 30 are :

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\dag \:\:\large\underline { \underline {\pink{\sf Required \; AnswEr \:\:-\: }}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Factors of x⁸ - x⁴ - 30 :

$\qquad \dashrightarrow \sf x^8 - x^4 - 30 \:\\\\\qquad \dashrightarrow \sf x^8 - 6x^4 + 5x^4 - 30 \:\\\\\qquad \dashrightarrow \sf x^4\Big\{ x^4 - 6 \Big\} + 5 \Big\{ x^4 - 6 \:\Big\} \:\\\\\qquad \dashrightarrow \sf \Big\{ x^4 + 5 \Big\} \Big\{ x^4 - 6 \:\Big\} \:\\\\\qquad \dashrightarrow \underline {\boxed{{\frak{\purple { \Big\{ x^4 + 5 \Big\} \Big\{ x^4 - 6 \:\Big\} }}}}}\:$

$\qquad \therefore \underline {\sf Hence, \:Factors \:of \: x^8 - x^4 - 30 \:are \:{\bf \Big\{ x^4 + 5 \Big\} \Big\{ x^4 - 6 \:\Big\}}\:.\:}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\qquad \qquad \underline {\bigstar\pmb{\mathbb{ ADDITIONAL \:\:INFORMATION \::\:}}}\:$

$\dag \:\:\underline { \underline {\purple{\sf Algebraic \; Indentity \:\:-\: }}}$

$\qquad \sf ( I ) \:\:( a + b)^2 =\:a^2 + b^2 + 2ab \:$

$\qquad \sf ( II ) \:\:( a - b)^2 =\:a^2 + b^2 - 2ab \:$

$\qquad \sf ( III ) \:\: a^2 - b^2 =\:( a + b ) ( a - b ) \:$

$\qquad \sf ( IV ) \:\:( x + b ) ( x + b ) \:=\:x^2 + ( a + b ) x + ab \:$

$\qquad \sf ( V ) \:\: ( a + b + c )^2\:=\: a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \: \:$

$\qquad \sf ( VI ) \:\: ( a + b )^3\:=\: a^3 + b^3 + 3ab ( a + b ) \: \:$

$\qquad \sf ( VII ) \:\: ( a - b )^3\:=\: a^3 - b^3 - 3ab ( a - b ) \: \:$

$\qquad \sf ( VIII ) \:\: a^3 + b^3 + c^3 - 3abc\:=\: ( a + b + c ) \: ( a^2 + b^2 + c^2 - ab - bc - ca ) \: \:$