Question

The factors of x⁴+x²=25 are
A. (x²+3x+5)(x²3x+5)
B. (x²+3x+5)(x²+3x-5)
C. (x²+x+5)(x²-x+5)
D. none of these

Answer 1

Given :  x⁴ + x² + 25 [Mistake in the question]

Adding and subtracting 9x² in the given equation.

= x⁴ + 25 + x² + 9x² - 9x²

= x⁴ + 25 + 10x² - 9x²

= (x²)² + 5² + 2 × x² × 5 - (3x)²

[By Using Identity : a² + b² + 2ab = (a + b)² ]

= (x + 5)² - (3x)²

= (x + 5 + 3x) (x + 5 - 3x)

[By Using Identity : (a + b)(a – b) = a² - b²]

Hence the factors of x⁴ + x² + 25 is (x + 5 + 3x) (x + 5 - 3x).

Among the given options option (A) (x² + 3x + 5)(x² - 3x + 5) is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

Some questions of this chapter :

The factors of a²-1-2x-x² are

A. (a-x+1)(a-x-1)

B. (a+x-1)(a-x+1)

C. (a+x+1)(a-x-1)

D. none of these

https://brainly.in/question/15902777

The factors of x³-x²y-xy²+y³ are

A. (x+y)(x²-xy+y²)

B. (x+y)(x²+xy+y²)

C. (x+y)²(x-y)

D. (x-y)²(x+y)

https://brainly.in/question/15902779

Answer 2

$\sf \orange{ \huge{Answer}}$

$\sf \pink{ = (x4 + 10 \times 2 + 25) - 9 \times 2}$

$\bf \red{ = (x2 + 5 {)}^{2} - 9 \times 2}$

$\bf \green{(x2 + 5 - 3 x)(x2 + 5 + 3x}$

Answer : - A. (x²+3x+5)(x²3x+5)