Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 2 Basic Algebra Ex 2.7 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.7

Question 1.

Factorize x^{4} + 1

Answer:

The given equation is x^{4} + 1

x^{4} + 1 = (x^{2})^{2} + 1^{2}

= (x^{2} + 1)^{2} – 2 (x^{2}) (1)

[ a^{2} + b^{2} = (a + b)^{2} – 2ab]

= (x^{2} + 1)^{2} – (√2x)^{2}

= (x^{2} + 1 + √2x) (x^{2} + 1 – √2x)

x^{4} + 1 = (x^{2} + 2x + 1) (x^{2} – √2x + 1)

Question 2.

If x^{4} + x + 1 is a factor of the polynomial 3x^{3} + 8x^{2} + 8x + a, then find the value of a.

Answer:

Given that x^{2} + x + 1 is a factor of the polynomial 3x^{3} + 8x^{2} + 8x + a.

∴ 3x^{3} + 8x^{2} + 8x + a is divisible by x^{2} + x + 1

Since 3x^{3} + 8x^{2} + 8x + a is divisible by x^{2} + x + 1, the remainder must be zero.

a – 5 = 0

⇒ a = 5