Exercise 2.7 - Chapter 2 Basic Algebra 11th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Ex 2.7
Question 1.
Factorize: $\mathrm{x}^4+1$. (Hint: Try completing the square.)
Solution:
$
\begin{aligned}
x^4+1 & =x^4+1+2 x^2-2 x^2 \\
& =\left(x^2+1\right)^2-(\sqrt{2} x)^2 \\
& =\left(x^2+1-\sqrt{2} x\right)\left(x^2+1+\sqrt{2} x\right)
\end{aligned}
$
Question 2.
If $x^2+x+1$ is a factor of the polynomial $3 x^3+8 x^2+8 x+a$, then find the value of a.

Solution:
Let $3 x^3+8 x^2+8 x+a=\left(x^2+x+1\right)(3 x+a)$
Equating coefficient of $x$
$
\begin{aligned}
& 8=a+3 \\
& 8-3=a \\
& a=5
\end{aligned}
$