Factorize : x4+x2+25.
x4+x2+25⇒(x2)2+(5)2+2x2×5−2x2×5+x2⇒(x2)2+(5)2+10x2−10x2+x2=(x2)2+(5)2+10x2−9x2=(x2+5)2−(3x)2{∵a2−b2=(a+b)(a−b)}=(x2+5−3x)(x2+5+3x)=(x2−3x+5)(x2+3x+5)
The factors of x4+x2+25 are
Factorize
i) x4 - y4 + x2 - y2
The factors of x4 + x2 + 25 are (a) (x2 + 3x + 5) (x2 − 3x + 5) (b) (x2 + 3x + 5) (x2 + 3x − 5) (c) (x2 + x +5) (x2 − x + 5) (d) none of these