we know that
A quadratic equation is a polynomial with an order of two. Its general form is
[tex] ax^{2} + bx + c = 0 [/tex]
case a) [tex] 6(x + 2)^{2} + 8x + 2 + 1 = 0 [/tex]
[tex] 6(x + 2)^{2} + 8x + 2 + 1 = 0 \\ 6(x^{2} +4x+4)+8x+3=0\\ 6x^{2} +24x+24+8x+3=0\\ 6x^{2} +32x+27=0\\\\ a=6\\ b=32\\ c=27 [/tex]
The case a) is a quadratic equation
case b) [tex] 6x^{4} + 7x^{2} - 3 = 0 [/tex]
The case b) is a grade [tex] 4 [/tex] polynomial
case c) [tex] 5x^{6} + x^{4} + 12 = 0 [/tex]
The case c) is a grade [tex] 6 [/tex] polynomial
case d) [tex] x^{9} + x^{3} - 10 = 0 [/tex]
The case d) is a grade [tex] 9 [/tex] polynomial
therefore
the answer is
[tex] 6(x + 2)^{2} + 8x + 2 + 1 = 0 [/tex]
