Solution:

Let, \(p(x) = x^{2} - 5x + 5\)
∴ \(p(0) = (0)^{2} - 5(0) + 5\)
∴ \(p(0) = 0 - 0 + 5\)
∴ \(p(0) = 5\)

Solution:

 \(p(y) = y^{2} - 3\sqrt {2}y + 1\)

∴ \(p(3\sqrt{2}) = (3\sqrt{2})^{2} - 3\sqrt{2}(3\sqrt{2}) + 1\)

∴ \(p(3\sqrt{2}) = (9 \times 2) - (9 \times 2) + 1\)

∴ \(p(3\sqrt{2}) = \cancel{18} - \cancel{18} + 1\)

∴ \(p(3\sqrt{2}) = 1\)

Solution:

Given, \(p(m) = m^{3} + 2m^{2} - m + 10\)

To find \(p(a)\), substitute \(m = a\) in the given polynomial.
∴ \(p(a) = a^{3} + 2a^{2} - a + 10\)   …(1)

To find \(p(-a)\), substitute \(m = -a\) in the given polynomial.
∴ \(p(-a) = (-a)^{3} + 2(-a)^{2} - (-a) + 10\)
∴ \(p(-a) = -a^{3} + 2a^{2} + a + 10\)   …(2)

Adding (1) and (2),
\(p(a) + p(-a) = (a^{3} + 2a^{2} - a + 10) + (-a^{3} + 2a^{2} + a + 10)\)
\(p(a) + p(-a) = \cancel{a^{3}} \bbox[yellow, 5pt, border: 2px dotted red]{+ 2a^{2}} - \cancel{a} \bbox[pink, 5pt, border: 2px dotted red]{+ 10} - \cancel{a^{3}} \bbox[yellow, 5pt, border: 2px dotted red]{+ 2a^{2}} + \cancel{a} \bbox[pink, 5pt, border: 2px dotted red]{+ 10}\)
\(p(a) + p(-a) = 4a^{2} + 20\)

Solution:

 \(p(y) = 2y^{3} - 6y^{2} - 5y + 7\)
∴ \(p(2) = 2 \times 2^{3} - 6 \times 2^{2} - 5 \times 2 + 7\)
∴ \(p(2) = 2 \times 8 - 6 \times 4 - 10 + 7\)
∴ \(p(2) = 16 - 24 - 10 + 7\)
∴ \(p(2) = - 11\)