Without actually calculating the cubes, find the value of each of the following:
(i) (–12)3 + (7)3 + (5)3
(ii) (28)3 + (–15)3 + (–13)3
Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5 (ii) p(x) = x – 5 (iii) p(x) = 2x + 5 (iv) p(x) = 3x – 2 (v) p(x) = 3x
(vi) p(x) = ax, a ≠ 0 (vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.
Classify the following as linear, quadratic and cubic polynomials:
(i) x 2 + x (ii) x – x 3 (iii) y + y 2 + 4 (iv) 1 + x (v) 3t (vi) r 2 (vii) 7x 3
Write the degree of each of the following polynomials:
(i) 5x 3 + 4x 2 + 7x (ii) 4 – y 2 (iii) 5t – √7 (iv) 3.
Express the following in the form \(\frac{p }{ q}\) , where p and q are integers and q ≠ 0.
(i) 0.6(ii) 0.47 (iii) 0.001.
Find: (i) 9 \(\frac{3}{2}\) (ii) 32 \(\frac{2}{5}\) (iii) 16 \(\frac{3}{4}\) (iv) 125 -\(\frac{1}{3}\)
Rationalise the denominators of the following:
(i) \(\frac{1 }{ \sqrt{7 }}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)