problem archive
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Give one example each of a binomial of degree 35, and of a monomial of degree 100. -
Write the degree of each of the following polynomials: (i) 5x^4 + 4x^3 + 7x (ii) 4 - y^2 (iii) 5t - \sqrt{7} (iv) 3 -
Classify the following as linear, quadratic and cubic polynomials: (i) x^3 + x (ii) x - x^3 (iii) y + y^2 + 4 (iv) 1 + x (v) 3t (vi) r^4 (vii) 7u^3 -
Check whether -2 and 2 are zeroes of the polynomial x + 2. -
Find a zero of the polynomial p(x) = 2x + 1. -
Verify whether 2 and 0 are zeroes of the polynomial x^2 - 2x. -
Find the value of the polynomial 5x - 4x^2 + 3 at x = 0, x = -1, x = 2. -
Find p(0), p(1) and p(2) for each of the following polynomials: (i) p(x) = y^3 - y + 1, (ii) p(x) = 2 + t + 2t^2 - t^3, (iii) p(x) = x^3, (iv) p(x) = ... -
Verify whether the following are zeroes of the polynomial, indicated against them.(i) p(x) = 3x + 1, x = -1/3(ii) p(x) = 5x - π, x = -4/5(iii) p(x)... -
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) = 3... -
Find the value of k if x - 1 is a factor of 4x^3 + 3x^2 - 4x + k. -
Factorise 6x^2 + 17x + 5 by splitting the middle term, and by using the Factor Theorem. -
Factorise y^2 - 5y + 6 by using the Factor Theorem. -
Factorise \( x^3 - 23x^2 + 142x - 120 \) -
Determine which of the following polynomials has \((x+1)\) a factor: (i) \( x^3 + x^2 + x + 1 \) (ii) \( x^4 + x^3 + x^2 + x + 1 \) (iii) \( x^4 + 3x^... -
Use the Factor Theorem to determine whether \( g(x) \) is a factor of \( p(x) \) in each of the following cases: (i) \( p(x) = 2x^3 + x^2 - 2x - 1, g(... -
Find the value of k, if x - 1 is a factor of p(x) in each of the following cases: (i) p(x) = x^3 + x + k (ii) p(x) = 2x^3 + kx + √2 (iii) p(x) = kx^3 ... -
Factorise: (i) 12x^2 - 7x + 1 (ii) 2x^2 + 7x + 3 (iii) 6x^2 + 5x - 6 (iv) 3x^2 - x - 4 -
Factorise: (i) x^3 - 2x^2 - x + 2 (ii) x^3 - 3x^2 - 9x - 5 (iii) x^3 + 13x^2 + 32x + 20 (iv) 2x^3 + y^3 - 2y - 1 -
Evaluate 105 × 106 without multiplying directly.