EXERCISE
1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : (i) ${p(x) = x^3 – 3x^2 + 5x – 3}$, ${g(x) = x^2 – 2}$ Solution (ii) ${p(x) = x^4 – 3x^2 + 4x + 5}$, ${g(x) = x^2 + 1 – x}$ Solution (iii) ${p(x) = x^4 – 5x + 6}$, ${g(x) = 2 – x^2}$ Solution 2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: (i) ${t^2 – 3}$, ${2t^4 + 3t^3 – 2t^2 – 9t – 12}$ Solution (ii) ${x^2 + 3x + 1}$, ${3x^4 + 5x^3 – 7x^2 + 2x +2}$ Solution (iii) ${x^3 – 3x + 1}$, ${x^5 – 4x^3 + x^2 + 3x + 1 }$ Solution 3. Obtain all other zeroes of $3x^4 + 6x^3 – 2x^2 – 10x – 5$, if two of its zeroes are ${√{5/3}}$ and ${-√{5/3}}$ Solution 4. On dividing ${x^3 – 3x^2 + x + 2}$ by a polynomial ${g(x)}$, the quotient and remainder were ${x – 2}$ and ${–2x + 4}$, respectively. Find ${g(x)}$. Solution 5. Give examples of polynomials ${p(x)}$, ${g(x)}$, ${q(x)}$ and ${r(x)}$, which satisfy the division algorithm and (i) deg ${p(x)}$ = deg ${g(x)}$ (ii) deg ${q(x)}$ = deg ${r(x)}$ (iii) deg ${r(x)}$ = 0