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Cat 164% G2) 10:29 AM, , , , < MATHEMATIC... &, , , , , , CHAPTER 2: POLYNOMIA\, , , , VERY SHORT ANSWER TYPE QUESTIONS, QI. Write an example of an algebraic expression that is not a polynomial., Q2. p(x) = Vx? + 1 is not a polynomial. Give reason, Q3. Find the value of polynomial 8x3 - 6x? +2 at x = 1, QU. If p(x) = 6x? + 5x?—3x +2 find p(-1), QS. Find the zero of the polynomial p(y) = 2y +7, Q6. Find the remainder when x!°'— 1 is divided by x -1, QZ. Find whether x" + y*is divisible by x — y ( y #0) or not., Q8. Write the following polynomials in standard form, idy- dy? 43 -y!, ii.Sm? -6m +7 -2m*, Q9. Write the integral zeroes of the following polynomials, i(x-3)(x-7), a(x +1) (3x42), , , , , , SHORT ANSWER TYPE QUESTIONS, , QUO. If y=-1 is a zero of the polynomial q (y) = 4y?+ ky? - y -1, then find the value of k, , QUL. For what value of m is x— 2mx? + 16 divisible by x +2, , QI2. Prove that (a+ b +c)’ —a’ -b'-c3 = 3(atb) (b+) (c+a), , Q13. Ifx + 1/x=5, find the value of x3 + I/x?, , QU4. The polynomials x} + 2x? Sax -7 and x + ax?—12x +6 when divided by x + 1 and x —2, respectively, leave remainders R; and Rerespectively. Find the value of a in each of the, following cases:, , , , , , i Ri = Ry, ii, Ri+ Ro=0, iii, 2Ri+ R= 0, , , , QUIS. Ifa+b+, QU6. Ifarb +, , 9 and ab + be + ca = 26, find a? + b*+c*, , prove that, , , , , , , QI7. Find the zeroes of (x- 2)? = (x+2)?, , LONG ANSWER TYPE QUESTIONS, QU8. Factorise p(x) = x! + x'— 7x? —x + 6 by factor theorem, QU9. Prove that 2x! — 6x3 + 3x? + 3x —2 is exactly divisible by x? — 3x +2, i, By actual division, ii, Without actual division, 20. When a polynomial p(x) = x* — 2x? + 3x? — ax + b is divisible by x — 1 and x + 1, the, remainders are 5 and 19 respectively. Find the remainder when p(x) is divided by x — 2., , , , 1, , Q21. Simplify:, (4x2 — 9y?)? + (9y? — 16y?)? + (162? — 4x2)?, (2x —3yP + By— 42) + Gz— 2x, , Q22. If x —3 and x — 1/3 are both factors of ax? + 5x +b , show that a= b, , Q23. Factorize:, i 3(x+2)— 5(x42)+2 oO, , ii, x +y%, , iii, 3V3x?—Sy5y?