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YY, , ww, , 10., , 11., , 12., , 13., , 14,, , Exercise 3.2, , Fill up the blanks :, (i) When x? + 2x —3 is divided by (x -1), remainder = ....... :, , (ii) If (x -2) is a factor of the polynomial p(x), then P(2) = veveeee ;, What will be the remainder when y‘ -3y? + 2y +1 is divided by (y-1)?, , What will be the remainder when x? + 4x + 2 is divided by (x + 2) ?, , If for polynomial p(x), p(-1) = 3, then what will be the remainder when p(x) is, divided by (x + 1) ?, , If for polynomial p(x), »(-2) = 0, then write a factor of polynomial p(x)., , If for polynomial p(x), p(-3) = 0, then write a factor of polynomial p(x)., , . Find the remainder when x? + 3x? + 3x+1 is divided by, , : Pe 1, @x+1 (Wes, , (i) Find the remainder when x? +1 is divided by x +1., , (ii) Find the remainder when x* +x° — 2x? +x +1 is divided by x—1., , (iii) Find the remainder when x° — ax? + Gr —a is divided by x-a., , If p(x) =x* —3x? + 2x +1, then using remainder theorem, find the remainder, when p(x) is divided by :, , (i) x-2 (ii) x -4, , If p(x) = 4x° — 3x? + 2x —4, then using remainder theorem, find the remainder, when p(x) is divided by :, , @x-1 (ii)x +1, , If p(x) =x? + 4x + 2, then what will be the remainder when p(x) is divided by, x422, , Using factor theorem determine whether x—1 is a factor of the following :, (x2 +x? 2x41 (ii) 8x4 —12x° + 18x +14, , (iil) x? + 8x? —7x-2 (iv) W22x? + 5V2x? - W2 , Use factor theorem to determine whether g(x) is a factor of p(x) in each of the, following cases :, , (i) p(x) = 2x? + x? -2x-1, g(x) =x+1, , (ii) p(x) = x? + 3x? + 3x + 1g (x) =x +2, , (iii) p(x) = x? - 4x? +x + 6,g(x) =x-3 [NCERT], (i) Examine whether 7 + 3x is a factor of 3x? + Tx. [NCERT], (ii) Examine whether x +2 is a factor of the polynomials x° + 3x? + Sx + 6, , and 2x + 4, : (NCERT], , (iii) Examine whether q(t) = 4t° + 4¢? —¢ ~1is a multiple of 2¢ +1, [NCERT]