Cooperative Learning QS015
Polynomials
Given f, g and h are defined by f(x) =3 – x2, g(x) = x3 - 2x2 + 5, h(x) = 3x + 4.
i) State the leading coefficient and degree of the resulting polynomial
ii) give the coefficient of x3
1) Find each of the remainder when the polynomials x3 – 3x2 + 6x – 2 is divided by
a) x+ 2 b) x – 1 c) 2x-1 /
2) If P(X) = 2x3 + bx2 +4 is divided by x-b, the remainder is 85. Find the value of b.
3. Given P(x) = x3 + px2 + qx -2. When P(X) is divided by x-3 and x+2, the remainders are 4 and
-16 respectively. Find the values of p and q. / 4. When the polynomial x3 -3x+6 and x3-2x2+x+4 are each divided by x-m the remainders are equal. Find the possible value of m.
5. When a polynomial is divided by x+1, the remainder is 5 and when it is divided by x-4, the remainder is 15. Find the remainder when P(x) is divided by (x+1)(x-4).
/ 6. The polynomials ax4+2x3+bx +3 leaves a remainder of 15x+19 when divided by x2-x-2. Find the values of a and b.
1. x = is a root of polynomial equation 4x3 – 33x2 + bx + 175 = 0, b a real number.
Find a) the value of b b) all the roots of the equation
2. Given P(x) = 2x3 + 5x2 –x -6
a) Show that - 2 is a zero of P(x) b) Find a, b, c such that P(x) = (x+2)(ax2+bx+c)
c) Factorize completely d)Solve the equation P(x) = 0
e)Write all the zeros of P(x) f) Write the solution of equation P(x+1) = 0
Express the following as partial fractions.
TRY THIS
1. Express in partial fractions. 2. Use the factor theorem to factorize 2x3-x2-2x+1.
Hence express in partial
fractions.
TRY THIS!!
1. Express as partial fractions. (JAN 2000)
2 Given where , and are constants.
a) Find the values of , and . b) Express as a partial fractions. (UPS 04/05)
Never give Up!!
3. Given that has a remainder of 5 when divided by .
a) Find the value of .
b) By using the positive value of from part (a),
i) find all the zeros of ii) solve the inequality (UPS 05/06)
4. Given a polynomial . (UPS 06/07)
a) Show that is a factor of b) Factorize completely.
c) Find the remainder when is divided by . d) Express as a partial fractions.
1 | Prepared by : Pn Nuraini Abdullah