MEI AS Mathematics Polynomials
Topic assessment
Add ( x3  2 x2  3x  1) to (2 x3  5x  3)
Subtract 2 x3  3x 2  x  2 from ( x4  x3  2 x2  1)
Multiply ( x3  4 x2  2 x  3) by (2 x  1)
Multiply ( x2  2 x  3) by ( x2  x  1)
Divide (2 x3  x2  3x  4) by ( x  1)
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[3]
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[3]
2. ( x  3) is a factor of the polynomial x3  ax 2  5 x  6 .
Find the value of a.
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3. (i) Solve the equation 2 x3  x 2  5 x  2  0 .
(ii) Sketch the graph of y  2 x3  x2  5x  2 .
[4]
[3]
4. (i) Show that ( x  3) is a factor of 6 x3  17 x 2  5 x  6 .
(ii) Hence solve the equation 6 x3  17 x 2  5 x  6  0 .
(iii) Sketch the graph of y  6 x3  17 x2  5x  6 .
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[2]
[3]
5. f ( x)  x3  ax2  bx  8 .
(i) ( x  1) and ( x  2) are factors of f ( x) .
Find the values of a and b.
(ii) Factorise f ( x) completely and hence solve the equation f ( x)  0 .
(ii) Sketch the graph of y  f ( x) .
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1. (i)
(ii)
(iii)
(iv)
(v)
Sketch the curve y  (2 x  1)( x  2)2 .
Draw the line y  x  2 on your graph and show that it intersects with the
curve at the point x  1 .
[5]
(ii) Show that the x-coordinates of the points where the line and the curve
intersect satisfy the equation 2 x3  7 x 2  3x  2  0 .
[3]
(iii) Find the x-coordinates of the other two points of intersection of the line and
the curve, giving your answers to 2 decimal places.
[4]
Th
6. (i)
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01/10/17 © MEI