Alevel_C1C2
Alevel_C1C2
Alevel_C1C2
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5. (a) f(2) = 32 + 4a + 2b - 15 = 63 M1<br />
4a + 2b = 46, then 2a + b = 23 …. (*)<br />
A1<br />
f(-1) = -4 + a - b - 15 = -6<br />
M1<br />
a - b = 13 …… (**)<br />
A1<br />
Adding (*) and (**):<br />
3a = 36, then a = 12, and b = -1 A2 (6)<br />
(b) f(x) = 4x 3 + 12x 2 - x - 15 B1<br />
f(1) = 4 + 12 - 1 - 15 = 0<br />
M1<br />
Therefore (x - 1) is a factor of f(x)<br />
B1<br />
f(x) = (x - 1)(4x 2 + 16x + 15)<br />
M1oe<br />
f(x) = (x - 1)(2x + 5)(2x + 3) A1 (5)<br />
(c) y = f(x) crosses the x-axis at: x = 1, x = − 5 2 , x = − 3 2<br />
A2 (2)<br />
13<br />
© Oxford University Press 2008<br />
Core C2
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