WISKUNDE
GRAAD 12
NOG OEFENINGE
Die Resstelling.
MATHEMATICS
GRADE 12
MORE EXERCISES
The Remainder theorem.
1. Bepaal die res as f(x) deur g(x) gedeel word :
1.1 f(x) = x2 − 3x + 4 ; g(x) = x − 3
1.3 f(x) = 3x3 − 2x2 + 4x − 8 ; g(x) = 3x − 2
1.5 f(x) = −2x3 + 3x2 − 8x + 1 ; g(x) = 4 − 3x
1. Determine the remainder if f(x) is divided by g(x) :
1.2 f(x) = 3x2 + 4x −7 ; g(x) = x + 5
1.4 f(x) = 4x3 + 3x2 − 5x + 2 ; g(x) = 2x + 3
1.6 f(x) = −3x4 + 5x3 − 3x2 + 2x ; g(x) = 5 − 2x
2. Bepaal die waarde van p as f(x) deur g(x)
gedeel word en die res r is :
2. Determine the value of p if f(x) is divided by g(x)
and the remainder is r :
2.1 f(x) = px2 + 4x − 15 ; g(x) = x − 3 en / and r = 6
2.2 f(x) = 3x2 + px + 6 ; g(x) = x + 2 en / and r = 26
2.3 f(x) = x3 − 2x2 + px + 1 ; g(x) = x − 3 en / and r = 19
2.4 f(x) = x3 + px2 − 13x + 10 ; g(x) = x + 2 en / and r = 40
2.5 f(x) = 2x3 + px2 + 2x + 15 ; g(x) = x + 3 en / and r = −144
2.6 f(x) = 3x3 − 4x2 + px + 6 ; g(x) = x − 2 en / and r = −20
2.7 f(x) = x4 − 3x3 + px2 + 3x + 15 ; g(x) = x + 3 en / and r = 15
2.8 f(x) = x4 − 4x3 + 9x2 + px − 3 ; g(x) = x − 2 en / and r = −5
3. Faktoriseer :
3.1 x3 − 2x2 − 5x + 6
3.3 x3 + 3x2 − 10x − 24
3.5 2x3 − 3x2 − 3x + 2
3.7 3x3 + 5x2 − 16x − 12
3. Factorise :
3.2 x3 + 4x2 − 11x − 30
3.4 x3 + 4x2 − 27x − 90
3.6 6x3 + 17x2 + 6x − 8
3.8 8x3 − 14x2 − 25x + 42