The number of common factor(s) of two polynomials x2 - 9 and x3 - x2 - 9x + 9 is /are :
one
two
three
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Factorizing x2 - 9,
⇒ (x + 3)(x - 3)
Factorizing x3 - x2 - 9x + 9,
⇒ x2(x - 1) - 9(x - 1)
⇒ (x2 - 9)(x - 1)
⇒ (x + 3)(x - 3)(x - 1)
The number of common factor(s) of two polynomials x2 - 9 and x3 - x2 - 9x + 9 are two i.e.,(x + 3) and (x - 3).
Hence, Option 2 is the correct option.
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The remainder, when x3 - x2 + x - 1 is divided by x + 1, is :
0
-4
2
4
Is (x - 2) a factor of x3 - 4x2 - 11x + 30 ?
yes
no
nothing can be said
none of the above is true
4x2 - kx + 5 leaves a remainder 2 when divided by x - 1. The value of k is :
-6
6
7
-7