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Question

If one of the factors of the polynomial (3x3+25x2+36x36) is (x+3), then find the other factors using synthetic division.

A
(x+6)
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B
(3x2)
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C
(3x+2)
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D
(x6)
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Solution

The correct options are
A (x+6)
B (3x2)
p(x)=(3x3+25x2+36x36)
One factor = (x+3)

Using synthetic division,
x3x2x1x0325363639483631612|0

p(x)=(x+3)(3x2+16x12) Now, (3x2+16x12)=(3x2+18x2x12) =3x(x+6)2(x+6) =(3x2)(x+6) Hence, x32x2+9x+18 =(x+3)(3x2)(x+6)

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