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Question

The factors of the polynomial equation P(x) = 4x3+x2+5x+8 are


A
(x+1), (4x23x+8)
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B
(x+2), (x23x+8)
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C
(x+3), (x2+8x3)
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D
(x+4), (4x2+3x8)
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Solution

The correct option is A (x+1), (4x23x+8)
Let us assume that atleast one of the zeroes is an integer. Product of the factors is equal to the constant term (+8). Possible roots are the factors of +8. Hence, possible factors are:
±1,±2,±4,±8.

Trying -1, we get:
p(1)=4×(1)3+(1)2+5×(1)+8
p(1)=4+15+8=0
So, (x + 1) is a factor of the polynomial P(x).

The quotient obtained when p(x) is divided by (x + 1) is the other factor.

4x23x+8x+1 )¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 4x3+x2+5x+8 4x3±4x2–––––––––– 3x2+5x3x23x–––––––––– 8x+88x±8––––––– 00

The factors are x+1 & 4x23x+8.

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