check wheather the polynomial f(x)=4x^3+4x^2-x-1 is a multiple of (2x+1)
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Yes it's a possible...
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2x + 1 = 0 => x = -1/2
Use the factor theorem:
2x + 1 is a factor of p(x) <=> p(-1/2) = 0.
p(-1/2) = 4*(-1/8) + 4*(1/4) + 1/2 - 1
= -1/2 + 1 + 1/2 - 1 = 0
Therefore p(x) is a multiple of 2x + 1.
Use the factor theorem:
2x + 1 is a factor of p(x) <=> p(-1/2) = 0.
p(-1/2) = 4*(-1/8) + 4*(1/4) + 1/2 - 1
= -1/2 + 1 + 1/2 - 1 = 0
Therefore p(x) is a multiple of 2x + 1.
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