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Mathematics
Algebraic Expressions
Factors of the Expression with Fractional Coefficients
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Multiple Choice
Which of the following is a correct step in factoring $a^3 + 1$ using fractional coefficients?
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$a^3 + 1 = \frac{1}{8}(8a^3 + 8)$
$a^3 + 1 = \frac{1}{27}(27a^3 + 27)$
$a^3 + 1 = \frac{1}{16}(16a^3 + 16)$
$a^3 + 1 = \frac{1}{64}(48a^3 + 48)$
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What is the remainder when the polynomial $f(x) = x^3 + 1$ is divided by $x + 1$?
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$3$
$0$
$1$
$-1$
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What is the value of the polynomial $f(a) = a^3 + 1$ when $a = -1$?
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$-1$
$0$
$1$
$2$
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What is the factorization of $(3a)^3 + 27$ as used in the fractional coefficients method?
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$(3a + 3)(9a^2 + 3a + 3)$
$(3a + 3)(9a^2 - 9a + 9)$
$(3a + 3)(9a^2 - 3a + 3)$
$(3a + 3)(9a^2 + 9a + 9)$
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Which expression represents the factorization of $x^3 + 1$ using the sum of cubes?
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$(x + 1)(x - 1)^2$
$(x + 1)(x^2 - x + 1)$
$(x - 1)(x^2 + x + 1)$
$(x + 1)^3$
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