Prealgebra · Question of the Day

Prealgebra Question of the Day

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Thursday, September 17, 2026

A polynomial is written as $P(x) = 2x^3 - x^2 + 4x + 1 + kx^2 - 3x + 2$ , where $k$ is a constant. For what value of $k$ will $P(x)$ have no $x^2$ term after combining like terms?

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A polynomial is written as $P(x) = 2x^3 - x^2 + 4x + 1 + kx^2 - 3x + 2$ , where $k$ is a constant. For what value of $k$ will $P(x)$ have no $x^2$ term after combining like terms?

$k = 0$
$k = -1$
$k = 1$ (correct answer)
$k = 3$

Explanation: When you encounter a polynomial with like terms that need to be combined, your goal is to group terms with the same power of $x$ and simplify the expression. Let's rewrite $P(x) = 2x^3 - x^2 + 4x + 1 + kx^2 - 3x + 2$ by grouping like terms:

$x^3$ terms: $2x^3$
$x^2$ terms: $-x^2 + kx^2 = (-1 + k)x^2$
$x$ terms: $4x - 3x = x$
Constant terms: $1 + 2 = 3$

P(x) = 2x^3 + (-1 + k)x^2 + x + 3

. For the

x^2

term to disappear completely, its coefficient must equal zero:

-1 + k = 0

, which means

k = 1

. Looking at the wrong answers: Choice A (

k = 0

) would give us

(-1 + 0)x^2 = -x^2

, so the

x^2

term remains. Choice B (

k = -1

) results in

(-1 + (-1))x^2 = -2x^2

, making the

x^2

term even larger. Choice D (

k = 3

) gives us

(-1 + 3)x^2 = 2x^2

, which also leaves an

x^2

term. Only choice C (

k = 1

) eliminates the

x^2

term entirely. Study tip: When asked to eliminate a term from a polynomial, set the coefficient of that term equal to zero after combining like terms. This type of question tests your ability to manipulate algebraic expressions systematically.