C-02 — Algebraic Expression

When one or more numbers and symbols representing numbers are combined meaningfully by $+, -, \times, \div$, power or rational sign, the new symbol is called:

A literal symbol denoting any unscheduled element of a number set with more than one element is called:

A symbol denoting a definite number whose value remains fixed throughout a discussion is called:

The set of values from which a variable can take its value is called the:

In a polynomial, each term is the product of a constant and:

Which of the following is a polynomial?

Which of the following is NOT a polynomial?

In the term $cx^p$ of a polynomial of variable x, the value p is called the:

In the term $cx^p$ of a polynomial, c is called the:

The degree of a polynomial of one variable is:

The term having the largest degree in a polynomial is called the:

The coefficient of the term with the largest degree in a polynomial is called the:

The term independent of variable x (with degree 0) in a polynomial is called the:

The degree of the polynomial $2x^6 - 3x^5 - x^4 + 2x - 5$ is:

The leading coefficient of $2x^6 - 3x^5 - x^4 + 2x - 5$ is:

The constant term of $2x^6 - 3x^5 - x^4 + 2x - 5$ is:

Any non-zero constant is a polynomial of degree:

The degree of a zero polynomial is considered:

A polynomial arranged in descending order of the degrees of its terms is said to be in:

If $P(x) = 3x^3 + 2x^2 - 7x + 8$, then $P(2)$ equals:

If $P(x) = 3x^3 + 2x^2 - 7x + 8$, then $P(-2)$ equals:

In the term $cx^p y^q$ of a polynomial of two variables, the degree of the term is:

The degree of the polynomial $P(x,y) = 8x^3 + y^2 - 4x^2 + 7xy + 2y - 5$ is:

For $P(x,y) = 8x^3 + y^2 - 4x^2 + 7xy + 2y - 5$, the value of $P(1,0)$ is:

The expression $5x^2 - 2xy + 3y^2$ is a polynomial of:

In the term $cx^p y^q z^r$ of a polynomial of three variables, the degree of the term is:

The degree of $P(x,y,z) = x^3 + y^3 + z^3 - 3xyz$ is:

For $P(x,y,z) = x^3 + y^3 + z^3 - 3xyz$, the value of $P(1,1,-2)$ is:

The degree of the polynomial $6a^2 b^2 c^2$ is:

The result of multiplication of two polynomials is:

The result of division of two polynomials is:

The product of $(x^2 + 2)$ and $(x + 1)$ is:

If $P(x)$ and $Q(x)$ are polynomials of degree $m$ and $n$, the degree of $P(x) \cdot Q(x)$ is:

If the leading coefficients of $P(x)$ and $Q(x)$ are $p$ and $q$, the leading coefficient of $P(x) \cdot Q(x)$ is:

If the quotient $R(x) = P(x)/Q(x)$ is also a polynomial, the degree of $R(x)$ equals:

According to the division algorithm, $P(x) =$:

In the division algorithm, the remainder $R(x)$ satisfies:

If $ax + b = px + q$ holds for all $x$, then:

If $ax^2 + bx + c = px^2 + qx + r$ holds for all $x$, then:

The two coefficients of $x^k$ on both sides of an identity in $x$ are:

If two polynomials $P(x)$ and $Q(x)$ are equal for all values of $x$, their equality is called:

Which of the following symbols denotes identity?

Which of the following is an identity?

By the Remainder Theorem, if $P(x)$ is divided by $(x-a)$, the remainder is:

If $P(x) = x^2 - 5x + 6$ is divided by $(x-4)$, the remainder is:

If $P(x) = x^3 - 8x^2 + 6x + 60$ is divided by $(x+2)$, the remainder is:

If $P(x)$ is divided by $(ax + b)$ where $a \neq 0$, the remainder is:

If $P(x) = 36x^2 - 8x + 5$ is divided by $(2x - 1)$, the remainder is:

If dividing $P(x) = 5x^3 + 6x^2 - ax + 6$ by $(x - 2)$ yields remainder 6, the value of $a$ is:

By the Factor Theorem, if $P(a) = 0$ then:

If $(x - a)$ is a factor of $P(x)$, then:

$(x - 1)$ is a factor of $P(x) = ax^3 + bx^2 + cx + d$ if and only if:

$(x + 1)$ is a factor of a polynomial of positive degree if and only if:

The factorization of $x^3 - 6x^2 + 11x - 6$ is:

The factorization of $18x^3 + 15x^2 - x - 2$ is:

For a polynomial $ax^3 + bx^2 + cx + d$ with integer coefficients, if integer $r$ gives factor $(x-r)$, then $r$ is a factor of:

For a polynomial with integer coefficients, if $r = p/q$ (in reduced form) gives factor $(x - r)$, then:

To search integer factors of $P(x) = x^3 - 6x^2 + 11x - 6$, possible integer values of $r$ are:

If $P(x) = x^3 + 5x^2 + 6x + 8$ yields the same remainder when divided by $(x - a)$ and $(x - b)$ where $a \neq b$, then:

A polynomial in which each term has the same degree is called:

The expression $x^2 + 2xy + 5y^2$ is a homogeneous polynomial of degree:

An expression in more than one variable that remains unchanged when any two of its variables are interchanged is called:

Which of the following is symmetric?

The expression $2x^2 + 5xy + 6y^2$ is:

An expression in three variables that remains unchanged when the first variable is replaced by the second, the second by the third, and the third by the first is called:

Which of the following is cyclic but NOT symmetric?

Which statement is correct?

Consider the following statements:

If $(a - b)$ is a factor of a cyclic polynomial in $a, b, c$, the other factors include:

The factorization of $bc(b - c) + ca(c - a) + ab(a - b)$ is:

The factorization of $a^3(b - c) + b^3(c - a) + c^3(a - b)$ is:

The factorization of $(b + c)(c + a)(a + b) + abc$ is:

The expression $a^3 + b^3 + c^3 - 3abc$ equals:

$a^3 + b^3 + c^3 - 3abc$ also equals:

If $a + b + c = 0$, then $a^3 + b^3 + c^3$ equals:

If $a^3 + b^3 + c^3 = 3abc$, then:

The factorization of $(a - b)^3 + (b - c)^3 + (c - a)^3$ is:

A fraction whose numerator and denominator are both polynomials is called a:

The simplification of $\dfrac{a}{(a-b)(a-c)} + \dfrac{b}{(b-c)(b-a)} + \dfrac{c}{(c-a)(c-b)}$ is:

If a given fraction is expressed as a sum of two or more fractions, each of these fractions is called a:

A rational fraction $N(x)/D(x)$ is called a proper fraction if:

A rational fraction $N(x)/D(x)$ is called an improper fraction if:

Which of the following is a proper fraction?

Resolving $\dfrac{5x - 7}{(x - 1)(x - 2)}$ into partial fractions gives:

Resolving $\dfrac{x + 5}{(x-1)(x-2)(x-3)}$ as $\dfrac{A}{x-1} + \dfrac{B}{x-2} + \dfrac{C}{x-3}$, the constants are:

To express an improper fraction as a partial fraction, the first step is to:

The partial fraction setup for $\dfrac{x}{(x-1)^2 (x-2)}$ is:

The partial fraction setup for $\dfrac{x}{(x-1)(x^2 + 4)}$ is:

Suppose $P(x) = ax^5 + bx^4 + cx^3 + cx^2 + bx + a$ where $a \neq 0$. If $(x - r)$ is a factor of $P(x)$, then another factor of $P(x)$ is:

The factorization of $x^4 + 7x^3 + 17x^2 + 17x + 6$ is:

The factorization of $15x^2 + 2xy - 24y^2 - x + 24y - 6$ is:

Which one of the following expressions is symmetric?

If $P(x, y, z) = x^3 + y^3 + z^3 - 3xyz$, then consider: