Polynomials Calculus/Algebra

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What is the result of the sum of 2 or more polynomials?

A linear expression

A rational expression

Another polynomial (correct)

An irrational number

What is the result of the product of 2 or more polynomials?

A linear expression

A rational expression

Another polynomial (correct)

A quadratic expression

What is the relation between the degree of polynomials P and Q, and their sum or difference?

Degree(P ± Q) = 0

Degree(P ± Q) ≤ Degree(P or Q) (correct)

Degree(P ± Q) = Degree(P) × Degree(Q)

Degree(P ± Q) ≥ Degree(P or Q)

What is the relation between the degree of polynomials P and Q, and their product?

Degree(P ∗ Q) = Degree(P) + Degree(Q) Signup and view all the answers

What is the condition for a polynomial P(x) to be divisible by a binomial (x − a)?

P(a) = 0 Signup and view all the answers

What is the relation between the degree of polynomials P and Q, and the degree of their difference?

Degree(P - Q) ≤ Degree(P or Q) Signup and view all the answers

What is the result of multiplying 5x2 and (4x2 + 3x2)?

20x4 + 15x3 - 7x(2x2 - 5x + 1) Signup and view all the answers

What is the result of dividing 9a2 + 6a by 3a?

3a + 2 Signup and view all the answers

What is the result of dividing 27y4 + 6y2 - 18 by -6y?

y - 3 Signup and view all the answers

What is the factorization of x3 + 4x2 - 11x - 30?

(x + 2)(x + 5)(x - 3) Signup and view all the answers

What is the purpose of the factor theorem?

To find the factors of a polynomial Signup and view all the answers

What is the result of simplifying the quadratic x3 + 4x2 - 11x - 30?

(x + 2)(x + 5)(x - 3) Signup and view all the answers

What is the definition of a polynomial?

A polynomial is an algebraic expression consisting of variables and coefficients with whole number exponents. Signup and view all the answers

What is the highest power of the variable present in a polynomial called?

Degree Signup and view all the answers

What is NOT a violation of a polynomial?

A variable in the numerator. Signup and view all the answers

What is the leading coefficient of a polynomial?

The coefficient of the highest power of the variable. Signup and view all the answers

What is true about the exponents of variables in a polynomial?

They can be whole numbers. Signup and view all the answers

What is NOT a characteristic of a polynomial?

It has a negative exponent. Signup and view all the answers

What is the result of the addition of two or more polynomials?

Another polynomial Signup and view all the answers

If P(x) is divisible by the binomial (x - a) with remainder r, what is the value of P(a)?

P(a) = r Signup and view all the answers

What is the degree of the product of two polynomials P and Q?

Degree(P) + Degree(Q) Signup and view all the answers

What is the condition for a polynomial P(x) to be divisible by the binomial (x - a)?

P(a) = 0 Signup and view all the answers

What is the result of the subtraction of two polynomials P and Q?

Another polynomial Signup and view all the answers

What is the relationship between the degrees of polynomials P and Q and their sum or difference?

Degree(P ± Q) ≤ Degree(P or Q) Signup and view all the answers

What is the result of adding f(x) = 3x4 − 5x3 + x − 4 and g(x) = 4x3 − 3x2 + 4x + 3?

3x4 + 3x2 + 5x − 1 Signup and view all the answers

What is the result of subtracting (9x2 + 10x + 5) from (−15x2 + 12x + 20)?

6x2 + 2x + 15 Signup and view all the answers

What is the result of multiplying 5x2 by (4x2 + 3x2)?

20x4 + 15x2 Signup and view all the answers

What is the result of adding (−5x3 − 10x + 2) and (3x2 + 7x − 4)?

− 2x2 − 3x − 2 Signup and view all the answers

What is the result of subtracting (7x3 + 5x3 − 8x + 10) from (14x3 + 3x2 − 5x + 14)?

7x3 − 2x2 + 3x + 4 Signup and view all the answers

What is the result of adding f(x) = 3x4 − 5x3 + x − 4 and g(x) = 4x3 − 3x2 + 4x + 3, in terms of x?