Polynomials Calculus/Algebra - Math 157/171
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Questions and Answers

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?

<p>Degree(P ∗ Q) = Degree(P) + Degree(Q) (C)</p> Signup and view all the answers

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

<p>P(a) = 0 (B)</p> Signup and view all the answers

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

<p>Degree(P - Q) ≤ Degree(P or Q) (B)</p> Signup and view all the answers

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

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

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

<p>3a + 2 (A)</p> Signup and view all the answers

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

<p>y - 3 (D)</p> Signup and view all the answers

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

<p>(x + 2)(x + 5)(x - 3) (D)</p> Signup and view all the answers

What is the purpose of the factor theorem?

<p>To find the factors of a polynomial (D)</p> Signup and view all the answers

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

<p>(x + 2)(x + 5)(x - 3) (D)</p> Signup and view all the answers

What is the definition of a polynomial?

<p>A polynomial is an algebraic expression consisting of variables and coefficients with whole number exponents. (D)</p> Signup and view all the answers

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

<p>Degree (C)</p> Signup and view all the answers

What is NOT a violation of a polynomial?

<p>A variable in the numerator. (C)</p> Signup and view all the answers

What is the leading coefficient of a polynomial?

<p>The coefficient of the highest power of the variable. (D)</p> Signup and view all the answers

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

<p>They can be whole numbers. (D)</p> Signup and view all the answers

What is NOT a characteristic of a polynomial?

<p>It has a negative exponent. (C)</p> Signup and view all the answers

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

<p>Another polynomial (D)</p> 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>P(a) = r (C)</p> Signup and view all the answers

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

<p>Degree(P) + Degree(Q) (A)</p> Signup and view all the answers

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

<p>P(a) = 0 (C)</p> Signup and view all the answers

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

<p>Another polynomial (C)</p> Signup and view all the answers

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

<p>Degree(P ± Q) ≤ Degree(P or Q) (A)</p> 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?

<p>3x4 + 3x2 + 5x − 1 (C)</p> Signup and view all the answers

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

<p>6x2 + 2x + 15 (C)</p> Signup and view all the answers

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

<p>20x4 + 15x2 (A)</p> Signup and view all the answers

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

<p>− 2x2 − 3x − 2 (B)</p> Signup and view all the answers

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

<p>7x3 − 2x2 + 3x + 4 (D)</p> 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?

<p>3x4 + 3x2 + 5x − 1 (C)</p> Signup and view all the answers

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