M2 Core Midterm Review

Which of the following is NOT a type of polynomial?

• Monomial

• Binomial

• Trinomial

• Geonomial

Answer explanation

A monomial, binomial, and trinomial are all types of polynomials based on the number of terms they contain (one, two, and three, respectively). 'Geonomial' is not a recognized type of polynomial.

• 3

• 2

• 1

• 0

Answer explanation

The degree of a polynomial is the highest power of the variable. In the polynomial P(x)=4x^3+2x^2−5x+7, the term with the highest power is 4x^3, which has a degree of 3. Therefore, the correct answer is 3.

Which of these is a monomial?

Answer explanation

A monomial is a single term with no addition or subtraction. Among the options, '4x^3' is a monomial, while '2x^2+3x+1' and 'x-5' are polynomials, and '\frac{1}{x}\times3' is a product of terms.

Identify the polynomial NOT in standard form (descending order):

Answer explanation

The polynomial 4x−x^2−7 is not in standard form because the terms are not arranged in descending order of their degrees. It should be written as -x^2 + 4x - 7.

• 7

• 5

• −1

• −3

Answer explanation

To find P(2), substitute x=2 into the polynomial: P(2) = 2^3 - 2(2^2) + 2 - 3 = 8 - 8 + 2 - 3 = 7. Thus, the correct answer is 7.

• x={2,−3,−4}

• x={2,3,4}

• x={2,−3,4}

• x={−2,3,−4}

Answer explanation

To find the zeros of P(x)=(x−2)(x+3)(x−4), set each factor to zero: x−2=0 gives x=2, x+3=0 gives x=-3, and x−4=0 gives x=4. Thus, the solutions are x={2,−3,4}. The correct answer is x={2,−3,−4}.

Answer explanation

To add the polynomials, combine like terms: \(P(x) + Q(x) = (3x^2 + 5x^2) + (-x + 2x) + (4 - 1) = 8x^2 + x + 3\). Thus, the correct answer is \(8x^2 + x + 3\).

Answer explanation

To subtract P(x) from Q(x), combine like terms: (5x^2 - 3x^2) + (2x + x) + (-1 - 4) = 2x^2 + 3x - 5. Thus, the correct answer is 2x^2 + 3x - 5.

Answer explanation

To multiply (x+2)(x−3), use the distributive property: x(x−3) + 2(x−3) = x^2 - 3x + 2x - 6 = x^2 - x - 6. Thus, the correct answer is x^2−x−6.

Answer explanation

The expression (a^2−b^2) is a difference of squares, which factors into (a+b)(a−b). The other options do not represent this factorization correctly.