Algebra 2: 6.1-6.3 Check In Quiz

• 2

• 4

• 7

• 11

Answer explanation

The degree of a polynomial is determined by the highest power of the variable. In the function f(x)=4m^2-m+7m^4, the term with the highest power is 7m^4, which has a degree of 4. Thus, the correct answer is 4.

6.2 - If a polynomial has zeros at -3 and 2, which of the following could be a factor form of that polynomial?

• (x + 3)(x - 2)

• (x - 3)(x + 2)

• (x + 3)(x + 2)

• (x - 3)(x - 2)

Answer explanation

The zeros at -3 and 2 correspond to the factors (x + 3) and (x - 2). Thus, the correct factor form of the polynomial is (x + 3)(x - 2). The other options do not match the given zeros.

Tags

CCSS.HSF-IF.C.7C

• The zero for (3x+2) is 0 with multiplicity 3, and the zero for (x-5) is 5 with multiplicity 5.

• The zero for (3x+2) is 2/3 with multiplicity 3, and the zero for (x-5) is -5 with multiplicity 5.

• The zero for (3x+2) is -2/3 with multiplicity 3, and the zero for (x-5) is 5 with multiplicity 5.

• The zero for (3x+2) is -2/3 with multiplicity 1, and the zero for (x-5) is 5 with multiplicity 5.

Answer explanation

To find the zeros, set each factor to zero. For (3x+2)=0, x=-2/3 (multiplicity 3). For (x-5)=0, x=5 (multiplicity 5). Thus, the correct answer is -2/3 with multiplicity 3 and 5 with multiplicity 5.

Tags

CCSS.HSF-IF.C.7C

Answer explanation

To divide \(x^3 + 3x^2 - x - 3\) by \(x - 1\), use polynomial long division. The result is \(x^2 + 4x + 3\), which matches the correct answer choice.

Tags

CCSS.HSA.APR.D.6

6.2 - Write the simplest polynomial in standard form given the following zeros. x = -2, 1, 4

Answer explanation

The zeros x = -2, 1, and 4 give the factors (x + 2), (x - 1), and (x - 4). Multiplying these factors results in the polynomial f(x) = x^3 - 3x^2 - 6x + 8, which is in standard form.

Tags

CCSS.HSA.APR.B.3