Algebra Test Polynomials 3

Question 1

What is the end behavior of y = -x³ + 2x as x → +∞?

Accepted Answer

y → -∞

Answer

With odd degree and negative leading coefficient, y goes to -∞ as x → +∞.

Question 2

Factor: 2x² + 8x

Accepted Answer

2x(x + 4)

Answer

The GCF is 2x, so 2x² + 8x = 2x(x + 4).

Question 3

How many terms does (a + b)(c + d) produce before combining like terms?

Accepted Answer

4

Answer

Using FOIL gives exactly 4 terms: ac, ad, bc, and bd.

Question 4

Which polynomial has roots at x = 1 and x = -5?

Accepted Answer

x² + 4x - 5

Answer

(x - 1)(x + 5) = x² + 5x - x - 5 = x² + 4x - 5.

Question 5

Expand: (3x - 2)²

Accepted Answer

9x² - 12x + 4

Answer

Using (a - b)² = a² - 2ab + b²: (3x)² - 2(3x)(2) + 4 = 9x² - 12x + 4.

Algebra Test Practice Test