Polynomials

Spot the Mistake

100

Spot the mistake in: (x+2)(x+3) = x²+6x+6

It should be x²+5x+6

200

Spot the mistake in x²+4x ÷ (x+4) = 1

It should be x²+4x ÷ (x+4) = x

300

Spot the mistake:

"If the leading coefficient is negative, the graph is concave up."

"If the leading coefficient is positive" / "The graph is concave down"

400

Spot the mistake:

"A cubic function will always have 3 x-axis intercepts."

It may have between 0 and 3 x-axis intercepts.

Degrees and Coefficients

100

What's the degree of the following polynomial?

x³ + 2x² + 3

3 (Cubic)

200

What's the leading coefficient of -2x³+5x²+x+7

-2

300

What's the degree of x(x+3)

2 (Quadratic)

400

What is the leading coefficient in 2x²+3x-x⁴

-1 (x⁴ is the leading term)

Expand the Polynomial

100

Expand: 3x(2x+1)

= 6x²+3x

200

Expand: 

(x+2)(x-2)

x² - 4

300

Expand:

(x²+3)(4-x)

= -x³+4x²-3x+12

400

Expand:

(x²+1)(4x+2)(x-3)

= 4x⁴−10x³−2x²−10x−6