Checkpoint: coefficients, cancelling and testing

A second bay has area 5x² + 13x + 6. What must the pair multiply to?

• 6, because that is the last number
• 30, because it is the first number times the last
• 13, because that is the middle number

Which striking-out leaves the same number at every value of x?

• (4x + 8)/4 becomes x + 2
• (x + 7)/(x + 9) becomes 7/9
• (x + 6)/6 becomes x

Two taps fill 1/x and 2/(x + 1) of a tank each hour. What do they fill together?

• 3/(2x + 1), from adding tops and adding bottoms
• 2/(x² + x), from multiplying the two
• (3x + 1) over x(x + 1)

A line reads x² = 4x. Both sides give 16 at x = 4. Someone calls it an identity. What is wrong?

• It needs two values, not one
• Nothing. Both sides give 16
• Agreement at one value does not settle a claim