Algebraic Concepts and Expressions Flashcards

What is the degree of the polynomial 5x³ - 2x⁴ + x - 7?

Answer: 4

The degree is the highest exponent, which is 4 (from the -2x⁴ term).

Simplify: (5x² - 3x + 2) - (2x² + x - 4)

Answer: 3x² - 4x + 6

Distribute the negative sign and combine like terms: 5x²-2x²=3x², -3x-x=-4x, 2+4=6.

For what value of x does the expression 3x + 7 equal 22?

Answer: 5

Solve 3x + 7 = 22: subtract 7 to get 3x = 15, then divide by 3 to get x = 5.

Which expression is equivalent to x² - 9?

Answer: (x + 3)(x - 3)

x² - 9 is a difference of squares: a² - b² = (a + b)(a - b), so x² - 9 = (x + 3)(x - 3).

If 2(x + 3) = 14, what is the value of x + 3?

Answer: 7

Dividing both sides by 2 gives x + 3 = 7, without needing to solve for x alone.

A formula for simple interest is I = prt. Which expression gives p in terms of I, r, and t?

Answer: I/(rt)

To isolate p, divide both sides of I = prt by rt, giving p = I/(rt).

Which term is a 'like term' with 4x²y?

Answer: -7x²y

Like terms must have the same variables raised to the same powers; -7x²y matches x²y.