NJSLA Algebraic Concepts and Expressions 4

Question 1

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

Accepted Answer

4

Answer

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

Question 2

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

Accepted Answer

3x² - 4x + 6

Answer

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

Question 3

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

Accepted Answer

5

Answer

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

Question 4

Which expression is equivalent to x² - 9?

Accepted Answer

(x + 3)(x - 3)

Answer

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

Question 5

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

Accepted Answer

7

Answer

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

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