Exercises
Put your algebra knowledge to the test with this advanced algebra quiz. Solve and simplify expressions, identify linear functions, evaluate polynomials, find y-intercepts, and work through linear and quadratic equations. You will also practice determining polynomial degree and solving inequalities. Covering core skills such as substitution, factoring, equation solving, and algebraic reasoning, this quiz is ideal for students who want to review essential algebra concepts and check their confidence before an exam.
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To find the result, substitute 4 for x in the expression: 2(4) + 3 equals 8 + 3, which is 11.
A linear function is of the form y = mx + b. The equation y = 3x + 1 fits this form.
Solve for x: 5x - 15 = 0 becomes 5x = 15, so x = 15/5 = 3.
The expression x^2 - 4 is a difference of squares, which factors to (x + 2)(x - 2). Cancel out (x - 2) to get x + 2.
The y-intercept is the value of y when x is 0. Substitute 0 for x: y = 2(0)^2 - 3(0) + 1, which equals 1.
Distribute 3: 3x - 15 = 2x + 7. Subtract 2x: x - 15 = 7. Add 15 to both sides: x = 22.
The equation 4x^2 - 9 = 0 becomes (2x + 3)(2x - 3) = 0. Solving gives x as 1.5 and -1.5.
The degree of a polynomial is the highest power of x. In this case, it is 5 from 7x^5.
Substitute -1 for x: 3(-1)^3 - 2(-1)^2 + (-1) equals -3 - 2 - 1, resulting in -6.
Subtract 1 from both sides: 2x < 6. Divide by 2: x < 3.
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