HiSET Math Domain 4: Algebra Concepts

If \( f(x) = 2x^2 - 4x + 3 \) and \( g(x) = x - 5 \), what is \( f(g(3)) \)?

What are the solutions to the equation \( 3x^2 - 7x - 6 = 0 \)?

If \( h(x) = x^3 - 4x \), find \( h(-2) \).

Solve for \( x \): \( \frac{1}{2}(6x - 4) = 4x + 6 \).

What is the vertex of the parabola defined by \( y = 2x^2 - 8x + 3 \)?

If the roots of the equation \( x^2 - px + 16 = 0 \) are real and equal, what is the value of \( p \)?

Simplify the expression: \( (3x - 4)(2x + 5) \).

What is the inverse function of \( f(x) = \frac{2x - 3}{5} \)?

What is the remainder when \( 2x^3 - 3x^2 + 4x - 5 \) is divided by \( x - 2 \)?

If \( a(x) = x^2 + x - 6 \) and \( b(x) = x - 2 \), what is \( a(x) \div b(x) \)?

Solve for \( y \) in the equation \( 2y - 3x = 6 \).

Evaluate \( 4x^2 - 9 \) when \( x = 3 \).

For which value of \( k \) does the equation \( x^2 + kx + 9 = 0 \) have one real solution?

If \( f(x) = 3x^3 - 2x^2 + x - 5 \), what is the coefficient of the \( x^2 \) term in \( f(x + 1) \)?

What is the solution to the system of equations \( 2x + 3y = 5 \) and \( 4x - y = 3 \)?

What is the degree of the polynomial \( 7x^4 - 3x^3 + 2x^2 - x + 5 \)?

What is the axis of symmetry for the parabola given by \( y = -3x^2 + 12x - 7 \)?

If \( i^2 = -1 \), what is \( (3 + 4i)(2 - i) \)?

What is the standard form of the equation of the line passing through the points (1, 2) and (3, -2)?

Solve for \( x \) in the equation \( \frac{1}{x} + \frac{1}{x + 2} = \frac{1}{2} \).

Given the function \( f(x) = \frac{4x}{x^2 - 9} \), for which values of \( x \) is \( f(x) \) undefined?

What is the solution set for the inequality \( 3(x - 2) > 2x + 1 \)?

If the function \( g(x) \) is defined as \( g(x) = 2x^3 - 5x^2 + x - 1 \), then what is the value of \( g(-2) \)?

The quadratic equation \( 2x^2 - x - 1 = 0 \) has roots \( \alpha \) and \( \beta \). What is \( \alpha\beta + \alpha + \beta \)?

What are the x-intercepts of the function \( f(x) = x^2 - 4x + 3 \)?