Algebra
Quadratic Equations
If \((x + 4)(3x - 1) = ax^2 + bx + c,\) what is the value of \(a + b + c?\)
The area of a rectangle can be expressed as \((2x^2 + 11x - 21).\) If the width of the rectangle is \((x + 7),\) which expression could represent the length?
If \(bx^2 + 32x = 4x(x - a),\) what is the value of \(ab\, ?\)
The Smith family has \(2,581 \text{ft}^2\) available in their rectangular backyard to put in a swimming pool. They plan to use the entire space. If the pool will have dimensions of \(20 \text{ft}\) by \(80 \text{ft}\), and they want a patio of equal width around the pool, what will be the width of the patio, in feet?
