Factoring Quadratics

What is the role of the leading coefficient in factoring quadratics?

• It determines the number of roots of the quadratic expression.

• It affects the shape and direction of the parabola represented by the quadratic expression.

• It is irrelevant to the factoring process.

• It only affects the x-intercepts of the parabola.

What is the quadratic formula?

• x = (-b ± √(b² - 4ac)) / (2a)

• x = (b ± √(b² + 4ac)) / (2a)

• x = (-b ± √(b² + 4ac)) / (2a)

• x = (b ± √(b² - 4ac)) / (2a)

What is the standard form of a quadratic equation?

• ax² + bx + c = 0, where a ≠ 0

• ax² + bx + c = 1, where a ≠ 0

• ax² + bx + c = 2, where a = 0

• ax² + bx + c = 0, where a = 0

Factor the expression: 3a² + 4a + 1

• (3a + 1)(a + 1)

• (3a + 1)(a - 1)

• (3a - 1)(a + 1)

• (3a - 1)(a - 1)

Factor completely: 3x² - 7x + 2

• (x - 2)(3x - 1)

• (3x + 1)(x - 2)

• (x - 1)(3x - 2)

• (3x - 2)(x + 1)

Factor the polynomial: 5x² - 13x + 6

• (x - 2)(5x - 3)

• (5x - 2)(x - 3)

• (x - 1)(5x - 6)

• (5x + 2)(x - 3)

What does it mean to factor a quadratic expression completely?

• To express it as a sum of its roots.

• To express it as a product of linear factors, if possible, such that no further factoring is possible.

• To rewrite it in standard form with a leading coefficient of 1.

• To find the maximum or minimum value of the quadratic expression.

What is the difference of squares?

• a² - b² = (a - b)(a + b)

• a² + b² = (a + b)(a - b)

• a² - b² = (a + b)(a + b)

• a² + b² = (a + b)(a + b)

What is a quadratic expression?

• A polynomial of degree 1, typically in the form ax + b.

• A polynomial of degree 2, typically in the form ax² + bx + c.

• A polynomial of degree 3, typically in the form ax³ + bx² + cx + d.

• A constant value that does not change.

Factor the quadratic: 4x² - 16x - 9

• (2x - 9)(2x + 1)

• (2x - 3)(2x + 3)

• (4x - 9)(x + 1)

• (4x + 3)(x - 3)