Algebra: Factoring Review

What is the first step in factoring a polynomial?

• Look for the GCF of all the terms.

• Multiply all the terms together.

• Add all the coefficients of the terms.

• Subtract the constant from the polynomial.

What is the difference between factoring and expanding?

• Factoring is breaking down an expression into products, while expanding is multiplying out the factors to get the original expression.

• Factoring involves adding terms together, while expanding involves subtracting terms.

• Factoring is the process of finding the roots of an equation, while expanding is simplifying an expression.

• Factoring and expanding are two terms that mean the same thing in mathematics.

What is the significance of the leading coefficient in factoring?

• 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 indicates the maximum value of the quadratic expression.

• It is irrelevant to the factoring process.

What is the role of the zero product property in factoring?

• It states that if the product of two factors is zero, at least one of the factors must be zero.

• It helps in simplifying fractions by eliminating common factors.

• It allows for the addition of two numbers to equal zero.

• It indicates that the sum of two factors must always be greater than zero.

What is the difference of squares?

• (a^2 - b^2) = (a - b)(a + b)

• (a^2 + b^2) = (a - b)(a + b)

• (a^2 - b^2) = (a + b)(a + b)

• (a^2 - b^2) = (a - b)(a - b)

Factor the expression: x^2 - 9

• (x - 3)(x + 3)

• (x - 9)(x + 1)

• (x - 1)(x + 1)

• (x + 3)(x + 3)

What is a perfect square trinomial?

• A quadratic expression that can be factored into two identical binomials.

• A polynomial that has three terms and is always positive.

• A quadratic expression that can be expressed as the square of a binomial.

• A type of equation that has no real solutions.

What is a binomial?

• A polynomial that contains exactly two terms.

• A polynomial that contains three terms.

• A polynomial that contains only one term.

• A polynomial that contains four or more terms.

Factor the expression: x^2 + 2x – 3

• (x - 1)(x + 3)

• (x + 1)(x - 3)

• (x - 3)(x + 1)

• (x + 3)(x + 1)

Factor the expression: x^2 + 5x + 6

• (x + 1)(x + 6)

• (x + 2)(x + 3)

• (x + 3)(x + 2)

• (x + 4)(x + 1)