Factoring Polynomials Mixed Review

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

How do you factor a trinomial of the form ax^2 + bx + c?

Back

To factor a trinomial, find two numbers that multiply to ac (the product of a and c) and add to b.

Front

What does it mean to factor by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors.

Front

What is the difference between a prime polynomial and a composite polynomial?

Back

A prime polynomial cannot be factored into simpler polynomials with integer coefficients, while a composite polynomial can.

Front

Factor the trinomial: 7x^2 + 4x - 3

Back

(7x - 3)(x + 1)

Front

Factor by grouping: 20x^2 - 16x - 25x + 20

Back

(5x - 4)(4x - 5)

Front

Factor the trinomial completely: 3x^2 + 15x + 12

Back

3(x + 4)(x + 1)

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, e.g., (a + b)^2 = a^2 + 2ab + b^2.

Front

Factor: x^2 + 4xy + 4y^2

Back

(x + 2y)(x + 2y)