Factoring and Multiplying Polynomials Review

Vocabulary practice flashcards covering key terms, patterns, and problem types for factoring quadratic expressions, factoring trinomials, extracting GCF, and multiplying polynomials.

Trinomial Pattern $x^2 + bx + c$

A quadratic expression form illustrated by $x^2 + 7x + 10 = (x)^2 + (2 + 5)x + (2)(5) = (x + 2)(x + 5)$.

Trinomial Pattern $ax^2 + bx + c$

A general quadratic expression form where the leading coefficient $a$ is not equal to $1$, illustrated by $2x^2 - 5x - 3 = (2x + 1)(x - 3)$.

GCF Factoring

The process of finding and factoring out the greatest common factor from each term in a polynomial expression, such as factoring $16p^4 + 4p^3$.

Prime Polynomial

An algebraic expression that cannot be factored into lower-degree polynomials with integer coefficients, written as prime if it cannot be factored.

Difference of Squares Expression

A quadratic binomial expression of the form $a^2 - b^2$, such as $x^2 - 4$, $x^2 - 9$, or $9x^2 - 1$.

Perfect Square Trinomial $x^2 + 4x + 4$

A quadratic expression in Practice 5-4 that factors completely into identical binomial factors $(x + 2)^2$.

Common Monomial Factor in $9x + 36$

The greatest common factor $9$ extracted from the polynomial $9x + 36$, resulting in the factored form $9(x + 4)$.

Square of a Binomial Expression $(4p - 1)^2$

A polynomial multiplication problem representing the product of a binomial with itself, written as $(4p - 1)(4p - 1)$.

Binomial by Trinomial Product $(4a + 2)(6a^2 - a + 2)$

A polynomial multiplication problem involving a two-term polynomial $(4a + 2)$ and a three-term polynomial $(6a^2 - a + 2)$.

GCF and Difference of Squares Expression $2x^2 - 98$

An expression requiring factoring out a common factor of $2$ first to yield $2(x^2 - 49)$, which then factors completely into $2(x + 7)(x - 7)$.

Factoring Expression $2x^2 + 13x + 15$

A quadratic trinomial with leading coefficient $a = 2$ from Section VIII that factors into linear binomials $(2x + 3)(x + 5)$.

Polynomial Expression $3m^2 + 9m + 27$

A trinomial whose terms share a greatest common factor of $3$, factoring as $3(m^2 + 3m + 9)$.

Binomial Product $(7x - 6)(5x + 6)$

A multiplication expression consisting of two linear binomial factors with different linear coefficients and constants.

Quadratic Trinomial $x^2 - 29x + 100$

A monic quadratic expression with a negative linear coefficient $-29$ and positive constant term $100$, factoring into $(x - 4)(x - 25)$.

Trinomial by Trinomial Product $(6n^2 - 6n - 5)(7n^2 + 6n - 5)$

A polynomial multiplication problem consisting of the product of two second-degree trinomial expressions.