Find the GCF of the coefficients 84 and 210 by prime factorization, showing the factors used.

Factor completely: $x^3+x^2-9x-9$

Which factoring strategy is most efficient for $x^4-16$, and what is the complete factorization?

Which condition correctly describes the pair of numbers m and n used to factor $x^2+bx+c$ as $(x+m)(x+n)$?

A box manufacturer models the number of items per layer as: $N\left(x\right)=x^2+9x+20$. They want to solve for the linear expressions for the length and width in terms of $x$. Factor $N\left(x\right)$.

A manufacturer models volume per layer as: $V\left(x\right)=x^2-11x+30$. If $x$ must be an integer and the company needs to solve for positive linear dimensions, which factorization will yield positive expressions for both linear factors?

Given a trinomial: $3x^2+kx+4$ which is factored as: $(3x+m)(x+n)$, which condition must $m$ and $n$ satisfy in order for the FOIL expansion to give back the original trinomial expression?

Use the AC method to factor $8x^2-2x-15$.

Factor by trial-and-error: $12x^2+7x-10$

Factor the trinomial $x^2-7x+12$ completely.

Two integers differ by $4$ and their product is $45$. Using a variable and a quadratic equation, find those integers.

A rectangular playground has an area equal to three times the square of its width. If the length is $9$ meters greater than the width, find the width and length.