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

In order to factor the polynomial: $x^3+6x^2+9x$ completely, should you factor out a GCF first? Why or why not?

Factor completely by grouping, after any necessary rearrangement: $2x^3-x^2-8x+4$

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 $N\left(x\right)$.

Which statement best explains why the method of finding two integers that multiply to $c$ and add to $b$ fails for: $2x^2+5x+3$?

A design engineer examines the quadratic expression: $P\left(x\right)=x^2+\left(k\right)x+41$, where $k$ is an integer. They want to solve for the integer linear factors, but they must note that $41$ is prime. For which integer value(s) of $k$ can $x^2+kx+41$ be factored into integers $(x+m)(x+n)$?

What is the product of the binomials $(2x+3)(x+4)$ when expanded by FOIL?

Factor the trinomial $15x^2+20x+5$ by first extracting the GCF. What is the final factored form?

Use the AC method to factor $6x^2+17x+5$.

Factor the perfect square trinomial $x^2+6x+9$ completely.

Factor the expression: $6x^2+11x-35$ completely by using the grouping method or a trial-and-error approach when necessary.

Find two consecutive positive even integers whose squares sum to $340$.