Given the terms $18x^3{y}^2$ and $24x^2{y}^5$, what is the variable part of the GCF?

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

Factor completely, and show the GCF extraction and the resulting expression: $18x^4{y}^3-12x^2{y}^5+6x^3{y}^2$

Multiply the binomials $(x-6)(x+2)$.

You encounter the expression: $3x^2+14x+8$. A peer suggests that directly finding integers which will add to 14 and multiply to 8 will factor this expression. Is this suggestion valid? Choose the best justification.

A landscaper models the area (in units of square meters) of a rectangular flower bed as: $A\left(x\right)=x^2+5x+6$, where $x$ is a side-length adjustment in units of meters. Factor $A\left(x\right)$ to find expressions for the possible integer side lengths (in units of meters) and write the final results in terms of $x$.

Factor $4x^2+11x+6$ using a trial-and-error approach.

For the trinomial $101x^2+202x+101$, which factoring method is most effective for this expression, and why?

Factor by grouping: $x^3+3x^2+2x+6$

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

Write the equation $5x^2-3=2x$ in standard quadratic form $a{x}^2+bx+c=0$.

A rectangle has an area of 12 square meters, and a width that is 1 meter more than the length. Let length = L and the width = L + 1. Which numerical values represent the length and width of this rectangle?