Factoring Trinomials of the Form ax² + bx + c: Videos & Practice Problems

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

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

Use the AC method to factor $9x^2-30x+25$.

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?

For the trinomial: $5x^2-8x-12$, which pair of binomials correctly factors this expression?

If $c$ is negative in: $a{x}^2+bx+c$, what must be true about the signs of the two constants within the binomial factors, assuming that they are integer factors?

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

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

Given the trinomial $14x^2+15x+4$, which factoring strategy is more efficient, and what is the correct factorization?

Which factor pair and sign placement would you consider first when factoring $7x^2+x-12$ and why?

When using trial-and-error to factor $2x^2+5x+2$, which initial pairings of the leading-term factors should you consider?

A manufacturing model predicts profit: $P\left(t\right)=2t^2-11t-21$ dollars, where $t$ is in thousands of units. Factor $P\left(t\right)$ completely to identify production thresholds (in thousands of units) and interpret the roots.

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

Which is the correct expansion of $(x+6)(x-2)$?

Consider the trinomial $12x^2+7x+1$. When factoring trinomials where $a$ is small but has many factor pairs (such as $a=12$) and $c$ has several divisors, which method is generally faster to use: trial-and-error or AC (grouping)?

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

You try $(2x-7)(3x+4)$ as factors for $6x^2-x-28$. Multiply the binomials and determine whether this factorization is correct.

Use Descartes’ rule of signs to determine the correct signs of the factors and then factor $x^2+x-30$. Which factorization demonstrates a correct application of Descartes’ rule of signs?

Which method would you recommend for factoring $3x^2+5x+2$ on a timed exam, and why?

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

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

A student factors $16x^2-24x+9$ as $(4x-3{)}^2$. Evaluate whether this is correct and justify.

Which of the following is an effective first step when attempting to factor $10x^2-x-12$ by trial and error to reduce the number of candidate binomials?

When factoring a quadratic of the form $a{x}^2+bx+c$, different strategies may be appropriate depending on the coefficients. For $18x^2+13x+2$, use trial and error to determine an efficient factoring approach and find the factorization.