Factoring Trinomials: a = 1 (Continued) Answers
Which model shows the correct factorization of x2 – x – 2?
What did you include in your response? Check all that apply.
Complete the statements to explain how to factor x2 + x – 12 using algebra tiles.
–28✔ –31
–14 and 2✔ –7 and 4–4 and 7
(x – 14)(x + 2)✔ (x – 7)(x + 4)(x + 7)(x – 4)
Complete the statements to explain how to factor x2 + x – 12 using algebra tiles.
1 positive unit tile1 negative unit tile12 positive unit tiles✔ 12 negative unit tiles
noneone✔ three
(x + 3)(x + 4)(x + 3)(x – 4)(x – 3)(x – 4)✔ (x – 3)(x + 4)
What are the factors of x2 – 4x – 5? Check all that apply.x – 5x – 2x – 1x + 1x + 2x + 5
What side lengths should be used to model a rectangle with an area of x2 + 3x – 10 square units?
What is the four-term polynomial and factored form of the polynomial?
Which statement is true of x2 + 8x – 6?
Complete the equation to show two equivalent expressions.
The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n? Explain.
Since the trinomial is $x^2 + bx - c$ and its factors are $(x + m)(x - n)$, we know that $m + (-n) = b$ and $m(-n) = -c$. Because $b$ is positive, the sum of $m$ and $-n$ must be positive. This means the positive value, $m$, must have a greater absolute value than the negative value, $n$. Therefore, $m$ must be greater than $n$.
✔ –28–31
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