Questions: 3.2.4 Quiz: Factoring Trinomials (Advanced) Question 1 of 10 When asked to factor the trinomial 4x^2+20x+25, a student gives the (2x-5)(2x-5). What is one thing wrong with this answer? A. The minus signs should be plus signs B. There is nothing wrong with the answer C. The factors are not simplified D. 4 is also a factor of this trinomial

3.2.4 Quiz: Factoring Trinomials (Advanced)

Question 1 of 10 When asked to factor the trinomial 4x^2+20x+25, a student gives the (2x-5)(2x-5). What is one thing wrong with this answer? A. The minus signs should be plus signs B. There is nothing wrong with the answer C. The factors are not simplified D. 4 is also a factor of this trinomial

Transcript text: 3.2.4 Quiz: Factoring Trinomials (Advanced) Question 1 of 10 When asked to factor the trinomial $4 x^{2}+20 x+25$, a student gives the $(2 x-5)(2 x-5)$. What is one thing wrong with this answer? A. The minus signs should be plus signs B. There is nothing wrong with the answer C. The factors are not simplified D. 4 is also a factor of this trinomial

Solution

Solution Steps

Step 1: Analyze the Given Trinomial

The given trinomial is $4x^2 + 20x + 25$. We need to factor this trinomial and compare it with the student's answer to identify any mistakes.

Step 2: Factor the Trinomial

To factor the trinomial $4x^2 + 20x + 25$, we look for two binomials $(ax + b)(cx + d)$ such that:

$ac = 4$
$bd = 25$
$ad + bc = 20$

Notice that $4x^2 + 20x + 25$ is a perfect square trinomial. It can be rewritten as:

\[ (2x + 5)^2 = (2x + 5)(2x + 5) \]

Step 3: Compare with the Student's Answer

The student provided the factorization $(2x - 5)(2x - 5)$. Comparing this with the correct factorization $(2x + 5)(2x + 5)$, we see that the student used minus signs instead of plus signs.