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Fill in the blanks to factor the trinomial correctly: [tex]2c^2 + 11c + 5[/tex]

[tex]\[
(2c + \square)(c + \square)
\][/tex]

- The correct numbers are the last two digits of your code.

Sagot :

GinnyAnsweridn
To factor the trinomial [tex]\(2c^2 + 11c + 5\)[/tex], we'll use the method of factoring by grouping.

Let's break this process down step-by-step:

1. Identify the trinomial: [tex]\(2c^2 + 11c + 5\)[/tex].

2. Look for two numbers that multiply to the product of the coefficient of [tex]\(c^2\)[/tex] term (which is 2) and the constant term (which is 5), and add to the coefficient of the [tex]\(c\)[/tex] term (which is 11).

- We need two numbers that multiply to [tex]\(2 \times 5 = 10\)[/tex] and add to 11.

3. The numbers that meet these criteria are 10 and 1 because [tex]\(10 \times 1 = 10\)[/tex] and [tex]\(10 + 1 = 11\)[/tex].

4. Rewrite the middle term using these two numbers:
[tex]\[ 2c^2 + 10c + c + 5. \][/tex]

5. Group the terms into pairs:
[tex]\[ (2c^2 + 10c) + (c + 5). \][/tex]

6. Factor out the greatest common factor (GCF) from each pair of terms:
[tex]\[ 2c(c + 5) + 1(c + 5). \][/tex]

7. Factor out the common binomial factor [tex]\((c + 5)\)[/tex]:
[tex]\[ (c + 5)(2c + 1). \][/tex]

So, the factorization of the trinomial is:

[tex]\[ (c + 5)(2c + 1). \][/tex]

Thus, the correct numbers to fill in the blanks are:

[tex]\[ (2c + 1)(c + 5). \][/tex]
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