Question

Ginny factored 6x2 – 31x – 30 as shown: ac = –180 and b = 31 36(–5) = –180 and 36 + (–5) = 31 6x2 + 36x – 5x – 30 6x(x + 6) – 5(x + 6) (x + 6)(6x – 5) Determine if Ginny factored correctly. If not, explain where she made an error. Ginny made a mistake in step 1 when she identified b = 31. It should be b = –31. Ginny was correct until step 3 when she used 36 and –5 as the coefficients of x. Ginny was correct until step 4 when she incorrectly factored the GCF from 5x – 30. Ginny factored the trinomial correctly.

Answer 1

Answer:

Ginny made a mistake in step 1 when she identified b=31. It should be b=-31

Step-by-step explanation:

Answer 2

Ginny factored the polynomial incorrectly. The correct answer by factorizing the given term is (x - 6)(6x + 5).

What is factorizing a polynomial?

"The factorization of a polynomial expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain."

Ginny factored  the given polynomial as:

6x² - 31x - 30

ac = - 180 and b = 31    

36 × (- 5) = 180 and 36 + (- 5) = 31

6x² - 31x - 30

= 6x² + 36x - 5x - 30

= 6x(x + 6) - 5(x + 6)

= (x + 6)(6x - 5)

The given polynomial is 6x² - 31x - 30.

Here, b = - 31 = the coefficient of the term 'x'.

Therefore, Ginny made a mistake here.

She took: b = 31, which is wrong.

After that, she made a mistake when factorizing. As a result her answer is wrong.

The correct steps will be as:

6x² - 31x - 30

= 6x² - 36x + 5x - 30

= 6x(x - 6) + 5(x - 6)

= (x - 6)(6x + 5)

Learn more about factorizing here: https://brainly.com/question/15296598

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