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:

Ginny factored $6x^2 -31x -30$ as shown:

ac = –180 and

b = 31

36(–5) = –180 and 36 + (–5) = 31

$6x^2$ + 36x – 5x – 30

6x(x + 6) – 5(x + 6)

(x + 6)(6x – 5)

b is the coefficient of x and from the trinomial $6x^2 -31x -30$, b=-31.

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

The correct steps are: $6x^2 -31x -30$:

ac = –180 and

b = -31

36(–5) = –180 and -36+5 = -31

$6x^2-36x +5x -30$  

$6x(x-6)+5(x-6)$

$(x-6)(6x+5)$