Factor the trinomial. 5y4 + 12y3 - 9y2

y²(y + 3)(5y - 3)

Step-by-step explanation:

Given

5 + 12y³ - 9y² ← factor out y² from each term

= y²(5y² + 12y - 9) ← factor the quadratic

Consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y- term

product = 5 × - 9 = - 45 and sum = + 12

The factors are + 15 and - 3

Use these factors to split the y- term

5y² + 15y - 3y - 9 ( factor the first/second and third/fourth terms )

= 5y(y + 3) - 3(y + 3) ← factor out (y + 3) from each term

= (y + 3)(5y - 3), so

5y² + 12y - 9 = (y + 3)(5y - 3)

Then

5 + 12y³ - 9y² = y²(y + 3)(5y - 3) ← in factored form

this excerpt is taken from the book “we shall not be moved : the women’s factory strike of 1909 “ and is written by joan dash. it is the story of the great strike when almost 30thousand women working in factories in america formed a union to fight unsafe working conditions, long working hours and miserable wages.

question: which best states the author’s purpose for including this information in the text?

answer: to challenge the reader’s ideas about a historical event

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.