1. factor the expression 3x3 +4x2 -15x -20. show your work for full credit.

2.solve the equation p2 + 4p = -6 by completing the square.
show all your work. hint: find c by ( ½ b)2, then use the method in lesson 3.08
complete the square page 2. go through the example.

3. explain the steps on how you would factor the expression 25x2 + 9y2

answer:

1. answer is (x^2 - 5) • (3x + 4)

step 1: • (x^3)) +   22x^2) -   15x) -   20

step 2: ((3x^3 +   22x^2) -   15x) -   20

thoughtfully split the expression at hand into groups, each group having two terms :

group 1:   -15x-20

group 2:   3x3+4x2

pull out from each group separately :

group 1:   (3x+4) • (-5)

group 2:   (3x+4) • (x2)

add up the two groups : (3x+4)   •   (x^2-5)

2. answer is -2 -√ 2 • i or -2 + √ 2 •   i

take the coefficient of   p , which is   4 , divide by two, giving   2 , and finally square it giving   4

add   4   to both sides of the equation :

  on the right hand side we have :

  -6   +   4     or,   (-6/1)+(4/1)

  the common denominator of the two fractions is   1   adding   (-6/1)+(4/1)   gives   -2/1

  so adding to both sides we finally get :

  p2+4p+4 = -2

adding   4   has completed the left hand side into a perfect square :

  p2+4p+4   =

  (p+2) • (p+2)   =

  (p+2)^2

things which are equal to the same thing are also equal to one another. since

  p2+4p+4 = -2 and

  p2+4p+4 = (p+2)^2

then, according to the law of transitivity,

  (p+2)^2 = -2

we'll refer to this equation as   eq. #2.2.1  

note that the square root of

  (p+2)^2   is

  (p+2)2/2 =

  (p+2)1 =

  p+2

now, applying the square root principle to   eq. #2.2.1   we get:

  p+2 = √ -2

subtract 2 from both sides to obtain:

  p = -2 + √ -2

since a square root has two values, one positive and the other negative

  p2 + 4p + 6 = 0

  has two solutions:

  p = -2 + √ 2 •   i

  or

  p = -2 - √ 2 •   i

answer is 25x^2 + 9y^2 because the expression is not factorable with rational numbers.

step 1: (25 • (x^2)) +   32y^2

step 2: 52x^2 +   32y^2

24 units^2

Step-by-step explanation: