To factor the polynomial 25x^2 +15x - 4, find two numbers whose product is _ and whose sum is _.

Compare given polynomial with quadratic polynomial

, we get:

a=25, b=15, c=-4

Step1: find product of a and c which is 25*-4= -100

Step2: find two numbers whose product is ac and sum is b that is product is -100 and sum is 15

We see that 20 and -5 satisfy condition of step2.

Step3: Break middle term of into two parts -100x and +15x then proceed factor by grouping.

Hence final answer is .

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source: