Can someone factor 3x^2+30x+75...with an explanation....PLEASE!!?

Answer 1

75 times 3 =225
(x+15)(x+15) because if you multiply the 3 and 75 to get a number on the top of a diamond problem, and then on the bottom is 30, and 15+15 =30, and 15 times 15 =225, so therefore it has to be (x+15)(x+15)

Answer 2

Method 1: we can simplify 3x^2+30x+75 by taking the common term 3 and write it as 3(x^2+10x+25)
by looking at this we understand that u can compare this with a^2+2ab+b^2=(a+b)^2

where a=x and b=5

so we can write this as 3(x+5)^2.

method 2:for factorisation the basic clue is,

consider general term ax^2+bx+c and the expression 3x^2+30x+75.

here a=3,b=30,c=75

1.u have to find the product of the extreme terms=a x c.
in this case it is 3x 75=225

2. u have to work out combination of 2 numbers to add/subtract , so that u can arrive at the middle term b as well as get the value of(a x c)

here b=30, u can split 30 into 15 and 15 so their product (15 x 15) is the value of(3 x 75)

3.now the expression is writen as
3x^2+15x+15x+75
taking the common terms out we cxan simplify this as
3x(x+5)+15(x+5)
1.e (3x+15)(x+5)

u cab further simplify this as 3(x+5)(x+5)=3(x+5)^2

Answer 3

1. First find the common factor, which would be 3

3(x^2+10x+25)

2. Then just factor it the one in ( )

3(x+5)(x+5) = 3(x+5)^2

Answer 4

look for the lcd, so it would be 3 making the new equation
3(x2+10x+25) find the product and sum p s product is x2 times 25 and sum is 10. what times what equals 10 and at the same time equals 25? 5 + 5=10 and multiply its 25

so T-time 3l (x+5)(x+5)=0 3=0 x= -5 x= -5

Answer 5

You know it has to be (3x + something)(x + something).
What are some factors of 75? 3x25 15 x 5
15 x 5 looks pretty useful.

(3x + 15)(x + 5) will work.

Answer 6

fact out the 3
3^2/3=x^2
30x/3=10x
75/3=25
3(x^2+10x+25)
3(x+5)(x+5) or 3(x+5)^2