Answer:
3. a. Each side of the garden is 2x+7 ft
4. B 9a^2 -30a +25
5. B prime
Step-by-step explanation:
3. A = 4x^2 +28x+49
Factor
a^2 +2ab +b^2 = (a+b)^2
a =2x and b = 7 2ab = 2 *14x = 28x
A = (2x+7) ^2
We need to take the square root since the garden is square
A = s^2 = (2x+7) ^2
s = (2x+7)
Each side of the garden is 2x+7 ft
4. Perfect square trinomial
a^2 +2ab +b^2 = (a+b)^2
or
a^2 -2ab +b^2 = (a-b)^2
Options C and D do not fit these patterns so they do not work
A 49x^2 -28x +16
a=7x b =4 2ab = 2*7x*4 = 56x This does not work
B 9a^2 -30a +25
a = 3a b = 5 2ab = 2*3a*5 = 30
(3a-5)^2 This is a perfect square trinominal)
5.x^2 -7x-10
What 2 numbers multiply to -10 and add to -7
-5*2 = -10 but -5+2 = -3
-10 *1 = -10 but -10+1 = -9
-2*5 = -10 but -2+5 = 3
-1 *10 = -10 but -1+10 = 9
These are all the factors of 10 so we cannot factor
This is prime
