Question

Just answer these 4questions! (: 13 points!

Answer 1

Answer:

Step-by-step explanation:

1) GCF = Greatest common factor which would be 6x so lets get started.

$6x^3+36x+48=0\\6x(x^2+6x+8)=0\\x^2+6x+8=0$

now we solve this with by quadratic formula.

$x= -\frac{b+-\sqrt{b^2-4ac} }{2a}$

so a=1 , b=6, c =8

and we get two values of x which is

$x=-2 \\and \\x=-4$

but in the question it says we will end up with 3 solutions. Our third solution is actually $x=0$

because we took 6x common as the greatest common factor so

$6x=0\\x=0$

so now we have 3 solutions

$x=-4\\x=-2\\x=0$

2) (x-9)(4x+1)=0

since this equation is already in root form we equate each root to 0

$(x-9)(4x+1)=0\\x-9=0\\x=9 \\4x+1=0\\4x=-1\\x=-1/4$

so our solutions are x=9 and x=-1/4

3)

$(x+5)^2-12=132\\(x+5)^2=132+12\\(x+5)^2=144$

now since we need to solve using square roots we apply square roots on both sides

$\sqrt{(x+5)^2}=\sqrt{144}\\x+5=+12 \\x+5=-12$

since when we take the square root of a number we get positive and negative of that number example here

x+5=±12

so

x+5=12 and x+5=-12

x=7 and x=-17

4) Difference of two squares means we just need to factorize it in root form so lets begin,

$4x^2-49$

now if we see this expression can be written like this as well

$(2x)^2-(7)^2$

and if we expand this into the difference formula which is

$(a-b)(a+b)$

we get

$4x^2-49=(2x-7)(2x+7)$

where a is 2x and b is 7