Factoring help?

Question

can some one teach me how to facttor

can u factor
this as an exsample

3X to the 2 power +14x+8=0

can some one explan it in full dital

Answer 1

3x^2+14x+8
(3x+2)(x+4)

Answer 2

3x`2 + 14x +8 = 0

1. multiply 3*8 (the first and last) = 24

2. now think of two numbers that add to 14 (the second number) and multiply to 24 (the product of the 1st and last) = 12 and 2

3. separate the 14 in the middle into 12 and 2 = 3x`2+12x+2x+8

4. Split the equation in half and factor both
1st half 3x`2+12x= 3x(x+4)
2nd half 2x+8=2(x+4)

5. write the term in parenthesis in both ((x+4)) and then write the other two numbers in parenthesis (3x and 2)
(x+4)(3x+2)

all done!

Answer 3

the = implies you want to solve the equation by factoring

3x^2 + 14x + 8 = 0

You can do this by trial and error, the factors will look like

(ax + b)(cx + d)

Looking at your equation, you can see that one of the coefficients a & c must be 1 and the other 3 to get 3 as the coefficient of x^2

The constants b & c must be 1 & 8 or 2 & 4 to get 8 as the constant term

(3x + 2)(x + 4) = 3x^2 + 12x + 2x + 8

There is a formal scheme for factoring these kinds of quadratics at the link below

Answer 4

3x^2 + 14x +8=0
let me explain it to u by general form
ax^2 + bx +c=0
if this is the equation
then first
multiply 'a' with 'c'
then check that no.'s factor sum up or subtracts to result the number 'b'
like over here in ur e.g.
if u multiply 3 with 8 u will get 24
then make factors of 24
12*2 also gives u 24, right
and 12+2 also gives u 14
so now
3x^2 + 12x + 2x +8=0
take 3x common in first set and 2 in second
3x(x+4)+2(x+4)=0
now take x+4 common
(x+4)(3x+2)=0
x=-4; -2/3 ans

Answer 5

I usually factor using follwing method
1. Examine the last 8 and first number 3 in the eqaution.
Means that you look at 2nd degree number and the last one

Multiply both of them i.e 3x8=24
Now try to obtain factors that can help in making 14.
for 24 we have many different numbers like
1x24
2x12
3x8
4x6
but you can see 2x12 is perfect as it makes 24 by adding.
so i would go for 3x^2 +12x+2x+8=0

now its easy

3x( x + 4) +2(x + 4)=0
(3x+2)(x+4)=0

3x+2=0
x=-2/3
and
x=-4

Anyways factoring needs a lot of practice but i found this way very interesting.

remeber
1. See the numbers at degree 2 and last number and then multiply them.
2. Take the result and find compination of numbers that can make the middle number by addition or subtraction.

Answer 6

answer: (3x + 2)(x + 4).

remember FOIL: First, inside, outside, last...
first = 3x X x = 3x squared;
outside = 3x X 4 = 12x
inside = 2 X x = 2x
last = 2 X 4 = 8.

add them up to get 3x squared + 14X + 8.

you need to know that you have to factor the 8 into 2 components and the 3x squared into 2 components and match them up right so you get 14 x.

hope this helps

Answer 7

3x^2+14x+8=0
since c=8 is >0, both constants will have the same sign.
since b>0, both will be positive.
ac=3*8=24 so we need factoes of 24 that add uo to 14.
12*2 does the trick
12=3*4 so
(3x+2)(x+4)=0
by FOIL
3x^2+12x+2x+8=3x^2+14x+8

Roots are
3x=2=0
x=-2/3
x+4=0
x=-4

Answer 8

(3x + 4)(x + 2) I write the factors of the first and last number and place them in the standard form until the equation works

Answer 9

(3x + a) (x + b)

3x^2 + (3b + a) x + ab
try b=4, a = 2

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or,

3x^2+14x+8
a x^2 +b x + c

a = 3
b = 14
c = 8

x = (-b + sqrt(b^2-4*a*c))/(2*a)
x = (-b - sqrt(b^2-4*a*c))/(2*a) where sqrt means positive sqrt
x = (-14 +/- sqrt(196-96))/6

x = -4 or x = -2/3
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