Algebra anyone please help?

Question

I need to factor4x^2 + 44x + 96 I do not know how to do this and I need to show each step of factoring out the GCF before I go to the next step, can anyone please help with this I am so lost on this
Thanks a great deal

Answer 1

4x^2 + 44x + 96

Note that 4 is a common factor
4(x^2 + 11x + 24)

Look at the coefficients. Coefficient of x^2 is 1, coefficient of x is 11 and constant term is 24.
Multiply the constant term by the coefficient of x^2 ---- 24*1=24
Find two numbers whose product is 24 and whose sum is the coefficient of x (11) ---- 8 and 3
11x = 8x+3x

4(x^2 + 11x + 24)
= 4[x^2 + 8x + 3x + 24]
= 4[x(x+8) + 3(x+8)]
= 4(x+8)(x+3)

Answer 2

Common factor first

4x² + 44x + 96 = 0

4(x² + 11x + 24) = 0

The middle term inside the parenthesis is + 11x

Find the sum of the middle term

First term x² = 1

Multiply the first term 1 times the last term 24 equals 24 and factor

Factors of 24

1 x 24
2 x 12
3 x 8. . .<=. .use these factors
4 x 6

+ 3 and + 8 satisfy the sum of the middle term

Insert + 3x + 8x into the equation

4(x² + 11x + 24 = 0

Group factor

4(x² + 3x + 8x + 24 = 0

4[x(x + 3) + 8(x + 3) = 0

4(x + 8)(x + 3) = 0

- - - - - - - -

Roots

4 = 0

- - - - - - -

Roots

x + 8 = 0

x + 8 - 8 = 0 - 8

x = - 8

- - - - - - -

Roots

x + 3 = 0

x + 3 - 3 = 0 - 3

x = - 3

- - - - - - -s-

Answer 3

okay I don't know about how to show your work but that's a simple quadratic equation. You have 4x^2 so you know each factor is going to have 2x so now you have
(2x+?)(2x+?)
so you have to say, what two numbers will add to 22 and multiply to 96? (add to 22 because it's half of 44, because each number will be multiplied by 2) those numbers are 16 and 6. so now you have
(2x+6)(2x+16)
and you use foil to check your answer
2x*2x+2x*16+2x*6+6*16=
4x^2+32x+12x+96=
4x^2+44x+96 which was the original problem so you know it's right. The only method I know for finding the GCF is a computer algorithm so I don't think it'd help you much.

Answer 4

the general formula to find the factors as follows

ax^2+bx+c=0
for this equation the factors are

(-b+Sqr(b^2-4ac))/2a ... (1)
(-b-Sqr(b^2-4ac))/2a ...(2)

as per your question 4x^2 + 44x + 96=0
a=4
b=44
c=96

substitute the values in equation 1 and 2

as per equ 1
(-44+Sqrt( 44^2 - (4) (4) ( 96)) /(2)(4)
(-44+Sqrt( 1936 - 1536))/ 8
(-44+Sqrt( 400)) / 8
(-44+20) / 8
-24/8
-3

as per equ 2
(-44 - Sqrt( 44^2 - (4) (4) ( 96)) /(2)(4)
(-44 - Sqrt( 1936 - 1536))/ 8
(-44 - Sqrt( 400)) / 8
(-44 - 20) / 8
-64/8
-8
so roots are x= -3 and x=-8

Answer 5

(4x+12)(x+8), I just did it by looking at it and trying different numbers that multiply to 96, in otherwords, trial and error.