Question

2x^2+19x+24
How do u work this out?

Answer 1

AC Method
2x^2 + 19x + 24
General formula: ax^2 + bx + c
a=2, b=19, c=24

Step 1: Multiply a by c
2 * 24 = 48

Step 2: Find two numbers which multiply to make ac (in this case 48) and add to make b (in this case 19)
1 * 48 = 48, 1 + 48 does not equal 19
2 * 24 = 48, 2 + 24 does not equal 19
3 * 16 = 48, 3 + 16 equals 19

Step 3: Split bx into the two numbers from step 2
2x^2 + 19x + 24
=2x^2 + 16x + 3x +24
Step 4: Factorise the equation
2x^2 + 16x + 3x + 24
= [2x^2 + 16x] + [3x + 24] <----find the common factor
= 2x[x + 8] + 3[x + 8]

Step 5: Gather the numbers together
2x[x + 8] + 3[x + 8]
=(2x + 3)(x+8)

The answer is (2x + 3)(x + 8)

If question asks for solutions for x:

(2x + 3)(x + 8) = 0

2x + 3 = 0, x + 8 = 0

Therefore:

2x + 3 = 0 x + 8 = 0
2x = -3 x = -8
x = -3/2

Answer 2

2x2-19x=-24 Two solutions were found : x = 3/2 = 1.500
x = 8 Rearrange:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*x^2-19*x-(-24)=0 Step by step solution Step 1 :Equation at the end of step 1 : (2x2 - 19x) - -24 = 0 Step 2 :Trying to factor by splitting the middle term 2.1 Factoring 2x2-19x+24

The first term is, 2x2 its coefficient is 2 .
The middle term is, -19x its coefficient is -19 .
The last term, "the constant", is +24

Step-1 : Multiply the coefficient of the first term by the constant 2 • 24 = 48

Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -19 .
-48 + -1 = -49 -24 + -2 = -26 -16 + -3 = -19 That's it Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and -3
2x2 - 16x - 3x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-8)
Add up the last 2 terms, pulling out common factors :
3 • (x-8)
Step-5 : Add up the four terms of step 4 :
(2x-3) • (x-8)
Which is the desired factorizationEquation at the end of step 2 : (x - 8) • (2x - 3) = 0 Step 3