Answer:
Step-by-step explanation:
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p2-5p-24=0
Two solutions were found :
p = 8
p = -3
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "p2" was replaced by "p^2".
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring p2-5p-24
The first term is, p2 its coefficient is 1 .
The middle term is, -5p its coefficient is -5 .
The last term, "the constant", is -24
Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24
Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -5 .
-24 + 1 = -23
-12 + 2 = -10
-8 + 3 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 3
p2 - 8p + 3p - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (p-8)
Add up the last 2 terms, pulling out common factors :
3 • (p-8)
Step-5 : Add up the four terms of step 4 :
(p+3) • (p-8)
Which is the desired factorization
Equation at the end of step 1 :
(p + 3) • (p - 8) = 0
Step 2 :
Theory - Roots of a product :
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
2.2 Solve : p+3 = 0
Subtract 3 from both sides of the equation :
p = -3
Solving a Single Variable Equation :
2.3 Solve : p-8 = 0
Add 8 to both sides of the equation :
p = 8
