Factorise p²-2p-120
Answers
Answer:
Factoring p2+2p-120
The first term is, p2 its coefficient is 1 .
The middle term is, +2p its coefficient is 2 .
The last term, "the constant", is -120
Step-1 : Multiply the coefficient of the first term by the constant 1 • -120 = -120
Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is 2 .
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14
-15 + 8 = -7
-12 + 10 = -2
-10 + 12 = 2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 12
p2 - 10p + 12p - 120
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (p-10)
Add up the last 2 terms, pulling out common factors :
12 • (p-10)
Step-5 : Add up the four terms of step 4 :
(p+12) • (p-10)
Which is the desired factorization
Equation at the end of step
1
:
(p + 12) • (p - 10) = 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+12 = 0
Subtract 12 from both sides of the equation :
p = -12
Solving a Single Variable Equation:
2.3 Solve : p-10 = 0
Add 10 to both sides of the equation :
p = 10
Supplement : Solving Quadratic Equation Directly
Solving p2+2p-120 =
