p^2+27x-90 factoristion
Answers
Answer:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring x2-27x-90
The first term is, x2 its coefficient is 1 .
The middle term is, -27x its coefficient is -27 .
The last term, "the constant", is -90
Step-1 : Multiply the coefficient of the first term by the constant 1 • -90 = -90
Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -27 .
-90 + 1 = -89
-45 + 2 = -43
-30 + 3 = -27 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -30 and 3
x2 - 30x + 3x - 90
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-30)
Add up the last 2 terms, pulling out common factors :
3 • (x-30)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-30)
Which is the desired factorization
Equation at the end of step
1
:
(x + 3) • (x - 30) = 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 : x+3 = 0
Subtract 3 from both sides of the equation :
x = -3
Solving a Single Variable Equation:
2.3 Solve : x-30 = 0
Add 30 to both sides of the equation :
x = 30
Supplement : Solving Quadratic Equation Directly
Solving x2-27x-90 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula