Factories x2+27x+72..........?
Answers
Step-by-step explanation:
➡Given here .
↪X² + 27x + 72 = 0
↪X² + 24 x + 3x +72 =0
↪X(x+24)+3(x+24)=0
↪(X+3)(X+24)=0
➡This is Factor.
✏Hopes its helps u.
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Answer:
X=3 and X=72
Step-by-step explanation:
The first term is, x2 its coefficient is 1 .
The middle term is, -27x its coefficient is -27 .
The last term, "the constant", is +72
Step-1 : Multiply the coefficient of the first term by the constant 1 • 72 = 72
Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is -27 .
-72 + -1 = -73
-36 + -2 = -38
-24 + -3 = -27 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and -3
x2 - 24x - 3x - 72
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-24)
Add up the last 2 terms, pulling out common factors :
3 • (x-24)
Step-5 : Add up the four terms of step 4 :
(x-3) • (x-24)
Which is the desired factorization
Equation at the end of step
1
:
(x - 3) • (x - 24) = 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
Add 3 to both sides of the equation :
x = 3
Solving a Single Variable Equation:
2.3 Solve : x-24 = 0
Add 24 to both sides of the equation :
x = 24
Supplement : Solving Quadratic Equation Directly
Solving x2-27x+72 = 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