1) x2 - 110x + 2856 answer the questions please
Answers
Answer:
Step-by-step explanation:
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 x2-110x+2856
The first term is, x2 its coefficient is 1 .
The middle term is, -110x its coefficient is -110 .
The last term, "the constant", is +2856
Step-1 : Multiply the coefficient of the first term by the constant 1 • 2856 = 2856
Step-2 : Find two factors of 2856 whose sum equals the coefficient of the middle term, which is -110 .
-2856 + -1 = -2857
-1428 + -2 = -1430
-952 + -3 = -955
-714 + -4 = -718
-476 + -6 = -482
-408 + -7 = -415
-357 + -8 = -365
-238 + -12 = -250
-204 + -14 = -218
-168 + -17 = -185
-136 + -21 = -157
-119 + -24 = -143
-102 + -28 = -130
-84 + -34 = -118
-68 + -42 = -110 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -68 and -42
x2 - 68x - 42x - 2856
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-68)
Add up the last 2 terms, pulling out common factors :
42 • (x-68)
Step-5 : Add up the four terms of step 4 :
(x-42) • (x-68)
Which is the desired factorization
Equation at the end of step
1
:
(x - 42) • (x - 68) = 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-42 = 0
Add 42 to both sides of the equation :
x = 42
Solving a Single Variable Equation:
2.3 Solve : x-68 = 0
Add 68 to both sides of the equation :