Answer:
2t^2 - 37t + 171
Step-by-step explanation:
distrube the - to the (t-9) and then combine like terms
Answer:(2t2 + 27t) - 162 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 2t2+27t-162
The first term is, 2t2 its coefficient is 2 .
The middle term is, +27t its coefficient is 27 .
The last term, "the constant", is -162
Step-1 : Multiply the coefficient of the first term by the constant 2 • -162 = -324
Step-2 : Find two factors of -324 whose sum equals the coefficient of the middle term, which is 27 .
-324 + 1 = -323
-162 + 2 = -160
-108 + 3 = -105
-81 + 4 = -77
-54 + 6 = -48
-36 + 9 = -27
-27 + 12 = -15
-18 + 18 = 0
-12 + 27 = 15
-9 + 36 = 27 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 36
2t2 - 9t + 36t - 162
Step-4 : Add up the first 2 terms, pulling out like factors :
t • (2t-9)
Add up the last 2 terms, pulling out common factors :
18 • (2t-9)
Step-5 : Add up the four terms of step 4 :
(t+18) • (2t-9)
Which is the desired factorization
Equation at the end of step
2
:
(2t - 9) • (t + 18) = 0
STEP
3
:
Theory - Roots of a product
3.1 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:
Step-by-step explanation:
