What is the value of h such that 2h-3 \3-5h = - 6 \ 11 ?
Answers
Step-by-step explanation: Step by Step Solution:
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STEP
1
:
Equation at the end of step 1
STEP
2
:
Equation at the end of step
2
:
STEP
3
:
2h3 - 5h2 + 22h
Simplify ———————————————
2h + 3
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2h3 - 5h2 + 22h = h • (2h2 - 5h + 22)
Trying to factor by splitting the middle term
4.2 Factoring 2h2 - 5h + 22
The first term is, 2h2 its coefficient is 2 .
The middle term is, -5h its coefficient is -5 .
The last term, "the constant", is +22
Step-1 : Multiply the coefficient of the first term by the constant 2 • 22 = 44
Step-2 : Find two factors of 44 whose sum equals the coefficient of the middle term, which is -5 .
-44 + -1 = -45
-22 + -2 = -24
-11 + -4 = -15
-4 + -11 = -15
-2 + -22 = -24
-1 + -44 = -45
1 + 44 = 45
2 + 22 = 24
4 + 11 = 15
11 + 4 = 15
22 + 2 = 24
44 + 1 = 45
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Polynomial Long Division :
4.3 Polynomial Long Division
Dividing : 2h2-5h+22
("Dividend")
By : 2h+3 ("Divisor")
dividend 2h2 - 5h + 22
- divisor * h1 2h2 + 3h
remainder - 8h + 22
- divisor * -4h0 - 8h - 12
remainder 34
Quotient : h-4
Remainder : 34
Final result :
h • (2h2 - 5h + 22)
———————————————————
2h + 3
See results of polynomial long division:
1. In step #04.03