(4z²+8z+3/2z²-5z+3)(6z²-9z/1-4z²)
Answers
Answer:
0
Step-by-step explanation:
Equation at the end of step 1
3 z
(((((4•(z2))+8z)+(—•(z2)))-5z)+3)•(((6•(z2))-(9•—))-22z2)
2 1
STEP
2
:
z
Simplify —
1
Equation at the end of step
2
:
3
(((((4•(z2))+8z)+(—•(z2)))-5z)+3)•(((6•(z2))-(9•z))-22z2)
2
STEP
3
:
Equation at the end of step
3
:
3
(((((4•(z2))+8z)+(—•(z2)))-5z)+3)•(((2•3z2)-9z)-22z2)
2
STEP
4
:
3
Simplify —
2
Equation at the end of step
4
:
3
(((((4•(z2))+8z)+(—•z2))-5z)+3)•(2z2-9z)
2
STEP
5
:
Equation at the end of step 5
3z2
(((((4•(z2))+8z)+———)-5z)+3)•(2z2-9z)
2
STEP
6
:
Equation at the end of step
6
:
3z2
((((22z2 + 8z) + ———) - 5z) + 3) • (2z2 - 9z)
2
STEP
7
:
Rewriting the whole as an Equivalent Fraction
7.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 2 as the denominator :
4z2 + 8z (4z2 + 8z) • 2
4z2 + 8z = ———————— = ——————————————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
8
:
Pulling out like terms
8.1 Pull out like factors :
4z2 + 8z = 4z • (z + 2)
Adding fractions that have a common denominator :
8.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
4z • (z+2) • 2 + 3z2 11z2 + 16z
———————————————————— = ——————————
2 2
Equation at the end of step
8
:
(11z2 + 16z)
((———————————— - 5z) + 3) • (2z2 - 9z)
2
STEP
9
:
Rewriting the whole as an Equivalent Fraction :
9.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 2 as the denominator :
5z 5z • 2
5z = —— = ——————
1 2
STEP
10
:
Pulling out like terms :
10.1 Pull out like factors :
11z2 + 16z = z • (11z + 16)
Adding fractions that have a common denominator :
10.2 Adding up the two equivalent fractions
z • (11z+16) - (5z • 2) 11z2 + 6z
——————————————————————— = —————————
2 2
Equation at the end of step
10
:
(11z2 + 6z)
(——————————— + 3) • (2z2 - 9z)
2
STEP
11
:
Rewriting the whole as an Equivalent Fraction :
11.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 2 as the denominator :
3 3 • 2
3 = — = —————
1 2
STEP
12
:
Pulling out like terms :
12.1 Pull out like factors :
11z2 + 6z = z • (11z + 6)
Adding fractions that have a common denominator :
12.2 Adding up the two equivalent fractions
z • (11z+6) + 3 • 2 11z2 + 6z + 6
——————————————————— = —————————————
2 2
Equation at the end of step
12
:
(11z2 + 6z + 6)
——————————————— • (2z2 - 9z)
2
STEP
13
:
STEP
14
:
Pulling out like terms :
14.1 Pull out like factors :
2z2 - 9z = z • (2z - 9)
Trying to factor by splitting the middle term
14.2 Factoring 11z2 + 6z + 6
The first term is, 11z2 its coefficient is 11 .
The middle term is, +6z its coefficient is 6 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 11 • 6 = 66
Step-2 : Find two factors of 66 whose sum equals the coefficient of the middle term, which is 6 .
-66 + -1 = -67
-33 + -2 = -35
-22 + -3 = -25
-11 + -6 = -17
-6 + -11 = -17
-3 + -22 = -25
-2 + -33 = -35
-1 + -66 = -67
1 + 66 = 67
2 + 33 = 35
3 + 22 = 25
6 + 11 = 17
11 + 6 = 17
22 + 3 = 25
33 + 2 = 35
66 + 1 = 67
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
z • (11z2 + 6z + 6) • (2z + 9)
————————————————————————