Factor the polynomial: 7a–7b–bn+an
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Trying to factor a multi variable polynomial :
1.1 Split 7a - 7b - bn + an
into two 2-term polynomials
- 7b + 7a and - bn + an
This partition looks good
1.2 Pull out from each binomial separately
- 7b + 7a = + 7 • (-b + a)
- bn + an = + n • (-b + a)
1.3 Add up to arrive at the desired factorization
(7 + n) • (-b + a)
Factorization found :
(7 + n) • (-b + a)
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avabmoser:
You're so nice... thanks for all of your help!
is it okay if you help me with that other one?
Factor the polynomial: 1–bx–x+b
ok
Simplify x / b
Equation at the end of step 1 :
x
(— - 1) - (xb + 4) = 0
b
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using b as the denominator :
1 1 • b
1 = — = —————
1 b
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
Equation at the end of step 1 :
x
(— - 1) - (xb + 4) = 0
b
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using b as the denominator :
1 1 • b
1 = — = —————
1 b
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
Equation at the end of step 2 :
(x - b)
——————— - (xb + 4) = 0
b
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using b as the denominator :
xb + 4 (xb + 4) • b
xb + 4 = —————— = ————————————
1 b
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
(x - b)
——————— - (xb + 4) = 0
b
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using b as the denominator :
xb + 4 (xb + 4) • b
xb + 4 = —————— = ————————————
1 b
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Pulling out like terms :
4.1 Pull out like factors :
-xb2 + x - 5b = -1 • (xb2 - x + 5b)
Trying to factor a multi variable polynomial :
4.2 Factoring xb2 - x + 5b
Try to factor this multi-variable trinomial using trial and error
Factorization fails
4.1 Pull out like factors :
-xb2 + x - 5b = -1 • (xb2 - x + 5b)
Trying to factor a multi variable polynomial :
4.2 Factoring xb2 - x + 5b
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Equation at the end of step 4 :
-xb2 + x - 5b
————————————— = 0
b
Step 5 :
When a fraction equals zero :
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
-xb2 + x - 5b
————————————— = 0
b
Step 5 :
When a fraction equals zero :
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-xb2+x-5b
————————— • b = 0 • b
b
Now, on the left hand side, the b cancels out the denominator, while, on the right hand side, zero times anything is still zero.
-xb2+x-5b
————————— • b = 0 • b
b
Now, on the left hand side, the b cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-xb2+x-5b = 0
Solving a Single Variable Equation :
5.2 Solve -xb2+x-5b = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
No solutions found
-xb2+x-5b = 0
Solving a Single Variable Equation :
5.2 Solve -xb2+x-5b = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
No solutions found
Answered by
2
7a-7b-bn+an
=7(a-b)+n(a-b)=0
=(a-b)(7+n)=0
a=b or n=-7
:)
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