8x^2 + 6 + 16x ÷ 3 + 2x
3x − 6x^2 − 54 + 9x^3 ÷ 3x − 6
13x^2 − 13x + 3x^3 + 2 ÷ 3x − 2
Don't forget to ORDER the Dividend and Divisor Polynomials at the beginning.
HELP ME WITH THIS PLS
Answers
Answer:
ok I am taking step by step thank u
Answer:
STEP
1
:
Equation at the end of step 1
STEP
2
:
Equation at the end of step
2
:
STEP
3
:
6x2 - 13x - 5
Simplify —————————————
9x3 - x
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
9x3 - x = x • (9x2 - 1)
Trying to factor by splitting the middle term
4.2 Factoring 6x2 - 13x - 5
The first term is, 6x2 its coefficient is 6 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 6 • -5 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -13 .
-30 + 1 = -29
-15 + 2 = -13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 2
6x2 - 15x + 2x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x-5)
Add up the last 2 terms, pulling out common factors :
1 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(3x+1) • (2x-5)
Which is the desired factorization
Trying to factor as a Difference of Squares:
4.3 Factoring: 9x2-1
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (3x + 1) • (3x - 1)