Divide: (x^2 - 2x - 35) / (x +5)
Answers
Answer:
x�-2x-35
����������
x+5
There are 3 ways to do it, depending on
where you are in the book.
---------------------------------------
Method 1: Long division:
x - 7
x + 5)x� - 2x - 35
x� + 5x
-7x - 35
-7x - 35
0
So the answer is the quotient x - 7
----------------------------------------
Method 2: Synthetic division:
_________
-5|1 -2 -35
| -5 35
1 -7 0
So the answer is x - 7
----------------------------------------
Method 3: Factoring and canceling:
x�-2x-35
����������
x+5
Factor the trinomial numerator.
x�-2x-35
(x )(x )
Think of two integers whose product is 35
and whose difference is 2. They are 7 and 5
(x 7)(x 5)
Then since the 7 is larger it gets the same
sign as the -2x or -, and the 5 gets the
opposite sign, +
(x-7)(x+5)
So the fraction
x�-2x-35
����������
x+5
becomes
(x-7)(x+5)
������������
x+5
Now cancel the x+5 in the
denominator into the (x+5)
in the numerator:
1
(x-7)(x+5)
������������
x+5
1
This leaves
(x-7)
or just
x - 7
Step-by-step explanation: mark me as brainlist if this is correct
Simplify (x^2-2x-35)÷(x+5)
(x2−2x−35)÷(x+5)(x2-2x-35)÷(x+5)
Rewrite the division as a fraction.
x2−2x−35x+5x2-2x-35x+5
Factor x2−2x−35x2-2x-35 using the AC method.
Consider the form x2+bx+cx2+bx+c. Find a pair of integers whose product is cc and whose sum is bb. In this case, whose product is −35-35 and whose sum is −2-2.
−7,5-7,5
Write the factored form using these integers.
(x−7)(x+5)x+5(x-7)(x+5)x+5
Cancel the common factor of x+5x+5.
Cancel the common factor.
(x−7)(x+5)x+5(x-7)(x+5)x+5
Divide x−7x-7 by 11.
x−7