x^3+2x^2-5x-6, x+3
I need help factoring this problem
The answer that I got was
x^3+2x^2-11x+3
Exactly what is that comma in the first line? What are you factoring?
That is one of the problems that I had, The comma is there in the book, I've tried asking my teacher but he has not responded.If I find out I will let you know thanks so much for your help.
11x + 4y = 1
To factor the expression x^3+2x^2-5x-6 by the given factor (x+3), you can use the synthetic division method. Here's how you can do it:
Step 1: Write out the given expression as coefficients of each term in descending order of powers of x:
1x^3 + 2x^2 - 5x - 6
Step 2: Set up synthetic division by writing the factor (x+3) as -3 on the left side:
-3 | 1 2 -5 -6
Step 3: Bring down the first coefficient (1) under the line:
-3 | 1 2 -5 -6
1
Step 4: Multiply the factor (-3) by the value on the bottom row and write the result above the line, under the corresponding term:
-3 | 1 2 -5 -6
1 -3
Step 5: Add the two numbers vertically and write the sum under the line:
-3 | 1 2 -5 -6
1 -3
_______
1 -1
Step 6: Repeat steps 4 and 5 by multiplying the factor (-3) with the new value (-1) and adding the result under the line:
-3 | 1 2 -5 -6
1 -3 6
________
1 -1 1
Step 7: The numbers in the bottom row of the synthetic division represent the coefficients of the quotient after removing the factor (x+3). So, the quotient is: 1x^2 - 1x + 1
The factored form of the expression x^3+2x^2-5x-6 is (x+3)(1x^2 - 1x + 1).
Please note that checking your factored answer by multiplying it out should give you the initial expression.