How to Write Zeros as Factors and Find the Polynomial

When given zeros to find a function, we need to remember that factors multiply to give us our polynomial. For example, if we have the factors 6 and 2, they evenly divide into 12, meaning 6 times 2 gives us 12. The same applies to our polynomial. If we’re given zeros, we need to write them as factors.

To write zeros as factors, we need to remember how we go from factors to zeros. For instance, if we have x² + 9 and x – 1 = 0, we set the zero product property and solve for zero, which gives us x = 1. If we have a square, we have x² = -9, then we square root and get x = ± √(-9). If given one complex number as a root, we need to include the opposite value because when we take the square root to find the zero, it’s always going to be plus or minus.

Now that we have our zeros, we can write them as a series of factors. For example, x – 4, x + 3i, and x – 3i. To get x – 4, we set the x-intercept equal to 4, then subtract the 4 on the other side.

To multiply our factors and find our polynomial, we can use the difference of two squares to make it quicker. For instance, if our first two terms are the same as the last two terms, we can rewrite them as x² – 3i². Since i² is -1, -3i² equals +3. Then, we can multiply the two binomials to get our polynomial, which will be x³ – 4x² + 9x – 36.

In summary, when given zeros, we need to write them as factors to find our polynomial. We can use the zero product property to solve for zero, then multiply our factors using the difference of two squares.


Does full format write zeros?
By default in Windows Vista and later versions, the format command writes zeros to the whole disk when a full format is performed. In Windows XP and earlier versions of Windows, the format command doesn't write zeros to the whole disk when a full format is performed.
What is writing zeros?
Write Zero, also known as Single Overwrite, zero fill erase or zero-fill, is one of the most popular methods. The Write Zero data sanitization method replaces your regular, readable data with zeros, thus preventing all software-based file recovery methods from lifting information from the drive.
How do I write zeros to my hard drive?
Method 1: Zero format hard drive with Format Type cmd in the search box, right-click it and select Run as administrator. Step 2. Type format f: /fs: NTFS /p:2 and hit Enter. This command will format the F drive with the NTFS file system and write all zeros to every sectors of the hard drive twice.
What is zero format?
Zero filling is a method of formatting a hard disk whereby the formatter wipes the disk contents by overwriting them with zeros. Each bit present in the disk is replaced by a zero value, hence the name zero filling.