Final answer:
To find the multiplicity of a repeated zero in a polynomial, look at the exponent of the corresponding factor. Multiplicity equals the exponent indicating how many times the zero is repeated. Understanding exponents helps in manipulating numbers, such as moving the decimal point when multiplying by powers of ten.
Step-by-step explanation:
To find the multiplicity of the repeated zero, you need to look at the exponent of the factor in the polynomial that corresponds to that zero. The multiplicity is the number of times that particular zero appears as a root of the polynomial equation. For instance, if a polynomial has a factor of (x - 2)^3, the zero 2 has a multiplicity of 3 because the factor is raised to the power of 3.
By understanding exponents and their properties, you can determine the multiplicity of zeros. For example, the exponent indicates the number of times the base number is used as a factor. When dealing with powers of ten, this concept helps when you're moving the decimal point to perform multiplication without using the vertical format. Look at the number of zeros and move the decimal point accordingly. Remember that zeros or exponents in mathematical operations can change numbers significantly. For example, Rule 4 of significant figures states that not all trailing zeros may be significant, which is essential when dealing with decimal places.