find the value of b if b^2x^2+3bx - b is exactly divisible by x-3
Answers
Answer:
We can write large numbers in a shorter form using exponents.
Observe 10, 000 = 10 × 10 × 10 × 10 = 104
The short notation 104 stands for the product 10×10×10×10. Here ‘10’ is called the base and ‘4’ the exponent. The number 104 is read as 10 raised to the power of 4 or simply as fourth power of 10. 104 is called the exponential form of 10,000.
We can similarly express 1,000 as a power of 10. Since 1,000 is 10 multiplied by itself three times,
1000 = 10 × 10 × 10 = 103
Here again, 103 is the exponential form of 1,000.
Similarly, 1,00,000 = 10 × 10 × 10 × 10 × 10 = 105
105 is the exponential form of 1,00,000
In both these examples, the base is 10; in case of 103, the exponent is 3 and in case of 105 the exponent is 5.
Mathematics
We have used numbers like 10, 100, 1000 etc., while writing numbers in an expanded form. For example, 47561 = 4 × 10000 + 7 × 1000 + 5 × 100 + 6 × 10 + 1
This can be written as 4 × 104 + 7 ×103 + 5 × 102 + 6 × 10 + 1.
Try writing these numbers in the same way 172, 5642, 6374.
In all the above given examples, we have seen numbers whose base is 10. However the base can be any other number also. For example:
81 = 3 × 3 × 3 × 3 can be written as 81 = 34, here 3 is the base and 4 is the exponent.
Some powers have special names. For example,
102, which is 10 raised to the power 2, also read as ‘10 squared’ and
103, which is 10 raised to the power 3, also read as ‘10 cubed’.
Can you tell what 53 (5 cubed) means?
53 means 5 is to be multiplied by itself three times, i.e., 53 = 5 × 5 × 5 = 125
So, we can say 125 is the third power of 5.
What is the exponent and the base in 53?
Similarly, 25 = 2 × 2 × 2 × 2 × 2 = 32, which is the fifth power of 2.
In 25, 2 is the base and 5 is the exponent.
In the same way,
243 = 3 × 3 × 3 × 3 × 3 = 35
64 = 2 × 2 × 2 × 2 × 2 × 2 = 26
625 = 5 × 5 × 5 × 5 = 54
Step-by-step explanation: