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The sum of 3.0478 and 4.92 is , which have 5 significant digits.
<u>Step-by-step explanation:</u>
We have , and
. The significant digits of a number are digits that includes all digits except:
- All leading zeros. For example, "013" has two significant figures: 1 and 3;
- Trailing zeros when they are merely placeholders to indicate the scale of the number and ,
- Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.
Here and with significant digit rules
. Now, Sum of both numbers =
⇒Sum of both numbers =
⇒Sum of both numbers =
∴ The sum of 3.0478 and 4.92 is , which have 5 significant digits.
Answer:
f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8
Step-by-step explanation:
If p is a zero, then (x -p) is a factor. The multiplicity of the zero tells you how many times that is a factor (its exponent).
f(x) = (x -1)²(x +2)³ = (x² -2x +1)(x³ +6x² +12x +8)
f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8
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<em>Additional comment</em>
You can use the distributive property to write out the 12 terms of the product of the two expanded factors, or you can do a little mental arithmetic based on what you know about the exponent of a product term. (It is the sum of the exponents of its factors.)
The mental exercise can be made easier by writing the coefficients of the factors as though they were two cubics. It works well to write them in two rows:
The columns are in order of decreasing powers of x. A relatively simple and symmetrical pattern of sums of cross products is used to find the coefficients of the final polynomial. Working in order of decreasing exponents, we have ...
coefficient of x^6 = (0)(1) = 0
coefficient of x^5 = (0)(6) +(1)(1) = 1
coefficient of x^4 = (0)(12) +(1)(-2) +(1)(6) = 4
coefficient of x^3 = (0)(8) +(1)(1) +(1)(12) +(6)(-2) = 1
coefficient of x^2 = (1)(8) +(6)(1) +(-2)(12) = -10
coefficient of x^1 = (-2)(8) +(12)(1) = -4
coefficient of x^0 = (1)(8) = 8