Introduction to reasoning possibility math:
Math problems are not so hard if we perform in a proper step by step procedure the subject contains addition, subtraction, measurement, number sense, multiplication, functions, adding and subtraction of decimals, fractions & mixed numbers, division, algebra, geometry, algebra function, probability and statistics number using words decimals.
Additions of Polynomials- Reasoning Possibility Math:
In the higher degree polynomial, we add two polynomials by adding the coefficients of the like powers.
Example for higher degree polynomial
Example 1: Find the sum of `47x^4- 2x^2 + 8x + 10 and 4x^3- 4x^2 +3x - 1.`
Solution:
By using the distributive and associative properties, we obtain
`(57x^4 - 2x^2 + 8x + 10) + (4x^3- 4x^2 + 3x - 1)`
`= 57x^4 + 4x^3-4x^2 - 2x^2 + 8x + 3x + 10 - 1`
`= 57x^4 + 4x^3- (2+4) x^2 + (8+3) x + 9`
`= 57x^4 + 4x^3 - 6x^2+ 11x + 9.`
Reasoning possibility math-Subtraction of polynomials
We subtract polynomials like addition of polynomials.
Example of higher degree polynomial
Example 2: `Subtract 17x^4-7x^2 - 8 from 49x^4 + 4x^2 - 5x - 9.`
Solution:
`(49x^4 + 4x^2 - 5x - 9) - (17x^4 - 7x^2 - 8)`
`=49 x^4 + 4x^2 - 5x - 9 - 17x^4+ 7x^2 + 8`
`=49 x^4 - 17x^4 + 4x^2 + 7x^2 - 5x - 9 + 8`
`= (49x^4 - 17x^4) + (4x^2 + 7x^2) + (-5x) + (-9+8)`
`= 32x^4 + 11x^2 - 5x - 1.`
Reasoning possibility math- slope problems:
Problem 1:
Find the slope of the line which is passing through `(-1, 2) and (7,-3)`
Solution:
We are having the formula to find the slope `m = (y2 - y1) / (x2 - x1)`
Here `(x1, y1) = (-1, 2) (x2, y2) = (7, -3)`
So `m =(-3-2)/( 7+1)`
Slope `m = -5/8`
Slope `m = -5/8`
Here we solved the slope problem. m is the slope of the given line which is passing through the points.
Reasoning Possibility Math on Combining Like Terms:
It is common to simplify an expression using combine terms. We are combining the like terms based on the degree of the term.
Example:
`27x + 5 + 9x = 16x + 3`
`27x + 9x - 16x = 3 - 5`
`20x-0=-2`
`20x=-2.`
`x = -2/20`
Final result: `x= -2/20.`
Math problems are not so hard if we perform in a proper step by step procedure the subject contains addition, subtraction, measurement, number sense, multiplication, functions, adding and subtraction of decimals, fractions & mixed numbers, division, algebra, geometry, algebra function, probability and statistics number using words decimals.
Additions of Polynomials- Reasoning Possibility Math:
In the higher degree polynomial, we add two polynomials by adding the coefficients of the like powers.
Example for higher degree polynomial
Example 1: Find the sum of `47x^4- 2x^2 + 8x + 10 and 4x^3- 4x^2 +3x - 1.`
Solution:
By using the distributive and associative properties, we obtain
`(57x^4 - 2x^2 + 8x + 10) + (4x^3- 4x^2 + 3x - 1)`
`= 57x^4 + 4x^3-4x^2 - 2x^2 + 8x + 3x + 10 - 1`
`= 57x^4 + 4x^3- (2+4) x^2 + (8+3) x + 9`
`= 57x^4 + 4x^3 - 6x^2+ 11x + 9.`
Reasoning possibility math-Subtraction of polynomials
We subtract polynomials like addition of polynomials.
Example of higher degree polynomial
Example 2: `Subtract 17x^4-7x^2 - 8 from 49x^4 + 4x^2 - 5x - 9.`
Solution:
`(49x^4 + 4x^2 - 5x - 9) - (17x^4 - 7x^2 - 8)`
`=49 x^4 + 4x^2 - 5x - 9 - 17x^4+ 7x^2 + 8`
`=49 x^4 - 17x^4 + 4x^2 + 7x^2 - 5x - 9 + 8`
`= (49x^4 - 17x^4) + (4x^2 + 7x^2) + (-5x) + (-9+8)`
`= 32x^4 + 11x^2 - 5x - 1.`
Reasoning possibility math- slope problems:
Problem 1:
Find the slope of the line which is passing through `(-1, 2) and (7,-3)`
Solution:
We are having the formula to find the slope `m = (y2 - y1) / (x2 - x1)`
Here `(x1, y1) = (-1, 2) (x2, y2) = (7, -3)`
So `m =(-3-2)/( 7+1)`
Slope `m = -5/8`
Slope `m = -5/8`
Here we solved the slope problem. m is the slope of the given line which is passing through the points.
Reasoning Possibility Math on Combining Like Terms:
It is common to simplify an expression using combine terms. We are combining the like terms based on the degree of the term.
Example:
`27x + 5 + 9x = 16x + 3`
`27x + 9x - 16x = 3 - 5`
`20x-0=-2`
`20x=-2.`
`x = -2/20`
Final result: `x= -2/20.`
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