Yes, first you find the p(x) = 0. I'll give you an example.
x^3-13x+12
p(-4)=-64 + 52 + 12 = 0
so (x+4) is a factor
Now open the bracket for x+4 and fix the other bracket
Firstly, we know that to get x^3 with x, we need to multiply it by x^2
(x+4)(x^2....)
Now, as you can see, by getting the x^3, you have also created a 4x^2. And if you look back into your equation, you need a -13x, so we need to somehow get rid of the 4x^2. We can do this by subtracting 4x from the next bracket.
(x+4)(x^2-4x....)
See how the x will multiply with the -4x to give you -4x^2? But now we have also created a -16x (the 4 x -4x), and the equation wants -13x, so we need to add 3x back.
(x+4)(x^2-4x+3)
Now we have our -13x, but we have also created a +12. Looking back into the rule, we need the +12, and so we have found 2 factors of the polynomial.
Finally, we can simplify the second bracket into another 2 factors, which gives us:
(x+4)(x-3)(x-1) as our factors.
dividing polynomials is just like dividing whole nos..
the shortcut way of dividing is mutiplying
The multiple of ten can be reduced to the smaller number by moving the decimal place of the numerator one place to the left. However, this may only be a marginal short cut. For example, dividing 1256 by 3450 is equivalent to dividing 125.6 by 345 but that is hardly a shortcut!
Yes, polynomials are closed under the operations of addition, subtraction, and multiplication. This means that when you add, subtract, or multiply two polynomials, the result is always another polynomial. For example, if ( p(x) ) and ( q(x) ) are polynomials, then ( p(x) + q(x) ), ( p(x) - q(x) ), and ( p(x) \cdot q(x) ) are all polynomials as well. However, polynomials are not closed under division, as dividing one polynomial by another can result in a non-polynomial expression.
Dividing polynomials can be done using either long division or synthetic division. In long division, you divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by that result, subtract it from the dividend, and repeat the process with the new polynomial. Synthetic division is a faster method applicable when dividing by a linear binomial, where you use the coefficients of the polynomial and perform a series of multiplications and additions. Both methods will yield a quotient and a remainder.
dividing polynomials is just like dividing whole nos..
the shortcut way of dividing is mutiplying
no
The French mathematician Descartes is credited with developing synthetic division as a method for dividing polynomials. It is a useful technique for dividing polynomials by linear factors and is commonly used in algebra and calculus.
Dividing polynomials is a lot easier for me. You'll have to divide it term by term like dividing normal numbers.
The multiple of ten can be reduced to the smaller number by moving the decimal place of the numerator one place to the left. However, this may only be a marginal short cut. For example, dividing 1256 by 3450 is equivalent to dividing 125.6 by 345 but that is hardly a shortcut!
Yes, polynomials are closed under the operations of addition, subtraction, and multiplication. This means that when you add, subtract, or multiply two polynomials, the result is always another polynomial. For example, if ( p(x) ) and ( q(x) ) are polynomials, then ( p(x) + q(x) ), ( p(x) - q(x) ), and ( p(x) \cdot q(x) ) are all polynomials as well. However, polynomials are not closed under division, as dividing one polynomial by another can result in a non-polynomial expression.
lesson 5-2 dividing polynomials
Dividing polynomials can be done using either long division or synthetic division. In long division, you divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by that result, subtract it from the dividend, and repeat the process with the new polynomial. Synthetic division is a faster method applicable when dividing by a linear binomial, where you use the coefficients of the polynomial and perform a series of multiplications and additions. Both methods will yield a quotient and a remainder.
Other polynomials of the same, or lower, order.
Move the decimal point two places to the left. It is the same as dividing by 100.
This is a tough question. There aren't many jobs that use monomials and polynomials daily but if you want to have a career as a math teacher you have to know this.