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Q: If y³3y plus 4x0 find y by implicit differentiation?

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is 1

You would add 4.

identity property of multiplication

The first five multiples of four are: (Not including 4x0=0) 4,8,12,16,20

-4X0=0 because when you multiply 0 with another number the answer will always be 0 even if it is a negative number.

4x0=0 4x1=1 4x2=8 4x3=12 4x4=16 4x5=20

5x0=4x0 The answer at the end would be 0=0

double the number of itself , but when it is 1 or 0 , for 1 , you get 1 , for 0 you get 0 . Meaning for example , 1 . 1x1=1 2x1=2 3x1=3 4x1=4 The 2nd example would be , 1x0=0 2x0=0 3x0=0 4x0=0

3x5+ 15x3+ 12xAll of these terms have a common factor of 3x, so we can factor it out to get:3x(x4+ 5x2+ 4)Our 'bracketed' term now has the layout of a quadratic equation, except the powers of x have been doubled - x2+ 5x + 4x0(x0= 1, x0*2= x0)This means we can factorise it just like a quadratic, except making sure the x's are squared in the final brackets.x2+ 5x + 4 factorises to (x+1)(x+4), so x4+ 5x2+ 4 will factorise to give (x2+1)(x2+4).Put this all together to get:3x(x2+1)(x2+4)This could be factorised further by treating each of these new bracketed terms as quadratics, but only if complex numbers are allowed - so for simplicity's sake, this is the final product.Otherwise, you could turn it into:3x(x+i)(x-i)(x+2i)(x-2i)

It's really simple once you get the hang of it. Here, I'll show you how.Example:24 This is 2 digit by 2 digit.x10First you have to multiply 4x0 equals 0.Then you put the 0 under the ones place. Like this: 24x100After that, you multiply 0x2 equals 0. Then you put anotherzero under the tens place. Like this: 24x1000Time for step three! Ok, then you just add a zero under the ones place.(Anytime you multiple two digit by two digit, you ALWAYS have to put anotherzero under the ones place like this: 24x10000Right now I have to leave and go home. I will finish this lesson tomorrow. Bye!!

Add four times the last digit to the remaining leading truncated number. If the result is divisible by 13, then so was the first number. Apply this rule repeatedly as necessary. Here is an example. You want to know if 50661 is divisible by 13. Add 4 times the last digit to the remaining numbers you have after removing the last digit. So we add 1x4=4 to the number we have after taking the 1 after 50661. This is 5066+4=5070. Now do this again. 4x0 is 0 and add this to the number you get by taking 5070 and truncating the number.. ie drop the last 0. So we have 507+0=507. Now add 7x4=28 so 50. Of course 50 comes from 507 after dropping the 7. You have 78. Now since 78 is 6x13, the original number must have been divisible by 13 too. This is one of the more complicated divisibility rules.

Strictly we do not classify polynomials by the number of terms but by the highest power of the variable (its degree).For example, if x is the variable then a polynomial with highest power...... x0 (degree 0) is a constant e.g. 4x0 = 4... x1 (degree 1) is linear e.g. 2x1 + 5 = 2x + 5... x2 (degree 2) is a quadratic e.g. 3x2 - 2x + 1... x3 (degree 3) is a cubic e.g. 2x3 - 3x2 - 2x + 1... x4 (degree 4) is a quartic e.g. 7x4 + 2x3 - 3x2 - 2x + 1(degree 5) quintic, (degree 6) sextic, (degree 7) septic, (degree 8) octic,...Although it appears as if the degree of a polynomial is always one less than the number of terms, in general this not the case. For example, x3 - 9 is cubic with only 2 terms or 4x8 is an octic with only one term.

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