Divide 32x^8-32x^4+20x^2
by -4x^2
-4x^2 is a factor of each therm. It is, in fact the Greatest Common Factor of "GCF".
Divide each of the three terms of 32x^8-32x^4+20x^2 by -4x^2 and then add them up. The first term will be
32x^8/(-4x^2) = -8x^6
So, I come up with -8x^6-8x^2+-5
Would that simplify to x4+-5?
-8x^6 + 8x^2-5 plus sign on middle term
no you may not combine x^6 term and x^2 term like that.
if you had x^2 + x you would not say that was x^3 !
what is the greatest common factor of48x2 and 72x3?
To divide the polynomial 32x^8 - 32x^4 + 20x^2 by -4x^2, we need to perform polynomial long division. The steps are as follows:
Step 1: Divide the highest degree term of the dividend (32x^8) by the highest degree term of the divisor (-4x^2). The result is -8x^6 since 32x^8 divided by -4x^2 is -8x^6.
Step 2: Multiply the divisor (-4x^2) by the result from Step 1 (-8x^6). The product is 32x^8.
Step 3: Subtract the product from the dividend. The subtraction results in 0.
Step 4: Bring down the next term from the dividend (-32x^4).
Step 5: Divide the new highest degree term of the dividend (-32x^4) by the highest degree term of the divisor (-4x^2). The result is 8x^2 since -32x^4 divided by -4x^2 is 8x^2.
Step 6: Multiply the divisor (-4x^2) by the result from Step 5 (8x^2). The product is -32x^4.
Step 7: Subtract the product from the dividend (-32x^4 - (-32x^4)). The subtraction results in 0.
Step 8: No more terms to bring down from the dividend.
Step 9: The final result of the long division is -8x^6 + 8x^2.
Therefore, 32x^8 - 32x^4 + 20x^2 divided by -4x^2 is equal to -8x^6 + 8x^2.