Question

write the following polynomial in standard form and also write down their degree. (i) (x^2-1/5)(x/4+1/5) (ii) x^4+x^5-x^2x^6​

Answer 1

To write the polynomial (x^2 - 1/5)(x/4 + 1/5) in standard form, first, multiply the terms:

(x^2 - 1/5)(x/4 + 1/5) = (x^2 * x/4) + (x^2 * 1/5) - (1/5 * x/4) - (1/5 * 1/5)

Now, simplify the terms:

(x^3/4) + (x^2/5) - (x/20) - (1/25)

The polynomial in standard form is:
x^3/4 + x^2/5 - x/20 - 1/25

The degree of this polynomial is 3 because the highest power of x is 3.

(ii) To write the polynomial x^4 + x^5 - x^2x^6 in standard form, first, simplify the terms by combining like terms:

x^4 + x^5 - x^2x^6 = x^4 + x^5 - x^8

The polynomial in standard form is:
x^5 - x^8

The degree of this polynomial is 8 because the highest power of x is 8.