Algebra missing terms

Question

I don't understand missing terms in polynomials can you explain it simply. X^3-27

They have x^2,×

Is there an easier way to do this. I use mathway and I can get just about every answer right buy not this.

Answer 1

A polynomial, in standard form, has a leading term that is the highest degree in that polynomial. In your example x³ - 27, that would be the term x³. Polynomials in standard form then are placed in order of descending exponent, each next term a lower degree than the previous.

For example 3x⁵ - 7x⁴ + 5x³ + 3x² - 6x + 9 has 6 terms, the leading term being 3x⁵, the second term being -7x⁴, the third being 5x³ and so forth, each term going down one degree from the previous.

In your example, there are only 2 terms, x³ and -27. The second order term is missing (x²) and the first order term (x) is also missing so, you could say the missing terms are 0x² and 0x

Answer 2

x^3 - 27 = x^3 - 3^3 = (x-3)(x^2 +3x + 9)

general formula is a^3-b^3 = (a-b)(a^2 +ab + b^2)

substitute a=x and b = 3 to get (x-3)(x^2+3x+9)

x^3 -27 has a cubic term and a constant term. What's missing is a quadratic and linear term. But when you factor it, you get factors which have all terms, constant to cubic, including quadratic & linear.

Answer 3

Algebra missing terms: I don't understand missing terms in polynomials can you explain it simply. x³ – 27. They have x^2,×. Is there an easier way to do this. I use mathway and I can get just about every answer right buy not this.

Easier Way Answer: You asked for easier way to do this, Sure; here it is:

Your polynomial in standard form is: P(x) = x³ + 0x² + 0x – 27

Your polynomial: Degree is 3: 1st term is x³, 2nd term is 0x² (missing), 3rd term is 0x (missing), 4th term is -27

Note: 2nd term and 3rd term are because the coefficients are "0".