Question

if f and g are two polynomials of degree 3 and 4 respectively then what is the degree of f-g​

Answer 1

What is a polynomial ?

  An expression of the form

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ_₁x + aₙ

  where a₀, a₁, a₂, ..., aₙ (a₀ ≠ 0) are real or complex numbers, n is non negative integer and x is a variable, is called a polynomial in x. The highest power n is called the degree of a polynomial.

Solution :

Let, f(x) = ax³ + bx² + cx + d

     g(x) = ex⁴ + fx³ + gx² + hx + i

where a, b, c, d, e, f, g, h, i are constants with a ≠ 0, e ≠ 0

Now, f(x) - g(x)

= ax³ + bx² + cx + d - ex⁴ - fx³ - gx² - hx - i

= (- e)x⁴ + (a - f)x³ + (b - g)x² + (c - h)x + (d - i)

We see that in f(x) - g(x), the highest integral power of x is 4

Thus, the required degree of (f - g) is 4

Answer 2

the correct answer is 4

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