Question

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Answer 1

Correct Question:

Using Factor theorem show that: (x - 1) is factor of 2x⁴ + 9x³ + 6x² - 11 - 6 .

Solution:

• f(x) = 2x⁴ + 9x³ + 6x² - 11 - 6
• g(x) = x - 1

So,

Eliminate the factor value;

g(x) = (x - 1)

x - 1 = 0

x = 1

So in We have to put this value in place of (x), to find that :- Is this Equation a polynomials?

_______________________________

f(x) = 2x⁴ + 9x³ + 6x² - 11 - 6

After putting the g(x) value in f(x);

f(1) = 2 × 1⁴ + 9 × 1³ + 6 × 1² - 11 - 6

=> 2 + 9 + 6 - 17

=> 17 - 17

=> 0

Hence,

This Equation is a polynomial.

Note:-

After Dividing f(x) by g(x) , if the remainder is Zero so the equation is polynomial.

Answer 2

Step-by-step explanation:

Correct Question:

Using Factor theorem show that: (x - 1) is factor of 2x⁴ + 9x³ + 6x² - 11 - 6 .

Solution:

f(x) = 2x⁴ + 9x³ + 6x² - 11 - 6

g(x) = x - 1

So,

Eliminate the factor value;

g(x) = (x - 1)

x - 1 = 0

x = 1

So in We have to put this value in place of (x), to find that :- Is this Equation a polynomials?

_______________________________

f(x) = 2x⁴ + 9x³ + 6x² - 11 - 6

After putting the g(x) value in f(x);

f(1) = 2 × 1⁴ + 9 × 1³ + 6 × 1² - 11 - 6

=> 2 + 9 + 6 - 17

=> 17 - 17

=> 0

Hence,

This Equation is a polynomial.

Note:-

After Dividing f(x) by g(x) , if the remainder is Zero so the equation is polynomial.