Question

True or False statement 1. P(x) =x-1 and g(x) =x^2-2x +1 . p(x) is a factor of g(x) 2. The factor of 3x^2–x-4 are (x+1)(3x-4) 3. Every linear polynomial has only one zero 4. Every real number is the zero’s of zero polynomial 5. A binomial may have degree 4 6. 0,2 are the zeroes of x^2-2x 7. The degree of zero polynomial is not defined Please give good answers

Answer 1

Here u have Ur answer with explanation also.

Answer 2

Answer:

1) True ,2) true ,3)True ,4) True and 5) it is also true

Step-by-step explanation:

Explanation :

Given , p(x) = x-1 and g(x) = $x^{2} -2x +1$

p(x) = 0 ⇒ x-1 = 0 ⇒ x= 1

Step1:

Now , put the value of x in g(x) = $1^{2} - 2.(1) + 1$

⇒2-2 = 0 .

Therefore, p(x) is a factor of g(x).

Step2:

2)Given ,  $3x^{2} -x-4$

Therefore , $3x^{2} -x-4$

⇒$3x^{2} -4x+3x-4$

⇒x(3x-4)+1(3x-4)

⇒(3x-4)(x+1)

So , It is true that (x+1)(3x-4 are the factor of $3x^{2} -x-4$)

Step3:

3)Yes, linear polynomials have only one root, but quadratic and cubic polynomials have two and three roots, respectively.

4) Yes, it is true that all numbers are at zero in the zero polynomial. This is because a zero polynomial is a constant polynomial whose coefficients are all equal to zero. Zero in a polynomial is the value of a variable that makes the polynomial equal to zero. Therefore, zero in the zero polynomial is any real number.

5) Yes, since polynomial 0 has no terms  and is called a zero polynomial, it is true that the degree of the zero polynomial is not defined. Since zero polynomials have no non-zero terms, polynomials have no degree.

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