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.

Answer 1

1). True

2). True

3). True

4). True

5). True

6). True

Step-by-step explanation:

1). P(x) = x - 1

g(x) = $x^2-2x +1$

so,

g(x) = $x^2 - x - x + 1$

= $x(x - 1) - 1(x - 1)$

= $(x - 1) (x - 1) -(x - 1)^2$

Thus, p(x) is a factor of g(x). Hence, it is true.

2). $3x^{2} - x - 4$

= $3x^2 - 4x + 3x - 4$

= $3x(x + 1) - 4(x + 1)$

= $(x + 1) (3x - 4)$

∵ $(x + 1) (3x - 4)$ are the factors of $3x^{2} - x - 4$.

Thus, the statement is true.

3). A linear pair contains only one zero as it has 1 as its highest degree.

4). The statement asserting that each real number is characterized as the zero's of zero polynomial as it has more than one solution.

5). Since polynomial has several zeroes, it can possess 4 as its degree.

6). x^2 - 2x

= x(x - 2)

∵ 0 & 2 are the zeroes.

So, it is true.

7). The last statement is also true that zero of zero polynomial can not be defined.

Learn more: State true or false

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