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kolbaska11 [484]
3 years ago
11

P(x) is a polynomial with integer coefficients and p(-3) = 0.

Mathematics
2 answers:
natka813 [3]3 years ago
5 0

Answer:

x + 3 is a factor of the polynomial.

Step-by-step explanation:

We have been given that p(x) is a polynomial with integer coefficient.

Also p(-3)=0

Since, p(-3) =0, hence, we can say that -3 is a zero of the polynomial.

Now, we apply factor theorem.

Factor Theorem: If 'a' is a zero of a function f(x) then (x-a) must be a factor of the function f(x).

Applying this theorem, we can say that (x+3) must be a factor of the polynomial.

Hence, first statement must be true.

MA_775_DIABLO [31]3 years ago
3 0

Answer:  The correct option is (A) (x + 3) is a factor of the polynomial.

Step-by-step explanation:  Given that p(x) is a polynomial with integer coefficients and p(-3)=0.

We are to select the true statement from the given options.

<em><u>Factor Theorem:</u></em>  If q(x) is a polynomial with integer coefficients and q(a) = 0, then (q - a) will be a factor of q(x).

Here, it is given that

p(x) is a polynomial with integer coefficients and p(-3) = 0.

Therefore, by Factor theorem, we can say that (x-(-3)), ie., (x + 3) is a factor of the polynomial p(x).

Thus, (x + 3) is a factor of the polynomial.

Option (A) is CORRECT.

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The algebraic expressions, x + x + y + y + y + y - 5 + x + x + x + 8 - 4y and 5x + 3 are equivalent to 2x + 4y - 5 + 3x + 8 - 4y

To determine whether each expression is equivalent to 2x + 4y - 5 + 3x + 8 - 4y, apply the knowledge of algebra to solve each of the following in it's simplest form.

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Therefore, x + x + y + y + y + y - 5 + x + x + x + 8 - 4y is equivalent to 2x + 4y - 5 + 3x + 8 - 4y

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<u><em /></u>6xy + 3 - 4y<em> (cannot be simplified further)</em>

<em />6xy + 3 - 4y\neq 2x + 4y - 5 + 3x + 8 - 4y<em />

Therefore:

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<em><u>Third Option:</u></em>

<em><u /></em>-8y + 5x - 3<em><u> </u></em><em>(cannot be simplified further)</em>

<em />-8y + 5x - 3 \neq  2x + 4y -5 + 3x + 8 - 4y<em />

Therefore:

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<u><em>Fourth Option:</em></u>

<u><em /></u>5x + 3<u><em /></u>

<u><em /></u>5x + 3 = 2x + 4y - 5 + 3x + 8 - 4y<u><em /></u>

Therefore:

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