Find out whether or not the first polynomial is a factor of the second polynomial.
$x^{2} + 3, 4 x^{4} + 7 x^{2} - 15$

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Yes

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Can not determine

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None of the above

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Solution

The correct option is B Yes
Given: $4 x^{4} + 7 x^{2} - 15$

$4 x^{4} + 12 x^{2} - 5 x^{2} - 15$

$4 x^{2} (x^{2} + 3) - 5 (x^{2} + 3)$

$(x^{2} + 3) (4 x^{2} - 5)$

So, $x^{2} + 3$ polynomial is a factor of $4 x^{4} + 7 x^{2} - 15$ .

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Similar questions

Q. Find out whether or not the first polynomial is a factor of the second polynomial:

4 a - 1, 12 a^{2} - 7 a - 2

Check whether the first polynomial is a factor of the second polynomial by dividing second polynomial by the first polynomial.
$x^{2} + 3 x + 1, 3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$

Question 2 (ii)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

$x^{2} + 3 x + 1, 3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

Q. Determine whether

(x + 1)

is a factor of the polynomial:

2 x^{4} + 9 x^{3} + 2 x^{2} + 10 x + 15

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Find out whether or not the first polynomial is a factor of the second polynomial.x2+3, 4x4+7x2−15

The correct option is B YesGiven: 4x4+7x2−154x4+12x2−5x2−154x2(x2+3)−5(x2+3)(x2+3)(4x2−5)So, x2+3 polynomial is a factor of 4x4+7x2−15.

Find out whether or not the first polynomial is a factor of the second polynomial.
$x^{2} + 3, 4 x^{4} + 7 x^{2} - 15$

The correct option is B Yes
Given: $4 x^{4} + 7 x^{2} - 15$

$4 x^{4} + 12 x^{2} - 5 x^{2} - 15$

$4 x^{2} (x^{2} + 3) - 5 (x^{2} + 3)$

$(x^{2} + 3) (4 x^{2} - 5)$

So, $x^{2} + 3$ polynomial is a factor of $4 x^{4} + 7 x^{2} - 15$ .