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Standard X

Mathematics

Factorisation of Quadratic Polynomials - Factor Theorem

Question 2iCh...

Question

Question 2(i)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
$t^{2} - 3, 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$

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Solution

$t^{2} - 3, 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$
$t^{3} - 3 = t^{2} + 0 t - 3$

As the remainder is 0.
Hence, $t^{2} - 3$ is a factor of $2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$ .

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Similar questions

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

t^{2} - 3, 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12

Q. Check in which case the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
$t^2-3, 2t^4+3t^3-2t^2-9t-12$

Q. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
(i)

t^{2} - 3, 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12

(ii)

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

(iii)

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

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

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

Q. Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm :

(i)

g (t) = t^{2} - 3, f (t) = 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12

(ii)

g (x) = x^{3} - 3 x + 1, f (x) = x^{5} - 4 x^{3} + x^{2} + 3 x + 1

(iii)

g (x) = 2 x^{2} - x + 3, f (x) = 6 x^{5} - x^{4} + 4 x^{3} - 5 x^{2} - x - 15

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Factorisation of Quadratic Polynomials - Factor Theorem

Standard X Mathematics

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Question 2(i) Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: t2−3, 2t4+3t3−2t2−9t−12

t2−3, 2t4+3t3−2t2−9t−12 t3−3=t2+0t−3 As the remainder is 0. Hence, t2−3 is a factor of 2t4+3t3−2t2−9t−12.

Question 2(i)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
$t^{2} - 3, 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$

$t^{2} - 3, 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$
$t^{3} - 3 = t^{2} + 0 t - 3$

As the remainder is 0.
Hence, $t^{2} - 3$ is a factor of $2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$ .