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

Open in App

Solution

(i) Given polynomials $t^{2} - 3, 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$
Division of $2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$ by $t^{2} - 3$

Remainder is 0, hence $t^{2} - 3$ is a factor of $2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12$
(ii) Given $x^{2} + 3 x + 1, 3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$
Division of $3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$ by $x^{2} + 3 x + 1$ is

Remainder is 0, hence $x^{2} + 3 x + 1$ is a factor of $3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$

(iii) $x^{3} - 3 x + 1, x^{5} - 4 x^{3} + x^{2} + 3 x + 1$
Division of $x^{5} - 4 x^{3} + x^{2} + 3 x + 1$ by $x^{3} - 3 x + 1$ is

Remainder is 2, hence $x^{3} - 3 x + 1$ is not a factor of $x^{5} - 4 x^{3} + x^{2} + 3 x + 1$

Suggest Corrections

Similar questions

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

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

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

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

Join BYJU'S Learning Program

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:(i) t2−3,2t4+3t3−2t2−9t−12(ii) x2+3x+1,3x4+5x3−7x2+2x+2(iii) x3−3x+1,x5−4x3+x2+3x+1