Question

Using division of polynomials, state whether
(i) x + 6 is a factor of x² − x − 42
(ii) 4x − 1 is a factor of 4x² − 13x − 12
(iii) 2y − 5 is a factor of 4y⁴ − 10y³ − 10y² + 30y − 15
(iv) 3y² + 5 is a factor of 6y⁵ + 15y⁴ + 16y³ + 4y² + 10y − 35
(v) z² + 3 is a factor of z⁵ − 9z
(vi) 2x² − x + 3 is a factor of 6x⁵ − x⁴ + 4x³ − 5x² − x − 15

Answer 1

(i)

Remainder is zero. Hence (x+6) is a factor of x² -x-42
(ii)

As the remainder is non zero . Hence ( 4x-1) is not a factor of 4x² -13x-12



(iii)




$\because$ The remainder is non zero,
2y $-$ 5 is not a factor of $4y^4-10y^3-10y^2+30y-15$.

(iv)

Remainder is zero. Therefore, 3y² + 5 is a factor of $6y^5+15y^4+16y^3+4y^2+10y-35$.


(v)

Remainder is zero; therefore, z² + 3 is a factor of $z^5-9z$.

(vi)



Remainder is zero ; therefore, $2x^2-x+3$ is a factor of $6x^5-x^4+4x^3-5x^2-x-15$.