Question

Find Whether or not the first polynomial is a factor of the second:

(i) x + 1,2x² + 5x + 4

(ii) y - 2,3y³ + 5y² + 5y + 2

(iii) 4x² - 5,4x⁴ + 7x² + 15

(iv) 4 - z, 3z² - 13z + 4

(v) 2a - 3,10a² - 9a - 5

(vi) 4y + 1,8y² - 2y + 1

Answer 1

(i) x + 1, 2x² + 5x + 4

Quotient: 2x + 3

Remainder: 1

Since remainder is 1 therefore the first polynomial is NOT a factor of the second polynomial.

(ii) y - 2, 3y³ + 5y² + 5y + 2

Quotient: 3y² + 11y + 27

Remainder: 56 

Since remainder is 56 therefore the first polynomial is NOT a factor of the second polynomial.

(iii) 4x² - 5, 4x⁴ + 7x² + 15

Quotient: x² + 3

Remainder: 30 

Since remainder is 30 therefore the first polynomial is NOT a factor of the second polynomial.

(iv) 4 - z, 3z² - 13z + 4

Quotient: -3z + 1

Remainder: 0 

Since remainder is 0 therefore the first polynomial is a factor of the second polynomial.

(v) 2a - 3, 10a² - 9a - 5

Quotient: 5a + 3

Remainder: 4 

Since remainder is 4 therefore the first polynomial is NOT a factor of the second polynomial.

(vi) 4y + 1, 8y² - 2y + 1

Quotient: 2y - 1

Remainder: 2 

Since remainder is 2 therefore the first polynomial is NOT a factor of the second polynomial.