The expression 4x 3 - bx 2 + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

By remainder theorem, When a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a). ⇒ x + 1 = 0 ⇒ x = -1 Given, 4x 3 - bx 2 + x - c leaves remainder 0 on dividing it by (x + 1). ∴ 4(-1) 3 - b(-1) 2 + (-1) - c = 0 ⇒ 4(-1) - b(1) - 1 - c = 0 ⇒ -4 - b - 1 - c = 0 ⇒ b + c = -5 ⇒ b = -5 - c .........(1) Given, 4x 3 - bx 2 + x - c leaves remainder 30 on dividing it by (2x - 3). 2x - 3 = 0 ⇒ 2x = 3 ⇒ x = Substituting x = in 4x 3 - bx 2 + x - c should give result as 30, Substituting value of b from (1) in above equation : ⇒ 60 - 9(-5 - c) - 4c = 120 ⇒ 60 + 45 + 9c - 4c = 120 ⇒ 5c + 105 = 120 ⇒ 5c = 120 - 105 ⇒ 5c = 15 ⇒ c = = 3. Substituting value of c in (1), we get : ⇒ b = -5 - c = -5 - 3 = -8. Hence, b = -8 and c = 3.

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

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Show that 2x + 7 is a factor of 2x³ + 7x² - 4x - 14. Hence, solve the equation :
2x³ + 7x² - 4x - 14 = 0.

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If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

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Mathematics

The expression 4x³ - bx² + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

Factorisation

Related Questions

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

Show that 2x + 7 is a factor of 2x³ + 7x² - 4x - 14. Hence, solve the equation :
2x³ + 7x² - 4x - 14 = 0.

If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

Mathematics

The expression 4x3 - bx2 + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

Factorisation

Related Questions

What number should be subtracted from 2x3 - 5x2 + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

Show that 2x + 7 is a factor of 2x3 + 7x2 - 4x - 14. Hence, solve the equation :2x3 + 7x2 - 4x - 14 = 0.

If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

The expression 4x³ - bx² + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

Show that 2x + 7 is a factor of 2x³ + 7x² - 4x - 14. Hence, solve the equation :
2x³ + 7x² - 4x - 14 = 0.