Using the remainder theorem, factorise each of the following completely :
4x³ + 7x² - 36x - 63

Question

Using the remainder theorem, factorise each of the following completely : 4x³ + 7x² - 36x - 63

KnowledgeBoat · Accepted Answer

For x = -3 the value of 4x³ + 7x² - 36x - 63 = 4(-3)³ + 7(-3)² - 36(-3) - 63 = 4(-27) + 7(9) + 108 - 63 = -108 + 63 + 108 - 63 = 0. Hence, (x + 3) is the factor of 4x³ + 7x² - 36x - 63. On dividing 4x³ + 7x² - 36x - 63 by (x + 3), we get, quotient = 4x² - 5x - 21 Factorising 4x² - 5x - 21, = 4x² - 12x + 7x - 21 = 4x(x - 3) + 7(x - 3) = (4x + 7)(x - 3). ∴ 4x² - 5x - 21 = (4x + 7)(x - 3) Hence, 4x³ + 7x² - 36x - 63 = (x + 3)(4x + 7)(x - 3).

Mathematics

Using the remainder theorem, factorise each of the following completely :
4x³ + 7x² - 36x - 63

Factorisation

Related Questions

Using the remainder theorem, factorise each of the following completely :
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Using the Remainder Theorem, factorise the expression 3x³ + 10x² + x - 6. Hence, solve the equation 3x³ + 10x² + x - 6 = 0.

Mathematics

Using the remainder theorem, factorise each of the following completely :4x3 + 7x2 - 36x - 63

Factorisation

Related Questions

Using the remainder theorem, factorise each of the following completely :2x3 + x2 - 13x + 6

Using the remainder theorem, factorise each of the following completely :3x3 + 2x2 - 23x - 30

Using the remainder theorem, factorise each of the following completely :x3 + x2 - 4x - 4

Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x - 6. Hence, solve the equation 3x3 + 10x2 + x - 6 = 0.

Using the remainder theorem, factorise each of the following completely :
4x³ + 7x² - 36x - 63

Using the remainder theorem, factorise each of the following completely :
2x³ + x² - 13x + 6

Using the remainder theorem, factorise each of the following completely :
3x³ + 2x² - 23x - 30

Using the remainder theorem, factorise each of the following completely :
x³ + x² - 4x - 4

Using the Remainder Theorem, factorise the expression 3x³ + 10x² + x - 6. Hence, solve the equation 3x³ + 10x² + x - 6 = 0.