Using the Remainder and Factor Theorems, factorise the polynomial.x^3 + 10x^2 − 37x + 26.

Question

KnowledgeBoat · Accepted Answer

Let, f(x) = x3 + 10x2 - 37x + 26. Substituting, x = 1 in f(x) we get : f(1) = (1)3 + 10(1)2 - 37(1) + 26 = 1 + 10 - 37(1) + 26 = 37 - 37 = 0. Since, f(1) = 0, thus (x − 1) is a factor of f(x). Dividing, x3 + 10x2 - 37x + 26 by (x - 1), we get : ∴ x3 + 10x2 - 37x + 26 = (x - 1)(x2 + 11x - 26) = (x - 1)(x2 + 13x - 2x - 26) = (x - 1)[x(x + 13) - 2(x + 13)] = (x - 1)(x + 13)(x - 2). Hence, x3 + 10x2 - 37x + 26 = (x - 1)(x + 13)(x - 2).

Mathematics

Using the remainder and factor theorems, factorize the polynomial.
x³ + 10x² - 37x + 26

Factorisation

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Mathematics

Using the remainder and factor theorems, factorize the polynomial.x3 + 10x2 - 37x + 26

Factorisation

Related Questions

Using factor theorem, factorize the following:2x3 − x2 − 13x − 6

If (x - 2) is a factor of (x3 + 2x2 - kx + 10), find the value of k. Hence, determine whether (x + 5) is also a factor of the given expression.

If (x - 2) is a factor of the expression 2x3 + ax2 + bx - 14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the values of a and b.

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Using the remainder and factor theorems, factorize the polynomial.
x³ + 10x² - 37x + 26

Using factor theorem, factorize the following:
2x³ − x² − 13x − 6

If (x - 2) is a factor of (x³ + 2x² - kx + 10), find the value of k. Hence, determine whether (x + 5) is also a factor of the given expression.

If (x - 2) is a factor of the expression 2x³ + ax² + bx - 14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the values of a and b.

The polynomial 3x³ + 8x² - 15x + k has (x - 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.