Using factor theorem, factorize the following: x^3 + 7x^2 + 7x − 15

Question

KnowledgeBoat · Accepted Answer

Let, f(x) = x3 + 7x2 + 7x - 15. Substituting, x = 1 in f(x), we get : f(1) = (1)3 + 7(1)2 + 7(1) - 15 = 1 + 7 + 7 - 15 = 0. Since, f(1) = 0, thus (x - 1) is a factor of f(x). Dividing, f(x) by (x - 1), we get : ∴ x3 + 7x2 + 7x - 15 = (x - 1)(x2 + 8x + 15) = (x - 1)(x2 + 3x + 5x + 15) = (x - 1)[x(x + 3) + 5(x + 3)] = (x - 1)(x + 5)(x + 3). Hence, x3 + 7x2 + 7x - 15 = (x - 1)(x + 5)(x + 3).

Mathematics

Using factor theorem, factorize the following:
x³ + 7x² + 7x - 15

Factorisation

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Mathematics

Using factor theorem, factorize the following:x3 + 7x2 + 7x - 15

Factorisation

Related Questions

If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of a and b.

If (x3 + ax2 + bx + 6) has (x - 2) as a factor and leaves a remainder 3 when divided by (x - 3), find the values of a and b.

Using factor theorem, factorize the following:6x3 - 7x2 - 11x + 12

Using factor theorem, factorize the following:2x3 + 3x2 − 9x − 10

Using factor theorem, factorize the following:
x³ + 7x² + 7x - 15

If (x + 2) and (x + 3) are factors of x³ + ax + b, find the values of a and b.

If (x³ + ax² + bx + 6) has (x - 2) as a factor and leaves a remainder 3 when divided by (x - 3), find the values of a and b.

Using factor theorem, factorize the following:
6x³ - 7x² - 11x + 12

Using factor theorem, factorize the following:
2x³ + 3x² − 9x − 10