If (x + 2) and (x - 3) are the factors of x 3 + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

f(x) = x 3 + ax + b If (x + 2) or (x - (-2)) and (x - 3) are factors of f(x) then, f(-2) and f(3) = 0. Putting value of b = 2a + 8 from equation 1, Putting the values of a and b in f(x) we get, f(x) = x 3 - 7x - 6 Since, (x + 2) and (x - 3) are factors of f(x) hence, (x + 2)(x - 3) = (x 2 - x - 6) is also the factor. On dividing f(x) by x 2 - x - 6, we get, (x + 1) as quotient and remainder = 0. Hence, the value of a = -7 and b = -6; x 3 - 7x - 6 = (x + 2)(x - 3)(x + 1).

Find the value of the constants a and b, if (x - 2) and (x + 3) are both factors of the expression x³ + ax² + bx - 12.

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

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(x - 2) is a factor of the expression x³ + ax² + bx + 6. When this expression is divided by (x - 3), it leaves the remainder 3. Find the values of a and b.

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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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Mathematics

If (x + 2) and (x - 3) are the factors of x³ + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

Factorisation

Related Questions

Find the value of the constants a and b, if (x - 2) and (x + 3) are both factors of the expression x³ + ax² + bx - 12.

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

(x - 2) is a factor of the expression x³ + ax² + bx + 6. When this expression is divided by (x - 3), it leaves the remainder 3. Find the values of a and b.

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.

Mathematics

If (x + 2) and (x - 3) are the factors of x3 + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

Factorisation

Related Questions

Find the value of the constants a and b, if (x - 2) and (x + 3) are both factors of the expression x3 + ax2 + bx - 12.

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

(x - 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x - 3), it leaves the remainder 3. Find the values of a and b.

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.

If (x + 2) and (x - 3) are the factors of x³ + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

Find the value of the constants a and b, if (x - 2) and (x + 3) are both factors of the expression x³ + ax² + bx - 12.

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

(x - 2) is a factor of the expression x³ + ax² + bx + 6. When this expression is divided by (x - 3), it leaves the remainder 3. Find the values of a and b.

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.