If x + a is a common factor of expressions f(x) = x 2 + px + q and g(x) = x 2 + mx + n; show that : a =

x + a = 0 ⇒ x = -a. Since, (x + a) is factor of f(x) and g(x). ∴ f(-a) = g(-a) ⇒ (-a) 2 + p(-a) + q = (-a) 2 + m(-a) + n ⇒ a 2 - pa + q = a 2 - ma + n ⇒ a 2 - a 2 - pa + ma = n - q ⇒ ma - pa = n - q ⇒ a(m - p) = n - q ⇒ a = . Hence, proved that a = .

Given that x - 2 and x + 1 are factors of f(x) = x³ + 3x² + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

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The expression 4x³ - bx² + x - c leaves remainders 0 and 30 when divided by x + 1 and 2x - 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.

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The remainder, when x³ - x² + x - 1 is divided by x + 1, is :
0
-4
2
4

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If x - 3 is a factor of x² + kx + 15; the value of k is :
8
3
-5
-8

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Mathematics

If x + a is a common factor of expressions f(x) = x<sup>2</sup> + px + q and g(x) = x<sup>2</sup> + mx + n; show that : a =

Factorisation

Related Questions

Given that x - 2 and x + 1 are factors of f(x) = x³ + 3x² + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

The expression 4x³ - bx² + x - c leaves remainders 0 and 30 when divided by x + 1 and 2x - 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.

The remainder, when x³ - x² + x - 1 is divided by x + 1, is :
0
-4
2
4

If x - 3 is a factor of x² + kx + 15; the value of k is :
8
3
-5
-8

Mathematics

If x + a is a common factor of expressions f(x) = x<sup>2</sup> + px + q and g(x) = x<sup>2</sup> + mx + n; show that : a =

Factorisation

Related Questions

Given that x - 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

The expression 4x3 - bx2 + x - c leaves remainders 0 and 30 when divided by x + 1 and 2x - 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.

The remainder, when x3 - x2 + x - 1 is divided by x + 1, is :0-424

If x - 3 is a factor of x2 + kx + 15; the value of k is :83-5-8

Given that x - 2 and x + 1 are factors of f(x) = x³ + 3x² + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

The expression 4x³ - bx² + x - c leaves remainders 0 and 30 when divided by x + 1 and 2x - 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.

The remainder, when x³ - x² + x - 1 is divided by x + 1, is :
0
-4
2
4

If x - 3 is a factor of x² + kx + 15; the value of k is :
8
3
-5
-8