Given f(x) = ax 2 + bx + 2 and g(x) = bx 2 + ax + 1. If (x - 2) is a factor of f(x) but leaves the remainder -15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression f(x) + g(x) + 4x 2 + 7x

f(x) = ax 2 + bx + 2 Given, (x - 2) is a factor of f(x) hence, by factor theorem f(2) = 0 On dividing equation by 2, g(x) = bx 2 + ax + 1 Given, on dividing g(x) by (x - 2), remainder = -15 and by remainder theorem, remainder = g(2) On dividing equation by 2, Putting value of b = -1 - 2a from equation 1, Putting value of a = 2 and b = -5 in f(x) + g(x) + 4x 2 + 7x we get, Hence, the value of a = 2 and b = -5; f(x) + g(x) + 4x 2 + 7x = (x + 1)(x + 3).

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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If ax³ + 3x² + bx - 3 has a factor (2x + 3) and leaves remainder -3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.

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When 2x³ - x² - 3x + 5 is divided by 2x + 1, then the remainder is
6
-6
-3
0

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If on dividing 4x² - 3kx + 5 by x + 2, the remainder is -3 then the value of k is
4
-4
3
-3

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Mathematics

Given f(x) = ax² + bx + 2 and g(x) = bx² + ax + 1. If (x - 2) is a factor of f(x) but leaves the remainder -15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression
f(x) + g(x) + 4x² + 7x

Factorisation

Related Questions

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 ax³ + 3x² + bx - 3 has a factor (2x + 3) and leaves remainder -3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.

When 2x³ - x² - 3x + 5 is divided by 2x + 1, then the remainder is
6
-6
-3
0

If on dividing 4x² - 3kx + 5 by x + 2, the remainder is -3 then the value of k is
4
-4
3
-3

Mathematics

Given f(x) = ax2 + bx + 2 and g(x) = bx2 + ax + 1. If (x - 2) is a factor of f(x) but leaves the remainder -15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expressionf(x) + g(x) + 4x2 + 7x

Factorisation

Related Questions

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 ax3 + 3x2 + bx - 3 has a factor (2x + 3) and leaves remainder -3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.

When 2x3 - x2 - 3x + 5 is divided by 2x + 1, then the remainder is6-6-30

If on dividing 4x2 - 3kx + 5 by x + 2, the remainder is -3 then the value of k is4-43-3

Given f(x) = ax² + bx + 2 and g(x) = bx² + ax + 1. If (x - 2) is a factor of f(x) but leaves the remainder -15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression
f(x) + g(x) + 4x² + 7x

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 ax³ + 3x² + bx - 3 has a factor (2x + 3) and leaves remainder -3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.

When 2x³ - x² - 3x + 5 is divided by 2x + 1, then the remainder is
6
-6
-3
0

If on dividing 4x² - 3kx + 5 by x + 2, the remainder is -3 then the value of k is
4
-4
3
-3