Polynomials Tes...

R₁ and R₂ are the remainders when x³ + 2x² – 5ax – 7 and x³ + ax² – 12x + 6 are divided by x + 1 and x – 1, respectively. If 2R₁ + R₂ = 6, find the value of a.

The inequality b² + 5 > 16b - 23 is satisfied if

The factors of a² + b² + 2(ab + bc + ca) are (a + b+ m) and (a + b + nc). Find the value of m + n out of the given options.

Choose the factor of (p² – q²) (r² – s²) – 4pqrs out of the given options.

If b is the mean of interval 0 - 1, then the value of b + will be:

Which of the following options is true, if x² – 1 is a factor of ax⁶ + bx⁵ + cx² + dx + e .

f(x) = ax¹⁰¹ + bx⁹⁷ + cx – 5, where a, b and c are constants. Also f(– 7) = 7. Find the value of (7).

What is the zero of the binomial ax + b²?

Choose the factors of x² + 11x + 6 from the following options:

What is the value of (a + b)³ + (a - b)³ + 6a(a² - b²)?

The polynomials 2x³ + ax² + 3x – 5 and x³ + x² – 4x – a leave the same remainder when divided by x + 1. Find the value of a out of the following options.

Factorise x¹² -y¹² and choose the right answer.

If p(x) = 4x³ - 3x² + 2x + 1, q(x) = x³ - x² + x + 1 and r(x) = x² - 2x + 1, then the value of p(x) + 2q(x) - r(x) is

If 2y³ + my² + 11y + m + 3 is exactly divisible by 2y - 3, then the value of m is

If p + q + r = 0, then p³ + q³ + r³ equals

If y - 2 and y - 1 are the factors of py² + 5y + r, then

If p + q + r = 0, evaluate and choose the answer from the following:

Factorise (3 - 4y - 7y²)² - (4y + 1)² and choose the correct option:

If (x + 1) and (x –1) are the factors of px³ –2x + q, then the values of p and q are

When f(x) is divided by x+7/9, the remainder is