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121. Factorise
2y³ + y² - 2y - 1

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122. Use Factor Theorem to verify that x + a is a factor of xⁿ + aⁿ for any odd positive integer n.

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123. Determine the value of ‘b’ for which the polynomial 5x³ - x² + 4x + b is divisible by 1 - 5x.

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124. Find the values of a and b so that (x + 1) and (x - 1) are factors of x⁴ + ax³ - 3x² + 2x + b.

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125. For what value of a the polynomial 2x³ + ax² + 11x + a + 3 is exactly divisible by 2x - 1?

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126. Without actual division prove that x⁴ + 2x³ - 2x² + 2x - 3 is exactly divisible by x² + 2x - 3.

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127. Determine whether (3x — 2) is a factor of 3x³ + x² - 20x + 12?

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128. Factorise: x³ - 6x² + 11x - 6.

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129. If both (x - 2) and

open parentheses straight x minus 1 half close parentheses

are factors of px² + 5x + r, show that p = r.

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130. Using factor theorem, factorise the polynomial x⁴ + x³ - 7x² - x + 6.

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