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Polynomials

Short Answer Type

141. Check whether (p + 1) is a factor of (p¹⁰⁰ - 1) and (p¹⁰⁰ - 1).

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142. Factorise: 3u³ + 4u² - 12u + 16.

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143. Find if remainder obtained on dividing polynomial p(y) = y³ + ay² + 5y - 25 by (y + a) is a factor of polynomial f(a) = a² -5a + 25.

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144. If (2x - 3) is a factor of 2x⁴ - 3x² + 15x - 15k, find the value of $open parentheses 3 straight k minus square root of 5 space straight k close parentheses.$

Solution not provided.

Ans. $space fraction numerator left parenthesis 3 space minus square root of 5 right parenthesis 107 over denominator 120 end fraction$

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145.

Use suitable identities to find the following products:

(i) (x + 4)(x + 10)

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146.

Use suitable identities to find the following products:

(x + 8)(x - 10)

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147.

Use suitable identities to find the following products:

(3x + 4)(3x - 5)

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148.

Use suitable identities to find the following products:

$open parentheses straight y squared plus 3 over 2 close parentheses open parentheses y squared minus 3 over 2 close parentheses$

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149.

Use suitable identities to find the following products:
(3 - 2x)(3 + 2x)

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150. Evaluate the following products without multiplying directly:
103 × 107

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

144. If (2x - 3) is a factor of 2x4 - 3x2 + 15x - 15k, find the value of

144. If (2x - 3) is a factor of 2x⁴ - 3x² + 15x - 15k, find the value of $open parentheses 3 straight k minus square root of 5 space straight k close parentheses.$