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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.

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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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open parentheses straight y squared plus 3 over 2 close parentheses open parentheses straight y squared minus 3 over 2 close parentheses open parentheses straight y squared plus 3 over 2 close parentheses open parentheses y squared minus 3 over 2 close parentheses equals open parentheses z plus 3 over 2 close parentheses open parentheses z minus 3 over 2 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space vertical line space w h e r e space y squared equals z equals space left parenthesis z right parenthesis squared minus open parentheses 3 over 2 close parentheses squared space space space space space space space space space vertical line space Using space Identity space III equals space straight z squared minus 9 over 4 equals left parenthesis straight y squared right parenthesis squared minus 9 over 4 space space space space space space space space space space space space space space space space space

| Substituting the value of z

equals straight y to the power of 4 minus 9 over 4.

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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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