Find the remainder (without division) on dividing f(x) by (x + 3) where :

① f(x) = 2x² – 7x – 1
② f(x) = 3x³ – 7x²

2 thoughts on “Find the remainder (without division) on dividing f(x) by (x + 3) where :<br /><br />① f(x) = 2x² – 7x – 1<br />② f(x) = 3x³ – 7x²”

1. [tex]\huge\mathbb\fcolorbox{purple}{lavenderblush}{✰Answer}[/tex]

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   ✠ Since x + 3 = x – ( -3 ), by cor. 1 to remainder theorem :

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   ① f(x) = 2x² – 7x – 1

   ☆ Remainder ➤ f(-3)

   ➤ 2. (-3)² – 7. (-3) – 1

   ➤ 2.9 + 21 – 1

   ➤ 18 + 21 – 1

   ➤ 38

   Hence, the remainder is 38.

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   ② f(x) = 3x³ – 7x² + 11x + 1

   ☆ Remainder ➤ f(-3)

   ➤ 3. (-3)³ – 7. (-3)² + 11. (-3) + 1

   ➤ 3.(-27) – 7.9 – 33 + 1

   ➤ – 81 – 63 – 33 + 1

   ➤ -176

   Hence, the remainder is -176.

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   [tex] \bf \underline{ \purple{Regards:}}[/tex]

   [tex] \bf\: \: \: \: \: \: \: \underline{ \underline \pink{ ItzBlìnkìngstar}}[/tex]

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2. ✠ Since x + 3 = x – ( –3 ), by cor. 1 to remainder theorem :

   ━━━━━━━━━━━━━━━━━━

   ① f(x) = 2x² – 7x – 1

   ☆ Remainder ➤ f(-3)

   ➤ 2. (-3)² – 7. (-3) – 1

   ➤ 2.9 + 21 – 1

   ➤ 18 + 21 – 1

   ➤ 38

   • Hence, the remainder is 38.

   ━━━━━━━━━━━━━━━━━━

   ② f(x) = 3x³ – 7x² + 11x + 1

   ☆ Remainder ➤ f(-3)

   ➤ 3. (-3)³ – 7. (-3)² + 11. (-3) + 1

   ➤ 3.(-27) – 7.9 – 33 + 1

   ➤ – 81 – 63 – 33 + 1

   ➤ -176

   • Hence, the remainder is –176.

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