Question

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

① f(x) = 2x² - 7x - 1
② f(x) = 3x³ - 7x² + 11x + 1
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Answer 1

✠ 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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Answer 2

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✠ 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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