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II. Determine whether the second polynomial is a factor of the first by using the Factor Theorem. (Write YES if it is a factor and NO if not.)
____________11. 4x7 – 2x6 + x2 + 2x + 5; x – 1
____________12. a6 – a5 – 7a4 + a3 + 8a2 + 5a + 2; a + 2
____________13. 2x3 + 2x2 – 3x – 4; x + 5
____________14. 2x4 + 7x3 + 5x2 – 8x – 4; 2x + 1
____________15. x4 + 2x3 – 8x – 16; x + 2

III. Fill in the blank with the missing factor in each of the following using
synthetic division.
16. x3 – 3x + 2; (x – 1) and ___________
17. 2x3 – 3x2 – 23x + 42; (2x + 7) and ___________
18. x3 – 6x2 + 11x – 6; (x – 2) and __________
19. x3 –x2 -4x +4 ; (x-1) and _______________
20. x3 –x2 -4x +4 ; (x-2) and _______________
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GONDAYHANAGO

Answer:

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first polynomial. By the factor theorem, x + 2 is a factor of f (x) if and only if f (–2) = 0. Since f (–2) = 0, then x + 2 is a factor of f (x)

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