Math  /  Algebra

QuestionUse synthetic division to divide. SEE EXAMPLE 2
19. x425x2+144x^{4}-25 x^{2}+144 divided by x4x-4
20. x3+6x2+3x10x^{3}+6 x^{2}+3 x-10 divided by x+5x+5
21. x5+2x43x3+x1x^{5}+2 x^{4}-3 x^{3}+x-1 divided by x+2x+2
22. x4+7x3+x22x12-x^{4}+7 x^{3}+x^{2}-2 x-12 divided by x3x-3
23. Use synthetic division to show that the remainder of f(x)=x46x333x2+46x+75f(x)=x^{4}-6 x^{3}-33 x^{2}+46 x+75 divided by x9x-9 is P(9)P(9). SEE EXAMPLE 3

Studdy Solution
For problem 23, verify the remainder of f(x)=x46x333x2+46x+75 f(x) = x^4 - 6x^3 - 33x^2 + 46x + 75 divided by x9 x - 9 is f(9) f(9) .
- Write the coefficients: [1,6,33,46,75] [1, -6, -33, 46, 75] . - The divisor is x9 x - 9 , so c=9 c = 9 . - Set up the synthetic division:
916334675927547213683\begin{array}{c|ccccc} 9 & 1 & -6 & -33 & 46 & 75 \\ & & 9 & 27 & -54 & -72 \\ \hline & 1 & 3 & -6 & -8 & 3 \\ \end{array}
- The remainder is 3 3 , which confirms that f(9)=3 f(9) = 3 .

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