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a) Factored form:  (x - 5)(x² + 7x - 7) ;  P(5) = 0 Yes

              b) Factored form: (x + 1)(x³- 5x² - 4x - 1) ; P(-1) = 0 Yes

Step-by-step explanation:

Use synthetic division to verify the remainder (last digit) is zero.  The other digits represent the coefficients of the reduced polynomial.

a) x³ + 2x² - 42x + 35    ; x - 5 = 0  --> x = 5

5 |   1     2    -42    35

   |  ↓    5     35    -35

      1     7      -7       0     → remainder is zero

Reduced polynomial is:  x² + 7x - 7

Factored form: P(x) = (x - 5)(x² + 7x - 7)

b) x⁴ - 4x³ -9x² - 5x - 1   ; x + 1 = 0  --> x = -1

-1 |   1     -4    -9    -5    -1

   |  ↓     -1      5     4     1

      1     -5    -4     -1     0   → remainder is zero

Reduced polynomial is:  x³- 5x² - 4x - 1

Factored form: P(x) = (x + 1)(x³- 5x² - 4x - 1)

439400

step-by-step explanation:

130^2 = 16900

16900*26 = 439400

step-by-step explanation:

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