Find the remaining factors for x4 - 10x3 + 35x2 - 50x + 24 if two factors are x - 1, and x - 3.

Question

synthetic division

Answer 1

The factors are (x-1)(x-3)

(x-1)(x-3) =x² -4x+3

f(x) = x⁴ - 10x³ + 35x² -50x+24.

x² -4x+3)x⁴ - 10x³ + 35x² -50x+24 (x²-6x+8

            (-)       x⁴    - 4x³ + 3x²

            ---------------------------------

                             -6x³ +32x² -50x+24

                     (-)      -6x³ +24x² -18x

                  ---------------------------------

                                          8x² -32x+24

                     (-)                 8x²-32x+24

                     ---------------------------------

                                       0

         

f(x) = x⁴ - 10x³ + 35x² -50x+24 =(x² -4x+3)(x²-6x+8)

                                                    =(x-1)(x-3)(x²-6x+8)

Find the factors of (x²-6x+8)

(x²-6x+8) =(x²-4x-2x+8)

                       =x(x-4)-2(x-4)

                       =(x-2)(x-4)

Remaining factors are (x-2) and (x-4)         

Comments

i dont get it.

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dont understand,can you plz explain.

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where did the x²-6x+8 come from?

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please check modified solution

Answer 2

First find the reduced expression when (x-1) is factor.

Step 1 : Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients as shown at the right.

Step 2 : Write the constant r of the divisor (x - r ) to the left. In this case, r = 1. Bring the first coefficient, 1, down.

Step 3 : Multiply the first coefficient by r : 1(1) = 1. Write the product under the second coefficient, -10 and add : -10 + 1 = -9.

 

Step 4 : Multiply the first coefficient by r : 1(-9) = -9. Write the product under the second coefficient, 35 and add : 35 +( -9) = 26.

Step 5 : Multiply the first coefficient by r : 1(26) = 26. Write the product under the second coefficient, -50 and add :  -50 +(26) = -24.

Step 6 : Multiply the first coefficient by r : 1(-24) =- 24. Write the product under the second coefficient, 24 and add :  24 +(-24) = 0.

So reduced expression is x³- 9x² +26x - 24

Second factor is (x-3).

Next find the reduced form when  (x-3) is factor.

Answer 3

conti.....

Step 1 : Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients as shown at the right.

Step 2 : Write the constant r of the divisor (x - r ) to the left. In this case, r = 3. Bring the first coefficient, 3, down.

Step 3 : Multiply the first coefficient by r : 3(1) = 3. Write the product under the second coefficient, -9 and add : -9 + 3 = -6.

 

Step 4 : Multiply the first coefficient by r : 3(-6) = -18. Write the product under the second coefficient, 26 and add : 26 +( -18) = 8.

Step 5 : Multiply the first coefficient by r : 3(8) = 24. Write the product under the second coefficient, -24 and add :  -24 +(24) = 0.

So reduced expression is x²- 6x+8

Find the factors of (x²-6x+8)

(x²-6x+8) =(x²-4x-2x+8)

                       =x(x-4)-2(x-4)

                       =(x-2)(x-4)

Remaining factors are (x-2) and (x-4)