Given x^2 -4x+4 is a factor of the polynomial 2x^4 - 11x^3 +68x-80, completely factor the polynomial using algebraic methods.

1 answer:

4 0

Answer:

2x^4-11x^3+68x-80

2x^4-4x^3-7x^3+14x^2-14x^2+28x+40x-80

2x^3(x-2)-7x^2(x-2)-14x(x-2)+40(x-2)

(x-2)(2x^3-7x^2-14x+40)

(x-2)(2x^3-4x^2-3x^2+6x-20x+40)

(x-2)(2x^2(x-2)-3x(x-2)-20(x-2))

(x-2)(x-2)(2x^3-3x-20)

(x-2)(x-2)(2x^2+5x-8x-20)

(x-2)(x-2)(x(2x+5)-4(2x+5))

(x-2)(x-2)(2x+5)(x-4)

(x-2)^2(2x+5)(x-4)

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20 Point!

ludmilkaskok [199]

determinant: $\sqrt{b^2-4ac}$

(a) $x^2+4x+5=0\\D=4^2-4\cdot1\cdot5={-4}\\D$

D<0 means there are no real roots. there are two complex roots with imaginary components.

(b) D=16+20=36>0

D>0 means there are two real roots

D=0 means there is one real root with multiplicity 2

7 0

3 years ago

Jeremy used a total of 16 sticks to support his vegetables. The sticks were 55cm and 75cm long and the sum of their lengths was

svetoff [14.1K]

9 longer sticks were used.
This is how i get it.
1. change m to cm, 1m =100cm
2. add both together, divide by 16 =8.125. Which means 1 of the stick should more than 8, and 1 of the other stick should be less than 8
3. substitute the equation
4.(55 x 7)+(75 x 9) =1060