Question

The model represents a polynomial of the form ax2 + bx + c. Which equation is represented by the model?
a.) 3x2 – 4x – 1 = (3x + 1)(x – 1)
b.) 3x2 – 2x – 1 = (3x – 1)(x + 1)
c.) 3x2 – 4x + 1 = (3x – 1)(x – 1)
d.) 3x2 – 2x + 1 = (3x – 1)(x – 1)

Answer 1

Answer:

C) 3x2 – 4x + 1 = (3x – 1)(x – 1)

Answer 2

Option C

The equation represents a polynomial of the form ax^2 + bx + c is:

$3x^2 - 4x + 1 = (3x-1)(x-1)$

Solution:

Option A

$3x^2 - 4x - 1 = (3x +1)(x - 1)$

Expand the right side of equation

$\left(3x+1\right)\left(x-1\right)\\\\3xx+3x\left(-1\right)+1\cdot \:x+1\cdot \left(-1\right)\\\\3x^2-3x+x-1\\\\3x^2-2x-1$

$LHS \neq RHS$

Thus option A is wrong

Option B

$3x^2 -2x-1 = (3x-1)(x+1)$

Expand the right side of equation

$\left(3x-1\right)\left(x+1\right)\\\\3xx+3x\cdot \:1+\left(-1\right)x+\left(-1\right)\cdot \:1\\\\3x^2+2x-1\\\\Thus\\\\LHS \neq RHS$

Thus option B is wrong

Option C

$3x^2 - 4x + 1 = (3x-1)(x-1)$

Expand the right side of equation

$\left(3x-1\right)\left(x-1\right)\\\\3xx+3x\left(-1\right)+\left(-1\right)x+\left(-1\right)\left(-1\right)\\\\3x^2-4x+1\\\\Thus\\\\LHS = RHS$

Thus Option C is correct

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