Studdy Solution
STEP 1
1. We need to factor the quadratic expression 5x2−28x+32.
2. The given options are potential factorizations of the quadratic expression.
3. We will verify each option by expanding them and comparing the result with the original quadratic expression.
STEP 2
1. Expand each option to see if it matches the original quadratic expression.
2. Identify the correct factorization.
STEP 3
Expand the first option (3x−10)(x+6):
(3x−10)(x+6)=3x⋅x+3x⋅6−10⋅x−10⋅6
=3x2+18x−10x−60
=3x2+8x−60
This does not match 5x2−28x+32.
STEP 4
Expand the second option (5x−8)(x+7):
(5x−8)(x+7)=5x⋅x+5x⋅7−8⋅x−8⋅7
=5x2+35x−8x−56
=5x2+27x−56
This does not match 5x2−28x+32.
STEP 5
Expand the third option (x−8)(5x−4):
(x−8)(5x−4)=x⋅5x+x⋅(−4)−8⋅5x−8⋅(−4)
=5x2−4x−40x+32
=5x2−44x+32
This does not match 5x2−28x+32.
STEP 6
Expand the fourth option (5x−8)(x−4):
(5x−8)(x−4)=5x⋅x+5x⋅(−4)−8⋅x−8⋅(−4)
=5x2−20x−8x+32
=5x2−28x+32
This matches the original quadratic expression.
The correct factorization of 5x2−28x+32 is:
(5x−8)(x−4)
