Question

several students factored trinomials as shown below. sort each name according to whether or not they factored correctly.
claudio
$4x^{2}-16x + 15 \
ightarrow (2x - 3)(2x - 5)$
michelle
$5x^{2}+14x - 3 \
ightarrow (5x + 1)(x - 3)$
gianna
$3x^{2}+14x + 8 \
ightarrow (3x + 2)(x + 4)$
hakim
$14x^{2}+39x + 10 \
ightarrow (14x + 5)(x + 2)$
correct
incorrect
claudio michelle
gianna hakim
drag these

Explanation:

Step1: Verify Claudio's factorization

Expand $(2x - 3)(2x - 5)$:
$$(2x)(2x) + (2x)(-5) + (-3)(2x) + (-3)(-5) = 4x^2 -10x -6x +15 = 4x^2 -16x +15$$

Step2: Verify Michelle's factorization

Expand $(5x + 1)(x - 3)$:
$$(5x)(x) + (5x)(-3) + (1)(x) + (1)(-3) = 5x^2 -15x +x -3 = 5x^2 -14x -3$$

Step3: Verify Gianna's factorization

Expand $(3x + 2)(x + 4)$:
$$(3x)(x) + (3x)(4) + (2)(x) + (2)(4) = 3x^2 +12x +2x +8 = 3x^2 +14x +8$$

Step4: Verify Hakim's factorization

Expand $(14x + 5)(x + 2)$:
$$(14x)(x) + (14x)(2) + (5)(x) + (5)(2) = 14x^2 +28x +5x +10 = 14x^2 +33x +10$$

Answer:

CORRECT:

Claudio, Gianna

INCORRECT:

Michelle, Hakim