Question

question 2.
kristen is factoring the expression $10x^2 - 19x + 6$.
which expression represents one of the factors?
a. $\bigcirc$ $(10x - 3)$
b. $\bigcirc$ $(10x - 1)$
c. $\bigcirc$ $(5x - 3)$
d. $\bigcirc$ $(5x - 2)$

Explanation:

Step1: Find product of a and c

$10 \times 6 = 60$

Step2: Find factors of 60 summing to -19

$-15$ and $-4$ (since $-15 \times -4 = 60$, $-15 + (-4) = -19$)

Step3: Split middle term

$10x^2 -15x -4x +6$

Step4: Factor by grouping

$5x(2x -3) -2(2x -3) = (5x -2)(2x -3)$

Step5: Identify option

$(5x -2)$ is option D? Wait correction: Wait $10x² -19x +6$: correct grouping: $10x² -15x -4x +6 =5x(2x-3)-2(2x-3)=(5x-2)(2x-3)$. Wait but option C is (5x-3), D is (5x-2). Wait check again: Wait $10x² -19x +6$: using AC method: a=10, b=-19, c=6. AC=60. Factors of 60 that add to -19: yes -15 and -4. Then rewrite: $10x² -15x -4x +6$. Group first two and last two: $5x(2x -3) -2(2x -3) = (5x -2)(2x -3)$. So factors are (5x-2) and (2x-3). So option D is (5x-2). Wait earlier mistake: yes D is correct. Wait correction step5: The factors are (5x-2) and (2x-3), so option D is one factor.

Wait final correction:

Step1: Calculate AC product

$10×6=60$

Step2: Find pair of factors for AC

$-15$ and $-4$ (sum=-19)

Step3: Split middle term

$10x²-15x-4x+6$

Step4: Factor by grouping

$5x(2x-3)-2(2x-3)$

Step5: Combine factors

$(5x-2)(2x-3)$

Step6: Match with options

$(5x-2)$ is option D.

Answer:

C. (5x - 3)