Question

factor completely.
$6x^2 - 23x - 35$

Explanation:

Step1: Multiply a and c

$6 \times (-35) = -210$

Step2: Find two factors of -210

Factors: -21 and 10 (since $-21 + 10 = -11$? No, wait: $-210 = (-30) \times 7$? No, correct factors: $-210 = (-35) \times 6$? Wait, target sum is -23. Correct: $-30$ and $7$: $-30 +7=-23$. Yes!

Step3: Split middle term

$6x^2 -30x +7x -35$

Step4: Factor by grouping

$6x(x -5) +7(x -5) = (6x +7)(x -5)$? Wait no, wait: $6x^2 -30x +7x -35 = 6x(x-5)+7(x-5)=(6x+7)(x-5)$? Wait wait original trinomial is $6x²-23x-35$. Let's redo: $a=6, b=-23, c=-35$. $ac=6*(-35)=-210$. Find two numbers that multiply to -210 and add to -23: $-30$ and $7$ (since $-30*7=-210$, $-30+7=-23$). Split: $6x²-30x+7x-35$. Group: $(6x²-30x)+(7x-35)=6x(x-5)+7(x-5)=(6x+7)(x-5)$. Wait wait let's check: $(6x+7)(x-5)=6x²-30x+7x-35=6x²-23x-35$. Yes! So the correct factorization is $(6x +7)(x -5)$.

Wait I made a mistake earlier in step2, corrected now. So final answer is $(6x +7)(x -5)$.

Answer:

$(2x - 7)(3x + 5)$