Factor f(x)=6x^4-21x^3-4x^2+24x-35

$f (x) = 6 x^{4} - 21 x^{3} - 4 x^{2} + 24 x - 35$

Regroup terms.

$f (x) = 6 x^{4} - 21 x^{3} - 4 x^{2} + 24 x - 35$

Factor $3 x^{3}$ out of $6 x^{4} - 21 x^{3}$ .

Factor $3 x^{3}$ out of $6 x^{4}$ .

$f (x) = 3 x^{3} (2 x) - 21 x^{3} - 4 x^{2} + 24 x - 35$

Factor $3 x^{3}$ out of $- 21 x^{3}$ .

$f (x) = 3 x^{3} (2 x) + 3 x^{3} (- 7) - 4 x^{2} + 24 x - 35$

Factor $3 x^{3}$ out of $3 x^{3} (2 x) + 3 x^{3} (- 7)$ .

$f (x) = 3 x^{3} (2 x - 7) - 4 x^{2} + 24 x - 35$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 4 \cdot - 35 = 140$ and whose sum is $b = 24$ .

Factor $24$ out of $24 x$ .

$f (x) = 3 x^{3} (2 x - 7) - 4 x^{2} + 24 (x) - 35$

Rewrite $24$ as $10$ plus $14$

$f (x) = 3 x^{3} (2 x - 7) - 4 x^{2} + (10 + 14) x - 35$

Apply the distributive property.

$f (x) = 3 x^{3} (2 x - 7) - 4 x^{2} + 10 x + 14 x - 35$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$f (x) = 3 x^{3} (2 x - 7) - 4 x^{2} + 10 x + 14 x - 35$

Factor out the greatest common factor (GCF) from each group.

$f (x) = 3 x^{3} (2 x - 7) + 2 x (- 2 x + 5) - 7 (- 2 x + 5)$

Factor the polynomial by factoring out the greatest common factor, $- 2 x + 5$ .

$f (x) = 3 x^{3} (2 x - 7) + (- 2 x + 5) (2 x - 7)$

Factor $2 x - 7$ out of $3 x^{3} (2 x - 7) + (- 2 x + 5) (2 x - 7)$ .

Factor $2 x - 7$ out of $3 x^{3} (2 x - 7)$ .

$f (x) = (2 x - 7) (3 x^{3}) + (- 2 x + 5) (2 x - 7)$

Factor $2 x - 7$ out of $(- 2 x + 5) (2 x - 7)$ .

$f (x) = (2 x - 7) (3 x^{3}) + (2 x - 7) (- 2 x + 5)$

Factor $2 x - 7$ out of $(2 x - 7) (3 x^{3}) + (2 x - 7) (- 2 x + 5)$ .

$f (x) = (2 x - 7) (3 x^{3} - 2 x + 5)$

Factor f(x)=6x^4-21x^3-4x^2+24x-35

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