Question

factor by grouping 7c^4 - 4c^3 + 28c^2 - 16c

Answer 1

Answer:

The factor by grouping 7c^4 - 4c^3 + 28c^2 - 16c is $\left(c^{2}+4\right)(7 c-4) c$

Solution:

$\text { Given, expression is } 7 \mathrm{c}^{4}-4 \mathrm{c}^{3}+28 \mathrm{c}^{2}-16 \mathrm{c}$

We have to factor the given expression by grouping.

$\text { Now, } 7 c^{4}-4 c^{3}+28 c^{2}-16 c$

$\rightarrow 7 c^{4}+28 c^{2}-4 c^{3}-16 c$

By grouping the terms we get,

$\rightarrow\left(7 c^{4}+28 c^{2}\right)-\left(4 c^{3}+16 c\right)$

By taking the common terms out from groups,

$\rightarrow 7 c^{2}\left(c^{2}+4\right)-4 c\left(c^{2}+4\right)$

$\text { Taking } \mathrm{c}^{2}+4 \text { as common }$

$\rightarrow\left(c^{2}+4\right)\left(7 c^{2}-4 c\right)$

$\Rightarrow\left(c^{2}+4\right)(7 c-4) c$

Hence, the factorization of given expression is $\left(c^{2}+4\right)(7 c-4) c$