Question

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

Answer 1

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`