Question

Factor each polynomial. 20 points

5a^2b^2 + 10ab +25a
8m^2n^2 - 24mn^3 +16mn
9xz^3 + 18yz^2 + 24z^2
16x^6y + 16x^2y^4 + 32x^3y^2

Answer 1

So, here we are to factor the polynomials :

`\\ 1. \sf \qquad5a^2b^2 + 10ab +25a\\ \\`

`\longrightarrow\sf \qquad5a(ab^2 + 2b +5)\\ \\`

`\\ 2. \sf \qquad 8m^2n^2 - 24mn^3 +16mn\\ \\`

`\longrightarrow\sf \qquad 8mn(mn - 3n^2 +2)\\ \\`

`\\ 3. \sf \qquad 9xz^3 + 18yz^2 + 24z^2\\ \\`

`\longrightarrow \sf \qquad 3z(3xz^2 + 6yz+ 8z)\\ \\`

`\\ 4. \sf \qquad 16x^6y + 16x^2y^4 + 32x^3y^2\\ \\`

`\longrightarrow \sf \qquad 16 {x}^(2) y(x^4 + y^3 + 2xy)\\ \\`

Some points to know :

• Factorisation is the reverse process of multiplucation.

• The Factorisation is the process of finding two or more expressions such that their product is the given expression.