how to find the linear function factors If possible factor r

how to find the linear function factors?

If possible, factor r3-12r,2 + 36rs4 into linear factors in r. 122+36rs into linar actors If it is not possible, enter NA. Click here to enter or edit your answer -122 36rs4

Solution

1. r³ - 12 r²s² + 36rs⁴ = r( r² - 12rs² + 36s⁴) . Let s² = t. Then r² - 12rs² + 36s⁴ = r² - 12rt + 36t²  = ( r - 6t)² = (r - 6s²)² . Therefore, r³ - 12 r²s² + 36rs⁴ = r( r² - 12rs² + 36s⁴) = r (r - 6s²)^2.

2. ( r + 3)² + 10t ( r + 3) + 25 t² . Let r + t = p. Then, ( r + 3)² + 10t ( r + 3) + 25 t² = p² + 10pt + 25t² = (p + 5t)² = = ( 4r + 3 + 5t)²