Question

Please Solve all of them if you are genuis.

Answer 1

first solution is. (×+1)(×-2)(×-4)


second answer given below

Apply trial and error to the equation by substituting x as any random integer to the equation x3−6x2+3x+10=0" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">x3−6x2+3x+10=0x3−6x2+3x+10=0. If the equation gives a result of 0, then (x - root) will be one factor of the equation. 
 
In that case, consider x = 2, so 23−6(2)2+3(2)+10=0" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">23−6(2)2+3(2)+10=023−6(2)2+3(2)+10=0 
8−24+6+10=0" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">8−24+6+10=08−24+6+10=0 
 
Hence, (x - 2) is one of the roots of the equation. 
 
Now, apply long division, and accordingly we will obtain another factor as x2−4x−5=(x−5)(x+1)" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">x2−4x−5=(x−5)(x+1)x2−4x−5=(x−5)(x+1). 
 

Hence, x3−6x2+3x+10=(x+1)(x−2)(x−5)" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">x3−6x2+3x+10=(x+1)(x−2)(x−5)x3−6x2+3x+10=(x+1)(x−2)(x−5).

hop it is help full to you mark as brainliest answer