3x^2+17x+10
*you have to factor completley
51xcubed+12
Didn't I do this already? I remember it. What two factors of ten (hint: 5,2) will add to 17 when one factor is multiplied by 3? Hint: the five will be multiplied by three.
To factor the quadratic expression 3x^2 + 17x + 10 completely, we need to find two binomial factors that multiply together to give us the original expression. Here's how we can approach this:
Step 1: Identify the coefficient of the quadratic term, which is 3.
Step 2: Identify the constant term, which is 10.
Step 3: We need to find two factors of 10 (hint: 5, 2) that can be combined to give us the coefficient of the linear term, which is 17.
Step 4: Determine which factor will be multiplied by the coefficient of the quadratic term, which is 3. In this case, it is the factor 5.
Step 5: Rewrite the expression using these factors in place of the linear term:
3x^2 + 17x + 10
becomes
3x^2 + 5x + 12x + 10
Step 6: Group the terms into pairs:
(3x^2 + 5x) + (12x + 10)
Step 7: Factor out the common factor from each pair:
x(3x + 5) + 2(6x + 5)
Step 8: Combine the two binomial factors:
(x + 2)(3x + 5)
Therefore, the completely factored form of the quadratic expression is (x + 2)(3x + 5).