how do you simplify 3j cubed - 51j squared + 210j? I have the answer as j(j(3j-51)
= 210 or is it 3j ((j squared -17j + 70)? thank you for your assistance.
3j^3 - 5ij^2 + 210j
First, we factor out the most obvious factor (which is j, since all terms contain the variable j):
j (3j^2 - 51j + 210)
We can also see here that the terms inside the parenthesis have a common factor of 3, thus,
3j (j^2 - 17j + 70)
To factor the quadratic expression inside the parenthesis, we list all the factors of 70, and from these, we choose the pair that has a sum of -17.
1 x 70 || 2 x 35 || 5 x 14 || 7 x 10
-1 x -70 || -2 x -35 || -5 x -14 || -7 x -10
From these, the pair that has a sum of -17 is -7 and -10. Thus we rewrite the quadratic expression as such:
3j (j - 7) (j - 10)
hope this helps~ `u`
whats 3j cubed
To simplify the expression 3j^3 - 51j^2 + 210j, you need to factor out the greatest common factor. In this case, the greatest common factor is j.
Step 1: Factor out j from each term:
3j^3 - 51j^2 + 210j = j(3j^2 - 51j + 210)
Now, we need to factor the quadratic expression 3j^2 - 51j + 210 further. In order to do this, we can either use factoring or the quadratic formula.
Using factoring:
Step 2: Look for factors of the leading coefficient (3) and the constant term (210) that add up to the middle coefficient (-51).
The factors of 3 are 1 and 3, and the factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210. After testing combinations, we find that 6 and 35 add up to -51.
Step 3: Rewrite the middle term (-51j) using the found factors (6j and 35j):
3j^2 - 6j - 35j + 210
Step 4: Group the terms and factor by grouping:
(j^2 - 6j) - (35j - 210) = j(j - 6) - 35(j - 6)
Step 5: Observe that (j - 6) appears as a common term and factor it out:
(j - 6)(j - 35)
Therefore, the simplified expression is:
j(3j^2 - 51j + 210) = j(j - 6)(j - 35)
Hence, your first answer is correct: j(j - 6)(j - 35) = 0.
Your second answer, 3j(j^2 - 17j + 70), is incorrect.