2/9*i**3.
-2*i*(i + 1)**2/9
Let m = -693 + 699. Let o(g) be the third derivative of 0*g**3 + 0*g**4 + 0 + 0*g - 1/240*g**6 + m*g**2 + 1/60*g**5. Factor o(w).
-w**2*(w - 2)/2
Determine r so that -390/7*r**2 - 1116/7*r + 216/7 - 33/7*r**3 = 0.
-6, 2/11
Let j be ((-9)/30)/(135/(-25)). Let w(u) be the second derivative of j*u**3 - 1/36*u**4 - 3*u + 0*u**2 + 0. Solve w(r) = 0 for r.
0, 1
Suppose 0 = -s - 2*x + 2, 2*s - 4*x = -0*x + 4. Factor -20*b - 1 + 7 + 9 + 5*b**s.
5*(b - 3)*(b - 1)
Let o be (10 - (-4)/4) + -8. Factor -1/8*f**o + 9/8*f**2 - 11/8*f + 1/2 - 1/8*f**4.
-(f - 1)**3*(f + 4)/8
Factor -2*j**2 + 0*j**2 + j**4 - 5*j**2 + 8*j**2 + 4*j**3 - 2*j**3.
j**2*(j + 1)**2
Suppose 37*k = 33*k + 16. Let u(n) be the first derivative of 0*n - 1 + 1/10*n**5 + 0*n**3 - 1/4*n**k + 1/4*n**6 + 0*n**2. Factor u(c).
c**3*(c + 1)*(3*c - 2)/2
Let j(q) be the first derivative of -2*q**7/15 + 2*q**6/5 - q**5/5 - q**4/3 - 23*q**2 - 24. Let c(g) be the second derivative of j(g). Factor c(a).
-4*a*(a - 1)**2*(7*a + 2)
Let p(z) be the second derivative of -6*z**2 - 12*z + 13/4*z**4 + 0 - 3/4*z**5 - 2*z**3. Find m such that p(m) = 0.
-2/5, 1, 2
Let a be (-64)/144 + 20/45. Let s(c) be the second derivative of 0 + 1/5*c**5 + 0*c**3 + 0*c**4 + 7*c + a*c**2. Factor s(m).
4*m**3
Let h be 1*13/((-1053)/18)*-9. Factor -100/3 - 2*j**3 - 64/3*j**h - 190/3*j.
-2*(j + 5)**2*(3*j + 2)/3
Let u(c) be the first derivative of -c**4 - 14*c**3/3 - c**2 + 26*c - 16. Let t(h) = -4*h**3 - 13*h**2 - h + 27. Let y(w) = 2*t(w) - 3*u(w). Factor y(z).
4*(z - 1)*(z + 2)*(z + 3)
Let v be 2*(-20)/330*-11. Let 0 + 0*z + z**2 + 1/3*z**4 - v*z**3 = 0. What is z?
0, 1, 3
Factor -1/4*l**3 + 109744 - 4332*l + 57*l**2.
-(l - 76)**3/4
Let i(g) = -g**2. Let f(w) = -4*w**2 + 5*w + 18. Let j(c) = f(c) - 3*i(c). Let z be j(6). Determine l, given that -1 + l**2 - z*l - 3 + 9*l = 0.
-1, 4
Let v(f) be the second derivative of 3*f**5/20 + 129*f**4/4 + 5547*f**3/2 + 238521*f**2/2 + 78*f. Solve v(i) = 0 for i.
-43
Suppose -15*g - 37*g + 234 = 26. Factor 3/5*d**2 + 3/5*d - 3/5*d**3 + 0 - 3/5*d**g.
-3*d*(d - 1)*(d + 1)**2/5
Let w = 67 - 127. Let r be (-2)/8 - 55/w. Determine k so that r + 5/3*k**2 - 7/3*k = 0.
2/5, 1
Factor -12*a + 5*a**3 - 2*a**3 - 80891*a**2 + 80891*a**2.
3*a*(a - 2)*(a + 2)
Let j be ((-28)/140)/((-2)/20). Factor 0 + 0*a - 2/21*a**4 - 2/7*a**j + 8/21*a**3.
-2*a**2*(a - 3)*(a - 1)/21
Let l(u) be the first derivative of -10*u**6/3 + 29*u**5 + 165*u**4/4 - 370*u**3/3 + 40*u**2 + 127. Determine m so that l(m) = 0.
-2, 0, 1/4, 1, 8
Let n(v) = -v**2 - 6*v - 2. Let i be (-4)/(-10) - 114/10. Let q(s) = 7 - 2 + 6*s**2 + 13*s - 2 - 5*s**2. Let p(k) = i*n(k) - 6*q(k). Factor p(h).
(h - 2)*(5*h - 2)
Suppose 2*t = -4*n + 8, -3*t = -2*n + 5 + 7. Let q be t*(-5)/(20/6). Factor 3*o**3 + 15*o - o**q - 12*o**2 - 6 + 0*o**3 + o**3.
3*(o - 2)*(o - 1)**2
Let u(k) be the first derivative of 1/36*k**4 + 2/27*k**3 - 34 + 0*k + 1/18*k**2. Solve u(n) = 0.
-1, 0
Let f(p) = -p**2 - 7*p. Let u be f(-5). Let k(j) = -4*j - 6. Let d be k(-3). Suppose -4*a**3 + d*a + 3*a**3 + 15*a**2 + u*a**3 = 0. What is a?
-1, -2/3, 0
Let z be (4 + (-19)/5)/(1/8). Factor -28/5*j + 32/5*j**2 - 8/5*j**3 - z*j**4 + 4/5*j**5 + 8/5.
4*(j - 1)**4*(j + 2)/5
Let x = -376 + 380. Let w(z) be the third derivative of 0*z**x + 0*z + 8*z**2 + 1/80*z**6 + 0*z**3 - 1/30*z**5 + 1/420*z**7 + 0. Factor w(v).
v**2*(v - 1)*(v + 4)/2
Let b(t) = 2*t**3 - 4*t**2 + t + 2. Let h be b(2). Let j(r) be the first derivative of -4/3*r**3 + 4/5*r**5 - 1/3*r**6 + 0*r**h + 0*r + r**2 + 2. Factor j(s).
-2*s*(s - 1)**3*(s + 1)
Solve 108*w**2 + 4*w**4 + 37*w**2 + 63*w**2 - 43*w**3 - 169*w**3 = 0 for w.
0, 1, 52
Factor 0*r - 2*r**4 + 0 + 1/2*r**5 - 19/2*r**3 - 7*r**2.
r**2*(r - 7)*(r + 1)*(r + 2)/2
Let d(x) be the second derivative of -x**5/5 - 2*x**4 - 22*x**3/3 - 12*x**2 + 42*x + 2. Factor d(f).
-4*(f + 1)*(f + 2)*(f + 3)
Let i(l) be the second derivative of 0*l**2 + 1/36*l**3 - 3 + 1/120*l**5 + 1/36*l**4 + 3*l. Let i(w) = 0. What is w?
-1, 0
Let v(x) = -x**4 + 96*x**3 - 242*x**2 + 235*x - 83. Let r(u) = -48*u**3 + 120*u**2 - 117*u + 42. Let g(l) = 5*r(l) + 3*v(l). Let g(b) = 0. Calculate b.
1, 13
Let o(l) = -4*l**3 + 36*l**2 + 3. Let p be o(9). Let r(k) be the second derivative of -1/20*k**5 + 0 + 0*k**2 + 6*k + 1/6*k**p + 0*k**4. Factor r(y).
-y*(y - 1)*(y + 1)
Let x(z) be the second derivative of z**4/48 - 73*z**3/24 - 9*z + 37. Factor x(n).
n*(n - 73)/4
Let l = -23 - -25. Let x(g) = 2*g**2 - 4*g + 3. Let t be x(l). Factor -1/6*s + 1/2 - 1/2*s**2 + 1/6*s**t.
(s - 3)*(s - 1)*(s + 1)/6
Let a(n) = n**3 - 6*n**2 - 13*n + 18. Let d be a(8). Let g be -2*(-57)/d + (10 - 7). Factor 8/7 - g*k + 18/7*k**2.
2*(k - 2)*(9*k - 2)/7
Let m be ((-4)/(-16)*-9)/(3/8). Let b(x) = 10*x**2 + 2*x. Let w(d) = 9*d**2 + 3*d. Let i(v) = m*b(v) + 5*w(v). Factor i(u).
-3*u*(5*u - 1)
Let c(j) be the first derivative of j**6/5 + 14*j**5/25 - 3*j**4/5 - 179. Let c(d) = 0. What is d?
-3, 0, 2/3
Let l(t) = -t**2 - 8*t + 96. Let c be l(6). Let f(r) be the first derivative of -5*r**3 + c*r**2 + 3/4*r**4 - 12*r - 6. Suppose f(u) = 0. Calculate u.
1, 2
Let x = 591 - 2967/5. Let j = 46/15 + x. Solve -2*s**2 + 0*s - j*s**3 + 8/3 = 0.
-2, 1
Let q(l) be the first derivative of 2*l**6/3 - 4*l**5/5 - 3*l**4 + 20*l**3/3 - 4*l**2 - 516. Factor q(y).
4*y*(y - 1)**3*(y + 2)
Let i(v) be the first derivative of -v**3 - 15*v**2/2 - 18*v + 133. Let i(n) = 0. What is n?
-3, -2
Let s = 1126 + -3374/3. Solve -2/9*i - s*i**3 + 0 - 2/9*i**5 + 8/9*i**4 + 8/9*i**2 = 0 for i.
0, 1
Let f(y) be the first derivative of -2*y**5/5 + 3*y**4/2 - 2*y**3/3 - 3*y**2 + 4*y + 4. Let f(i) = 0. Calculate i.
-1, 1, 2
Let d = 126 + -114. Let f be (-2)/((-32)/d)*2. Factor 2*u + f + 1/2*u**2.
(u + 1)*(u + 3)/2
Suppose -4*s + 7*s - 5*s = 3*s. Let r be (2 + -1 + -1)*-1. Solve 1/3*z**4 + s - 2/3*z**2 + r*z - 1/3*z**3 = 0 for z.
-1, 0, 2
Determine i, given that 5/4*i + 1/4*i**2 - 3/2 = 0.
-6, 1
Let p(k) be the second derivative of 4*k + 0 - 4*k**2 + 1/3*k**4 + 2/3*k**3. Factor p(y).
4*(y - 1)*(y + 2)
Let x(u) = u**2 - 43*u + 101. Let s = 9 - 14. Let z(d) = -d**2 + 22*d - 50. Let y(q) = s*z(q) - 2*x(q). Suppose y(h) = 0. What is h?
4
Suppose 4*w = -2*z - 28, -26*w = -z - 23*w + 26. Solve 0 + 5/4*q**z + 3/2*q + 1/4*q**3 = 0.
-3, -2, 0
Let r(t) be the first derivative of t**6/18 - t**5/15 - t**4/4 + 5*t**3/9 - t**2/3 - 208. Factor r(l).
l*(l - 1)**3*(l + 2)/3
Let t(a) be the first derivative of -a**4/10 - 6*a**3/5 - 4*a**2 - 24*a/5 - 40. Let t(n) = 0. What is n?
-6, -2, -1
Let l = -35945 + 323519/9. Determine p so that l*p**2 + 8/3 - 88/9*p = 0.
2/7, 6
Suppose -2*v = -v + 4*i + 12, -3*v = 3*i. Suppose -21*l = -184*l. Determine s so that v*s**2 + 3*s**4 + 0 + 6*s**3 + l*s + 1/2*s**5 = 0.
-2, 0
Factor 9/4 - 1/4*o**2 - 2*o.
-(o - 1)*(o + 9)/4
Suppose 3*w + 5 = -c - 1, -3*c + 3*w + 42 = 0. Let j(o) = 7*o - 20. Let v be j(c). Factor -27*s - 7*s**3 - 12*s**2 + 5 + v*s**3 + 7*s - 9.
4*(s - 1)*(3*s + 1)**2
Let v(t) be the third derivative of -4/3*t**3 + 1/30*t**5 + 1/3*t**4 + 0 + 11*t**2 - 1/60*t**6 + 0*t. Factor v(z).
-2*(z - 2)*(z - 1)*(z + 2)
Let p be (261/54 - 5)/(-2). Let u(w) be the third derivative of -1/60*w**5 + 7*w**2 + 0 + 0*w**3 + 0*w + p*w**4. Factor u(v).
-v*(v - 2)
Let w = 1523 + -1071. Factor -40*i - w + 5*i**3 - 35*i**2 + 452.
5*i*(i - 8)*(i + 1)
Find n such that -16/11*n**3 + 16/11*n + 2/11*n**4 + 12/11*n**2 - 14/11 = 0.
-1, 1, 7
Let j(f) be the first derivative of -15*f**4/4 - 130*f**3/3 + 195*f**2/2 - 50*f - 167. Factor j(t).
-5*(t - 1)*(t + 10)*(3*t - 1)
Let j be 12796/90 - (-1)/(10/6). Let o = 431/3 - j. Factor 8/9*n - o*n**3 - 2/9 + 2/9*n**2.
-2*(n - 1)*(n + 1)*(4*n - 1)/9
Let k(j) = -26*j - 598. Let g be k(-23). Suppose g + 4/9*o + 2/9*o**2 = 0. What is o?
-2, 0
Let 24*k + 33/5*k**2 + 144/5 + 3/5*k**3 = 0. What is k?
-4, -3
Factor 100/3 - 46/3*x - 2/3*x**2.
-2*(x - 2)*(x + 25)/3
Let o be (15/(-35))/((-13)/91). Determine x so that -6/5*x**5 + 0 + 2/5*x + 0*x**2 - 16/5*x**4 - 12/5*x**o = 0.
-1, 0, 1/3
Let p = 13199/66 + 578/33. Let y = p + -217. Factor y*o**2 + 3*o + 5/2.
(o + 1)*(o + 5)/2
Let h(q) be the third derivative of -1/105*q**7 + 0*q**6 + 1/6*q**4 + 0*q + 0*q**3 - 15*q**2 + 1/10*q**5 + 0. Find o, given that h(o) = 0.
-1, 0, 2
Let x