
Let f(l) be the first derivative of -l**7/28 - l**6/5 - 3*l**5/8 - l**4/4 + l + 1. Let d(a) be the first derivative of f(a). What is t in d(t) = 0?
-2, -1, 0
Factor -1/3*r**3 + 0 + 1/3*r**2 + 0*r - 4*r**4.
-r**2*(3*r + 1)*(4*r - 1)/3
Let f(n) be the third derivative of n**5/240 - n**4/96 - 6*n**2. Factor f(h).
h*(h - 1)/4
Let i(h) be the first derivative of -h**5/20 + 3*h**4/4 - 9*h**3/2 + 27*h**2/2 - 81*h/4 - 20. What is s in i(s) = 0?
3
Let o be (-30)/4*(2 - 6). Determine c so that 3 - 3 + 12*c**2 + 15*c - 6*c**4 - o*c**3 - 6 + 15*c**5 = 0.
-1, 2/5, 1
Let b(x) = -x**2 + 6*x + 7. Let g be b(7). Let c(t) be the first derivative of 0*t**2 + 0*t + 1/4*t**4 + g*t**3 + 1/5*t**5 + 1. Factor c(v).
v**3*(v + 1)
Let m = -9 - -11. Suppose m = -3*u + 14. Factor 1/2*r**3 + 0 - 1/2*r + 1/2*r**u - 1/2*r**2.
r*(r - 1)*(r + 1)**2/2
Let c(p) be the second derivative of 0 + 0*p**2 - 1/27*p**3 + 1/27*p**4 - p - 1/90*p**5. Find w such that c(w) = 0.
0, 1
Let o(c) be the third derivative of c**5/270 + c**4/108 - 8*c**2. Factor o(y).
2*y*(y + 1)/9
Let t(d) = 3*d**3 - 20*d**2 + 17*d + 8. Let x(f) = -f**3 + 7*f**2 - 6*f - 3. Let a(g) = -3*t(g) - 8*x(g). Factor a(h).
-h*(h - 3)*(h - 1)
Let c = 1 - -3. Suppose 6*b - 2*b + c = 4*h, -4*b = -h - 5. Factor -u**4 - u - 2*u**4 + u**5 + u**4 + 2*u**b.
u*(u - 1)**3*(u + 1)
Let s(x) = -16*x**4 - 3*x**3 + 7*x**2 - 8*x - 13. Let o(y) = -y**4 - y - 1. Let m(k) = 22*o(k) - 2*s(k). Factor m(q).
2*(q - 1)*(q + 1)**2*(5*q - 2)
Let o(b) be the second derivative of 1/15*b**4 + 4/5*b**2 + 0 + 10*b - 2/5*b**3. Factor o(m).
4*(m - 2)*(m - 1)/5
Find n such that -33*n**2 - 8 - 35*n**3 - 4*n - 19*n**2 + 11*n**3 - 32*n = 0.
-1, -2/3, -1/2
Let v(i) be the second derivative of -3*i**5/25 - 7*i**4/20 + i**3/5 + 4*i. Determine x so that v(x) = 0.
-2, 0, 1/4
Let g(a) be the third derivative of 6*a**2 + 1/180*a**5 + 0*a**3 + 1/360*a**6 + 0*a + 0 - 1/36*a**4. Factor g(l).
l*(l - 1)*(l + 2)/3
Let m(z) be the third derivative of z**2 + 0*z**3 + 1/32*z**4 + 0 + 1/40*z**5 + 0*z - 3/160*z**6. Determine n, given that m(n) = 0.
-1/3, 0, 1
Determine i so that -2/15*i**4 + 0 - 2/15*i**5 + 2/15*i**3 + 2/15*i**2 + 0*i = 0.
-1, 0, 1
Let j(c) = c + 2. Let s be j(2). Factor 4/7*h**3 + 10/7*h**s + 0*h**2 + 0*h + 0.
2*h**3*(5*h + 2)/7
Suppose -3*k**4 - 18*k**2 + 52*k + 59*k - 111*k + 15*k**3 = 0. Calculate k.
0, 2, 3
Let t(i) be the second derivative of -i**4/78 - i**3/39 + i. Let t(k) = 0. Calculate k.
-1, 0
Let l(h) be the second derivative of 0 - 4*h + 1/12*h**4 + 0*h**2 + 1/20*h**5 + 0*h**3. Factor l(t).
t**2*(t + 1)
Let q = -3 + 1. Let b be 0*(8/(-12))/q. Determine k so that -k + 1/3*k**3 - 2/3 + b*k**2 = 0.
-1, 2
Let f(n) be the second derivative of -n**6/210 - 3*n**5/140 + 3*n**4/28 - 5*n**3/42 + n. Solve f(b) = 0 for b.
-5, 0, 1
Let x(y) be the first derivative of -y**5/5 + y**4 + 31. Factor x(w).
-w**3*(w - 4)
Let z(y) be the second derivative of -y**6/60 + y**4/24 + 17*y. Factor z(n).
-n**2*(n - 1)*(n + 1)/2
Let c be 78/(-663) - 246/(-357). Factor c*x - 2/7*x**3 + 0 + 2/7*x**2.
-2*x*(x - 2)*(x + 1)/7
Let a be 12/(-450)*-145 + (-6)/5. Factor -2/3*d**2 + a*d - 2.
-2*(d - 3)*(d - 1)/3
Solve -7865*f + 3*f**3 + 10 + 7883*f - 5*f**3 + 6*f**2 = 0 for f.
-1, 5
Let d = 196/5 + -39. Suppose 0 + d*i**2 + 1/5*i**5 + 0*i - 1/5*i**4 - 1/5*i**3 = 0. Calculate i.
-1, 0, 1
Let n(m) = -1. Let s(c) = 2*c**2 + 6*c + 2. Let r(b) = -4*n(b) + 2*s(b). Factor r(g).
4*(g + 1)*(g + 2)
Let d(i) be the second derivative of -i**6/60 - 3*i**5/40 - i**4/8 - i**3/12 - 7*i. Suppose d(j) = 0. Calculate j.
-1, 0
Let o = 15 + -11. Let f(d) be the third derivative of -25/6*d**6 - 2*d**2 - 10/3*d**o + 0*d + 125/84*d**7 + 4/3*d**3 + 0 + 5*d**5. Factor f(i).
(5*i - 2)**4/2
Suppose -5*a - 70 = -5*q, 4*q = -0*a + 5*a + 68. Let m be ((-8)/(-10))/((-8)/a). Factor 0*u + m*u**4 + 0 - 8/5*u**2 + 8/5*u**3.
2*u**2*(u + 2)*(3*u - 2)/5
Let f(a) be the third derivative of a**5/150 - a**4/30 + 4*a**2. Factor f(q).
2*q*(q - 2)/5
Let b(c) = -c**2 + 9*c + 4. Let h be b(7). Let d be (-3)/(h/8) - -2. Determine l so that -d*l - 2/3*l**2 + 4/3 = 0.
-2, 1
Let t(j) be the third derivative of 7*j**2 - 1/27*j**3 + 0 + 1/270*j**5 + 0*j**4 + 0*j. Factor t(w).
2*(w - 1)*(w + 1)/9
Suppose -2*j = -4*j - 3*g + 25, 2*j + 10 = 4*g. Suppose 6 = j*z + 1. Factor p**3 - p**2 + 2*p**2 - z + 3*p - 4*p**2.
(p - 1)**3
Suppose -3*h = -6*h + 18. Suppose 2*r + 2*r = -2*b + 2, -2*r - 11 = 5*b. Let -4 - 1/2*j**3 - 3*j**r - h*j = 0. Calculate j.
-2
Let b = -2/519 - -175/519. Factor 0*l**2 + 0*l + 0 + 1/3*l**3 + b*l**4.
l**3*(l + 1)/3
Let y = -3/1057 + -157478/5285. Let s = y + 30. Solve -1/5*q**2 + 0*q + s = 0.
-1, 1
Let v(k) = k + 5. Let g be v(-4). Factor 9*c**2 - 8*c**2 + c + 0 - c**3 + 0*c**3 - g.
-(c - 1)**2*(c + 1)
Let d(u) be the first derivative of -1/10*u**5 + 0*u + 2/3*u**3 - 1/12*u**4 + 1 - 1/2*u**2. Let b(l) be the second derivative of d(l). Solve b(m) = 0.
-1, 2/3
Let p be ((-14)/4 - 4)*-2. Suppose -5*f - 2*b - 1 = -p, 2*f = -2*b + 8. Suppose -2/7*g**4 - 2/7*g - 6/7*g**f - 6/7*g**3 + 0 = 0. What is g?
-1, 0
Let p(k) be the second derivative of k + 3/110*k**5 + 0*k**3 + 0 - 1/66*k**4 + 0*k**2 + 1/231*k**7 - 1/55*k**6. Suppose p(q) = 0. What is q?
0, 1
Let k(l) be the first derivative of l**6/3 + 6*l**5/5 + l**4 - 4*l**3/3 - 3*l**2 - 2*l - 47. Factor k(q).
2*(q - 1)*(q + 1)**4
Let x(q) be the first derivative of -30/11*q**3 + 2 - 8/11*q - 32/11*q**2 + 81/22*q**4. Factor x(n).
2*(n - 1)*(9*n + 2)**2/11
Let q(j) be the second derivative of j**6/10 - j**4/4 - 12*j. Let q(g) = 0. What is g?
-1, 0, 1
Let j(y) be the third derivative of y**6/120 - y**5/30 - 7*y**4/24 - 2*y**3/3 - 10*y**2. Factor j(s).
(s - 4)*(s + 1)**2
Let r(u) = -2*u**2 - 18*u. Let y be r(-9). Find b, given that -4*b**2 + 2*b + 0*b**2 + y - 2*b**3 + 4 = 0.
-2, -1, 1
Let j be (1 - 0)/((-4 + -1)/(-35)). Let u(b) be the second derivative of -1/6*b**4 + 0*b**2 - 1/10*b**5 + 0 + 1/21*b**j + 0*b**3 + 1/15*b**6 + 3*b. Factor u(d).
2*d**2*(d - 1)*(d + 1)**2
Let z(n) = -2*n - 5. Let h be z(-4). Let c = 5 - h. Factor t**c - 5*t**2 - 2*t + t.
-t*(4*t + 1)
Let i(s) = -s + 10. Let a be i(9). Let h(u) be the first derivative of 0*u**4 + 1/12*u**3 + 0*u - 1/20*u**5 + 0*u**2 - a. Solve h(t) = 0.
-1, 0, 1
Find l, given that 29*l**2 - 52*l**4 + 36*l**3 + 0*l + 4*l + 4*l + 23*l**2 - 44*l**5 = 0.
-1, -2/11, 0, 1
Let y(o) be the third derivative of o**5/360 - o**4/9 + 16*o**3/9 - 13*o**2. Factor y(n).
(n - 8)**2/6
Let r(l) be the second derivative of l**6/30 + l**5/20 - 4*l. Factor r(s).
s**3*(s + 1)
Let h(t) be the first derivative of -5*t**3/12 - 5*t**2/2 - 5*t - 11. Factor h(i).
-5*(i + 2)**2/4
Suppose 0*y + 3*y = 4*y. Factor 2/17*s**2 + y - 4/17*s.
2*s*(s - 2)/17
Let x(j) = -j**3 + 16*j + 24. Let y be x(-3). Suppose 0 + 0*c**y + 0*c + 0*c**2 + 2/5*c**4 = 0. What is c?
0
Suppose 4*p = 2*k + 140, -p - 3*k + 44 = -8*k. Let f = p - 32. What is x in -12/7*x**2 + 8/7*x**3 + 16/7*x**4 - 4/7 - f*x + 6/7*x**5 = 0?
-1, -2/3, 1
Let c(h) be the first derivative of -2*h**3/3 + 4*h**2 - 8*h - 10. Suppose c(d) = 0. What is d?
2
Suppose 5*s - 31 = -4*l + 2*s, 5*l + 4*s = 38. Suppose 2*b = l, -5*a = -6*a - 2*b + 12. Solve 2*z**2 + 4*z**4 - 2*z**4 + 2*z - 4*z**a - 2*z**3 = 0 for z.
-1, 0, 1
Determine n, given that -2*n**2 + 2/3*n**3 - 6*n - 10/3 = 0.
-1, 5
Let h(w) be the second derivative of -w**8/20160 + w**7/7560 - w**4/2 + 6*w. Let k(b) be the third derivative of h(b). Determine d so that k(d) = 0.
0, 1
Suppose -4*h = -0*h + 8, 0 = -4*k - 4*h - 16. Let x = k + 5. Factor 2*p**x + 3*p**2 + 3*p**2 - 2*p**2.
2*p**2*(p + 2)
Let y(p) be the second derivative of p**5/130 - p**4/39 + p**3/39 - 6*p. Suppose y(o) = 0. Calculate o.
0, 1
Let 0 + k + 1/2*k**2 = 0. What is k?
-2, 0
Let f be 12/(((-140)/5)/(-7)). Find a, given that 0 + 1/2*a - a**2 + 1/2*a**f = 0.
0, 1
Let l(b) be the second derivative of -b**5/20 + b**4 - 5*b**3/3 - 4*b**2 + 6*b. Let v be l(11). Factor -1/2 + 1/2*x**4 + 0*x**2 + x**v - x.
(x - 1)*(x + 1)**3/2
Suppose 12 - y**2 + 15*y - 2*y**2 + 10*y**2 - 4*y**2 = 0. Calculate y.
-4, -1
Let a(z) be the third derivative of z**7/63 - 13*z**6/720 + z**5/180 + 2*z**2. Factor a(x).
x**2*(4*x - 1)*(5*x - 2)/6
Let w(p) be the first derivative of p**6/12 - p**5/10 - 3*p**4/8 + p**3/6 + p**2/2 - 5.