Let j(d) be the first derivative of -3*d**5/5 + 9*d**4/4 - 3*d**3 + 3*d**2/2 + 18. What is l in j(l) = 0?
0, 1
Let t be 20 - (-1 + 2 + -2). Let z = t - 41/2. Find k such that 0 - z*k**2 + k - 21/2*k**3 = 0.
-1/3, 0, 2/7
Let b(v) be the first derivative of -v**6/8 - v**5/4 - v**4/16 + v**3/12 - 12. Solve b(t) = 0.
-1, 0, 1/3
Let z(p) be the second derivative of -6*p + 1/70*p**5 + 1/7*p**2 + 1/7*p**3 + 1/14*p**4 + 0. Find m such that z(m) = 0.
-1
Let u(o) be the first derivative of o**8/1680 + o**7/420 - o**5/60 - o**4/24 - o**3 + 3. Let m(n) be the third derivative of u(n). Solve m(s) = 0.
-1, 1
Let f = 57 - 55. Suppose 0*p + 1/3*p**f + 0 = 0. What is p?
0
Let g(a) = -a**3 + 3*a**2 + 5*a - 2. Let n be ((-2)/5)/((-4)/40). Let r be g(n). Let l**5 - 3*l**4 - r*l**4 + 4*l**4 = 0. What is l?
0, 1
Let k(m) be the second derivative of -2*m**7/27 + 11*m**6/30 - 131*m**5/180 + 79*m**4/108 - 7*m**3/18 + m**2/9 + 2*m - 2. What is f in k(f) = 0?
1/4, 2/7, 1
Let u(w) be the third derivative of 1/240*w**5 + 0 - 1/480*w**6 + 0*w**3 + 4*w**2 + 1/48*w**4 + 0*w. Determine b, given that u(b) = 0.
-1, 0, 2
Let d(k) be the third derivative of -k**9/15120 - k**8/6720 + k**7/2520 + k**6/720 - k**4/8 - k**2. Let b(v) be the second derivative of d(v). Factor b(c).
-c*(c - 1)*(c + 1)**2
Suppose 0 = -4*r - 0*r - 4*d - 48, d = 4*r + 38. Let f be (-16)/r - 2/(-5). Factor 1/2*x + 7/4*x**2 + f*x**3 + 3/4*x**4 + 0.
x*(x + 1)**2*(3*x + 2)/4
Let o(i) = 5*i**4 + i**3 + 3*i**2 - i - 4. Let p(l) = 4*l**4 + l**3 + 2*l**2 - l - 3. Let w be (-6)/15 + 44/10. Let t(j) = w*p(j) - 3*o(j). Factor t(x).
x*(x - 1)*(x + 1)**2
Let a(v) be the third derivative of -1/896*v**8 + 9*v**2 + 0*v + 1/40*v**5 - 1/8*v**3 + 0 + 1/160*v**6 - 1/280*v**7 - 1/64*v**4. What is t in a(t) = 0?
-2, -1, 1
Suppose -i - 2*i - 5*g - 37 = 0, -10 = 2*g. Let c(w) = -w - 1. Let b be c(i). Suppose -1/5*y**2 + 0 - 2/5*y**b + 0*y - 1/5*y**4 = 0. Calculate y.
-1, 0
Suppose -2/5*b**4 + 6/5*b**5 + 0 - 4/5*b + 18/5*b**2 - 18/5*b**3 = 0. What is b?
-2, 0, 1/3, 1
Find s, given that -2*s**3 - s**3 - 48 + 4*s + 21*s**2 - 9*s - 19*s = 0.
-1, 4
Let l = -189 + 192. Factor -3/2 - 3/2*v**2 + l*v.
-3*(v - 1)**2/2
Let j(z) = 43*z**2 - 28*z + 3. Let u(s) = -85*s**2 + 55*s - 5. Let b(g) = -5*j(g) - 2*u(g). Let b(p) = 0. What is p?
1/3
Factor 0 + 2/3*c**3 + 4/3*c**2 + 0*c - 2*c**4.
-2*c**2*(c - 1)*(3*c + 2)/3
Let f(z) = -15*z**2 - 18. Let h(i) = -i**2 - 1. Let g(n) = -f(n) + 18*h(n). Factor g(u).
-3*u**2
Suppose 4*a - 12 - 8 = 0. Suppose 25 = 5*w + 5*l, 0 = 5*w + l + 3*l - 25. Determine h, given that 0*h + 2*h**w - 4*h**3 - 4*h + a*h + h = 0.
-1, 0, 1
Let j(t) be the third derivative of -t**5/15 + 2*t**4/3 - 8*t**3/3 + 8*t**2. Factor j(y).
-4*(y - 2)**2
Factor -1/6*o**3 + 0*o + 0 + 1/6*o**2.
-o**2*(o - 1)/6
Suppose -3*v**2 - 3*v + 2*v**2 - 2*v**2 = 0. What is v?
-1, 0
Let h(j) = -j + 7. Let q be h(5). Factor 5*p**2 + p - 3*p**q - 3*p.
2*p*(p - 1)
Let x be (8/(-14))/((-14)/98). Find a such that -5/2*a**3 - 2*a - 4*a**2 + 0 - 1/2*a**x = 0.
-2, -1, 0
Suppose -k + 8 = k. Let -34*v**3 - 4*v**k - 6*v + 5 - 42*v**2 - 16*v**3 - 1 - 14*v**4 = 0. Calculate v.
-1, 2/9
Let l(q) be the first derivative of 3/2*q**2 - 3 + 3/4*q**4 - 2*q**3 + 0*q. Suppose l(g) = 0. Calculate g.
0, 1
Let l(f) = 3*f**2 - 79*f - 54. Let q be l(27). What is r in 6/5*r**3 + q*r + 0 + 3/5*r**2 = 0?
-1/2, 0
Let h(n) = 104*n**2 + 34*n + 2. Let v(x) = 311*x**2 + 101*x + 6. Let r be ((-1)/(-1))/(3/(-18)). Let u(a) = r*v(a) + 17*h(a). Solve u(j) = 0 for j.
-1/7
Let c be (-22)/902*3*-1. Let j = c + 32/123. Suppose 0 - 1/3*y - j*y**2 = 0. What is y?
-1, 0
Determine d, given that 2/3*d + 5/3*d**2 + 1/3*d**4 + 4/3*d**3 + 0 = 0.
-2, -1, 0
Suppose -3*t + 3 = -3. Let d be ((-8)/(-6))/(t/6). Factor 6/5*f**d + 0*f + 2/5*f**5 + 2/5*f**2 + 0 + 6/5*f**3.
2*f**2*(f + 1)**3/5
Let y(j) = -36*j**5 - 63*j**4 - 12*j**3 + 15*j + 15. Let k(o) = -9*o**5 - 16*o**4 - 3*o**3 + 4*o + 4. Let h(c) = -15*k(c) + 4*y(c). Let h(w) = 0. Calculate w.
-1, -1/3, 0
Let q(x) be the second derivative of -x**6/2160 - x**5/360 - x**4/144 - x**3/6 - x. Let z(d) be the second derivative of q(d). What is u in z(u) = 0?
-1
Let n(s) be the third derivative of 1/2016*s**8 + 1/36*s**3 + 1/252*s**7 + 0 + 0*s + 1/72*s**6 + 1/36*s**5 - 3*s**2 + 5/144*s**4. Find v, given that n(v) = 0.
-1
Suppose 0 = 4*h - 13 - 7. Let n(f) be the third derivative of 11/120*f**h + 0*f + 3*f**2 + 1/20*f**6 + 0 - 1/12*f**3 - 1/24*f**4. Factor n(p).
(p + 1)*(3*p - 1)*(4*p + 1)/2
Let q(x) = -x. Let k(y) = -7*y**2 + 6*y - 5. Let j(p) = -4*p**2 + 3*p - 3. Let m(g) = 5*j(g) - 3*k(g). Let i(n) = m(n) - q(n). Determine u, given that i(u) = 0.
0, 2
Let j = -14 + 16. Factor -2/3*b**j + 0*b + 1/3 + 1/3*b**4 + 0*b**3.
(b - 1)**2*(b + 1)**2/3
Factor -20*v + 13*v**3 - 5 - 3*v**4 - 15 + 15*v**2 + 7*v**3 + 8*v**4.
5*(v - 1)*(v + 1)*(v + 2)**2
Let o(m) be the second derivative of 0 + 6*m + 0*m**2 - 1/5*m**3 + 3/50*m**5 - 1/50*m**6 + 1/20*m**4. Let o(d) = 0. What is d?
-1, 0, 1, 2
Let l(d) = -2*d**3 - 4*d**2 + 2*d + 2. Let a(u) = -17*u + 10*u**3 + 12*u**2 + 6*u - 11 + 8*u**2. Let n(s) = -2*a(s) - 11*l(s). Factor n(f).
2*f**2*(f + 2)
Let p(h) = -4*h**2 + 2*h. Let x(b) = -b. Let l(s) = p(s) + 2*x(s). Determine r, given that l(r) = 0.
0
Let g(i) = 3*i**4 + 27*i**3 - 7*i**2 - 20*i - 10. Let c(u) = -2*u**4 - 13*u**3 + 3*u**2 + 10*u + 5. Let x(j) = 7*c(j) + 3*g(j). Factor x(z).
-5*(z - 1)*(z + 1)**3
Suppose 7*i - 16 = 3*i. Suppose 0 = -i*m + s + 24, -4*m + 0*s + 36 = -4*s. Factor -2/9*y**3 + 2/9*y**2 + 0*y + 2/9*y**m + 0 - 2/9*y**4.
2*y**2*(y - 1)**2*(y + 1)/9
Suppose 9*m - 11*m = 0. Let -3*y**4 + m*y**2 - 3*y**2 + 3*y**2 = 0. Calculate y.
0
Let g be 2 - (2 - 8)/3. Suppose 3*z = 7*z - 4*h - g, -1 = -z + 3*h. Factor -t**3 + 7*t - 6*t + 2*t**2 - z - t**2.
-(t - 1)**2*(t + 1)
Let f(t) be the first derivative of 0*t - 1/16*t**4 + 0*t**2 - 3 - 1/6*t**3. Factor f(s).
-s**2*(s + 2)/4
Factor 5*u**3 - 8*u - 6 - 18*u**2 - 13*u + 7*u**3 + 6*u**2.
3*(u - 2)*(2*u + 1)**2
Factor -3 + 4*t**2 - 5*t**2 + t**2 + 3*t**2.
3*(t - 1)*(t + 1)
Suppose -3*m + 15 = 0, 3*m = w - 0*m + 13. Factor 2 + 2*h**3 - h - h**w - h**3 - 1.
(h - 1)**2*(h + 1)
Suppose -h + 1 = -g, 0*h + 4*g + 4 = -5*h. Suppose -a - 2 + 4 = h. Factor 1/2*f**3 + a*f**2 + 5/2*f + 1.
(f + 1)**2*(f + 2)/2
Let x(u) = 2*u + 3*u - 4*u**3 + 5*u**3 - 6*u. Let i be x(0). Solve 0 + i*j**2 + 2/5*j - 2/5*j**3 = 0.
-1, 0, 1
Suppose 3*b - 2 = 4. Find k, given that -7*k**2 + b*k**2 - k**2 - k - k = 0.
-1/3, 0
Let t(m) be the first derivative of m**8/672 - m**7/240 - m**6/90 + m**5/60 - 2*m**3 + 1. Let q(s) be the third derivative of t(s). Factor q(w).
w*(w - 2)*(w + 1)*(5*w - 2)/2
Factor -2*z + 41 + 39 - 2*z**3 - 80 + 4*z**2.
-2*z*(z - 1)**2
Let p(m) = 2*m**2 - 3*m + 5. Let i(v) = -3*v**2 + 5*v - 8. Let b(h) = -5*i(h) - 8*p(h). Factor b(a).
-a*(a + 1)
Let r(n) = -3*n**2. Let f(b) = b**3 - 18*b**2 + 3*b + 1. Let l(u) = -3*f(u) + 21*r(u). Factor l(m).
-3*(m + 1)**3
Let m(t) be the first derivative of t**9/3024 - t**7/420 + t**5/120 - 2*t**3/3 + 1. Let h(w) be the third derivative of m(w). Let h(o) = 0. Calculate o.
-1, 0, 1
What is a in -1/3*a**2 - 1/3 + 2/3*a = 0?
1
Suppose -20/3*x + 5*x**2 + 20/3*x**3 + 5/3*x**4 - 20/3 = 0. What is x?
-2, -1, 1
Let p be (-4)/(-10) - 0/(-3). Let k(c) = 2*c - 11. Let t be k(7). Suppose 0 - p*r**2 + 2/5*r**t + 0*r = 0. Calculate r.
0, 1
Suppose 0 = 6*q - 3*q - 9. Suppose 2*s - 1 = 7, -2 = -q*z + s. Suppose j**4 + 0*j**2 - 2*j + 0*j**2 + 2*j**3 + 0*j**z - 1 = 0. What is j?
-1, 1
Let r(k) = k**2 + 2*k + 3. Let f be r(-2). Factor 4*d**2 - 2*d**3 + 2*d - 2 - 4*d**3 - 2*d**4 + 2*d**5 + 0*d + 2*d**f.
2*(d - 1)**3*(d + 1)**2
Let k(t) = 2*t**4 - 6*t**3 + 2*t**2 + 9*t - 1. Let r(i) = -2*i**4 + 6*i**3 - 2*i**2 - 8*i + 2. Let c(l) = -4*k(l) - 6*r(l). Factor c(p).
4*(p - 2)*(p - 1)**2*(p + 1)
Suppose -q + 0 + 1/3*q**2 = 0. What is q?
0, 3
Let o(t) be the first derivative of 3*t**5 - 5*t**4/4 - 15*t**3 + 45*t**2/2 - 10*t - 7. Determine b, given that o(b) = 0.
-2, 1/3, 1
Let t(u) = -10*u**2 - 15*u + 5. Let c(r) = r**3 - 9*r**2 - 14*r + 4. Let s(y) = -5*c(y) + 4*t(y). Let s(l) = 0. Calculate l.
-1, 0, 2
Let g = -19/10 + 191/90. Factor -g*q**3 + 0*q**2 + 0 + 2/9*q.
-2*q*(q - 1)*(q + 1)/9
Let x = -17 - -20. Factor 0*r + 0 + 2/5*