6*n**2 - p*n - 12*n**2 = 0. What is n?
-3, -1
Let t(c) be the first derivative of -15/8*c**4 + 0*c + 14/15*c**5 - 1/3*c**2 - 14/9*c**3 + 4 + 49/36*c**6. Find h, given that t(h) = 0.
-1, -2/7, 0, 1
Let v = -20 + 32. Determine l so that -9 - v*l - 12*l + 57 + 3*l**2 = 0.
4
Let j = -11 - -13. Let a(t) be the second derivative of -1/24*t**4 + 0 + t - t**j - 1/3*t**3. Solve a(h) = 0 for h.
-2
Let b = 980 + -2936/3. Suppose 2*v**3 + 0 + b*v - 10/3*v**2 = 0. What is v?
0, 2/3, 1
Let j(k) be the second derivative of 9*k**2 + 1/6*k**4 - 2*k**3 - 4*k + 0. Suppose j(n) = 0. Calculate n.
3
Let y(h) = -11*h**4 + 40*h**3 - 96*h**2 + 6*h + 141. Let d(p) = p**4 + p**2 - p - 1. Let g(r) = -6*d(r) - y(r). Factor g(f).
5*(f - 3)**3*(f + 1)
Let t be 26/8 + 1/(-4). Suppose -5*d + 13 = t. Solve 3*r**5 + 4*r**4 + r**3 - d*r**4 - 6*r**5 = 0 for r.
-1/3, 0, 1
Let 44*a**2 - 48*a + 6*a**4 - 4*a**3 - 17*a**4 + 16 + 4*a**5 + 7*a**4 - 8*a**4 = 0. Calculate a.
-2, 1, 2
Find h, given that -8*h + 3*h - 10*h**2 + 0*h**2 + 2 + 13*h**2 = 0.
2/3, 1
Let o(k) be the first derivative of k**6/1080 - k**5/360 - 8*k**3/3 - 5. Let t(v) be the third derivative of o(v). Let t(z) = 0. What is z?
0, 1
Let v = -2 - -5. Suppose -2*a = -3*c + v*a, 0 = -5*c - a. Factor 2/3*u + 0*u**4 + 0 - 4/3*u**3 + c*u**2 + 2/3*u**5.
2*u*(u - 1)**2*(u + 1)**2/3
Let t(o) = -o**2 + 6*o + 2. Let h be t(6). Suppose -4 - 16 = 4*l, 0 = -h*m + 5*l + 25. Factor 0 + m*i + 0*i**2 - 1/2*i**3.
-i**3/2
Factor -2/3*k**2 + 2/3 + 0*k.
-2*(k - 1)*(k + 1)/3
Let b(x) be the third derivative of -x**6/420 - x**5/105 - x**4/84 + x**3/3 + 3*x**2. Let d(i) be the first derivative of b(i). Factor d(z).
-2*(z + 1)*(3*z + 1)/7
Factor 0 + 3/2*c**2 + 3/2*c**3 + 0*c.
3*c**2*(c + 1)/2
Suppose -5*k + t - 6*t = 0, 0 = -3*t - 9. Let -1/2 + 1/4*s**k - 1/4*s + 1/2*s**2 = 0. Calculate s.
-2, -1, 1
Find v such that -2 - 2/5*v**2 - 12/5*v = 0.
-5, -1
Let u(h) = h**2 - 8*h + 4. Let o be u(9). Let g = o - 11. Factor -1/6 - 1/3*z - 1/6*z**g.
-(z + 1)**2/6
Let i(l) be the first derivative of -1/10*l**2 + 2 - 2/5*l + 1/15*l**3. Solve i(s) = 0.
-1, 2
Suppose 4/11*g + 1/11*g**2 + 0 = 0. Calculate g.
-4, 0
Let b(o) be the second derivative of o**5/20 - 5*o**4/12 + o**3/2 + 9*o**2/2 - 5*o. Determine m so that b(m) = 0.
-1, 3
Determine o, given that 18/5 + 3/5*o**3 + 18/5*o**2 + 33/5*o = 0.
-3, -2, -1
Let d(l) be the third derivative of l**6/90 - 4*l**5/45 + l**4/6 + 6*l**2. Determine w so that d(w) = 0.
0, 1, 3
Factor -5*j**3 + 5*j**5 + 3*j + 6*j**2 - 3*j + 4*j**2 - 10*j**4.
5*j**2*(j - 2)*(j - 1)*(j + 1)
Let t(z) be the second derivative of z**4/60 + z**3/30 - z**2/5 + 12*z. Let t(m) = 0. Calculate m.
-2, 1
Let h(g) be the third derivative of g**5/330 + 2*g**4/33 + 11*g**2. What is a in h(a) = 0?
-8, 0
Let k(z) = -z**3 + 3*z**2 + 6*z - 3. Let w be k(4). Find s, given that -1 + 1 + 3*s + 3 - 8*s**2 - 3*s**3 + w*s**2 = 0.
-1, 1
Factor -3/7*p**2 - 363/7 + 66/7*p.
-3*(p - 11)**2/7
Let a be 2*1/1 + 5. Determine q so that 3*q**2 - a*q + 0*q**3 + 5*q**2 + q**5 + 2 - 2*q**4 - 2*q**3 = 0.
-2, 1
Let b(i) = i**2 + 8*i + 7. Let v be b(-7). Factor 2/3*y - 2/3*y**2 + v.
-2*y*(y - 1)/3
Let b be -1 - 0 - 35/(-28). Let p = 3 - 3. Factor b*l**2 + 0 - 1/4*l**4 + p*l**3 + 0*l.
-l**2*(l - 1)*(l + 1)/4
Let h(u) be the second derivative of -u**5/10 - 19*u**4/12 + u**3/2 - u**2/2 + 3*u. Let d(n) = -n**3 - 6*n**2 + n. Let b(l) = 7*d(l) - 2*h(l). Factor b(j).
-(j + 1)**2*(3*j - 2)
Suppose -4*h + 2*n = -6, 9 = -n - 2*n. Suppose -6/7*s - 27/7*s**2 - 3*s**3 + h = 0. Calculate s.
-1, -2/7, 0
Let a(g) be the second derivative of -g**5/130 - g**4/78 + 12*g. Find c, given that a(c) = 0.
-1, 0
Let w(x) be the third derivative of 0*x + 1/22*x**4 + 4*x**2 - 1/330*x**5 + 0 - 3/11*x**3. Find j such that w(j) = 0.
3
Let h(a) = a - 5. Let o(v) = 3*v - 6. Let t be o(5). Let d be h(t). Factor -d*y**4 + 6*y**3 - 6*y + 2*y**4 + 3 - y**4.
-3*(y - 1)**3*(y + 1)
Let h(a) be the first derivative of a**6/105 - a**5/70 - a**4/42 + a**3/21 - 3*a - 1. Let u(v) be the first derivative of h(v). Factor u(s).
2*s*(s - 1)**2*(s + 1)/7
Let f = -5 + -15. Let r = f - -23. Suppose -2/5*x**r - 2/5*x + 0 - 4/5*x**2 = 0. Calculate x.
-1, 0
Suppose 26*t - 27*t = 0. Let r(l) be the second derivative of -1/36*l**4 + t + 0*l**3 + 0*l**2 + 1/60*l**5 - l. What is g in r(g) = 0?
0, 1
Let o(p) be the second derivative of 0 + 2*p - 3/10*p**6 - 3/10*p**5 + p**3 + 3/4*p**4 + 0*p**2. Suppose o(t) = 0. Calculate t.
-1, -2/3, 0, 1
Let 3/2*f**2 - 3 - 3/2*f = 0. What is f?
-1, 2
Suppose -d = -2*d - 9. Let s be 6/d*3 + 5. Solve -3*g + 5*g**2 - 2*g**s + g - g**2 = 0 for g.
0, 1
Let m(w) = 3*w**5 + 3*w**4 + w**3 + 15*w**2 + 9*w - 5. Let q(j) = -5*j**5 - 5*j**4 - j**3 - 23*j**2 - 14*j + 8. Let o(y) = 8*m(y) + 5*q(y). Factor o(d).
-d*(d - 2)*(d + 1)**3
Let x(t) = -9*t + 2*t**2 + 5 - t**2 + 3*t. Let o be x(6). Suppose -8*b**2 + 28*b**4 + o*b**5 - 10*b**4 + 12*b**3 + 0*b**5 = 0. What is b?
-2, 0, 2/5
Let z(y) be the third derivative of y**7/168 - y**6/32 + y**5/16 - 5*y**4/96 - 34*y**2. Factor z(x).
5*x*(x - 1)**3/4
Let l(a) be the first derivative of 4*a**3/9 + 4*a**2/3 - 4*a + 2. Suppose l(q) = 0. What is q?
-3, 1
Let -7 + 2*b**2 + 3 - 4*b + 4 = 0. Calculate b.
0, 2
Let w(i) be the second derivative of 3*i**8/140 - 2*i**7/105 + i**6/180 + i**4/12 - 5*i. Let s(k) be the third derivative of w(k). Factor s(q).
4*q*(6*q - 1)**2
Determine g so that -5/3*g**2 + 0 + 5/3*g**4 + 5/3*g - 5/3*g**3 = 0.
-1, 0, 1
Let k(p) be the third derivative of -4*p**7/315 - p**6/90 + 2*p**5/45 + p**4/18 - 7*p**2. Determine o so that k(o) = 0.
-1, -1/2, 0, 1
Let k(c) be the second derivative of -c**6/165 + 3*c**5/110 + 3*c**4/22 - 9*c**3/11 - 23*c. Factor k(t).
-2*t*(t - 3)**2*(t + 3)/11
Suppose 2*h - 73 = 45. Let -c - 55*c**3 + 8*c**2 - 3*c - 8 + h*c**3 = 0. Calculate c.
-2, -1, 1
Let g be 56/35*10/4. Let t(f) be the first derivative of -2 + 1/24*f**g + 0*f**2 - 1/36*f**6 - 1/30*f**5 + 1/18*f**3 + 0*f. Let t(v) = 0. What is v?
-1, 0, 1
Let d(a) = -10*a**5 - 2*a**4 + 6*a**3 + 6*a - 6. Let n(u) = 21*u**5 + 5*u**4 - 13*u**3 - 13*u + 13. Let k(t) = -13*d(t) - 6*n(t). Solve k(v) = 0.
0, 1
Let h(p) = p**2 + 9*p + 11. Let c be h(-8). Factor -o**2 - 1/3*o**c - o - 1/3.
-(o + 1)**3/3
Let y = 70 + 54. Let h = y - 618/5. Factor -8/5 - h*b**2 + 8/5*b.
-2*(b - 2)**2/5
Let j(q) be the first derivative of q**7/2520 + q**6/270 + q**5/90 - q**3/3 - 1. Let d(c) be the third derivative of j(c). Factor d(u).
u*(u + 2)**2/3
Let s(l) be the third derivative of l**8/40320 - l**5/60 + 2*l**2. Let a(h) be the third derivative of s(h). Factor a(k).
k**2/2
Let o(x) be the first derivative of x**4 - 7*x**3/3 - 7*x**2 - 3*x - 15. Find g, given that o(g) = 0.
-1, -1/4, 3
Suppose 5 - 12 = -x. Let p = 9 - x. Factor 2/3 + 4/3*u**p + 1/3*u**3 + 5/3*u.
(u + 1)**2*(u + 2)/3
Let 1/3*g**2 - 4/3 + 4/3*g - 1/3*g**3 = 0. Calculate g.
-2, 1, 2
Factor -21/5*n + 18/5 + 0*n**2 + 3/5*n**3.
3*(n - 2)*(n - 1)*(n + 3)/5
Let q(x) = -x**3 + x**2 + x + 2. Let i be q(0). Suppose -8 = -2*t - i*t. Suppose 3*w**3 - 2*w**3 + 3*w**t + 1 + 0 + 3*w = 0. Calculate w.
-1
Let h(r) be the third derivative of 27*r**6/100 + 3*r**5/10 - 8*r**4/15 + 4*r**3/15 + 3*r**2. Find q, given that h(q) = 0.
-1, 2/9
Let g(l) be the first derivative of 2*l**5/5 - 2*l**3/3 + 8. Determine d, given that g(d) = 0.
-1, 0, 1
Let a(q) be the first derivative of -4*q**4 + 12*q**3 - 12*q**2 + 4*q + 10. Determine i so that a(i) = 0.
1/4, 1
Solve o**3 - 2*o**2 - 6*o**4 - 2*o**5 + 0*o**3 - 7*o**3 = 0 for o.
-1, 0
Let a(k) = k - 5. Let x be a(5). Suppose 0 = -z - 4*o - 14, x = -z + 2*o + o + 14. Let 2 + 5*g**2 + 0 + g**2 + 0*g**2 - 6*g - z*g**3 = 0. Calculate g.
1
Suppose 1/3*r + 0*r**2 + 0 - 1/3*r**3 = 0. What is r?
-1, 0, 1
Let p(s) = 5*s**5 - 11*s**4 - 3*s**2 + 2*s + 7. Let r(k) = -2*k**5 + 5*k**4 + k**2 - 2*k - 3 + k - k + k. Let f(g) = 3*p(g) + 7*r(g). Find u such that f(u) = 0.
-1, 0, 1
Suppose -3*x + 11 + 4 = 0. Suppose -s = -x*u - 5*s + 27, 6 = u + s. Factor 1/3*r + 0 + 2/3*r**2 + 1/3*r**u.
r*(r + 1)**2/3
Let l = 13 + -11. Factor 33*n**l + n - 4 - 31*n**2 + 9*n + 48*n**2.
2*(5*n - 1)*(5*n + 2)
Let q be ((-27)/6)/(-9) + 6/4. Suppose 2*d**q + 0 + 1/2*d = 0. Calculate d.
-1/4, 0
Let b(c) be the third derivative of 5*c**8/784 - 9*c**7/245 + 11*c