 = 0.
-1, 0, 81
Let v(j) be the second derivative of -j**7/3780 + j**5/540 + 2*j**3 - j. Let i(z) be the second derivative of v(z). Determine q so that i(q) = 0.
-1, 0, 1
Suppose 5 = -5*h - 0*c - 5*c, -h = 4*c + 4. Suppose 0 = -h*r - 4*r + 12. Factor -3*u**2 + 0*u**2 + r*u**2 + u**2.
u**2
Let h(g) be the third derivative of g**8/112 - 2*g**7/35 + g**6/40 + 3*g**5/10 - 93*g**2. Determine y so that h(y) = 0.
-1, 0, 2, 3
Suppose 2*i + 1 = 4*j + 11, 2*i + 14 = -2*j. Let t be ((-150)/21)/2 - j. Factor -3/7*y**3 - t*y**2 - 9/7 + 15/7*y.
-3*(y - 1)**2*(y + 3)/7
Solve 1/2*c**4 + 9/10 - 7/5*c**2 + 1/5*c**3 - 3/10*c + 1/10*c**5 = 0.
-3, -1, 1
Suppose 3*n + 4 = -5. Let k(g) = 2*g**2 + 5*g - 3. Let z be k(n). Factor -16/5*i + z - 16/5*i**2 - 4/5*i**3.
-4*i*(i + 2)**2/5
Suppose -26*b**2 + 18 + 68*b**2 + 15*b - 39*b**2 = 0. What is b?
-3, -2
Factor -15*p - 13/4*p**3 - 1/4*p**4 + 0 - 13*p**2.
-p*(p + 2)*(p + 5)*(p + 6)/4
Let l(h) = 8*h**3 + 17*h**2 - h + 3. Let d(y) be the second derivative of -2*y**5 - 7*y**4 + y**3 - 7*y**2 - 23*y. Let o(j) = -6*d(j) - 28*l(j). Solve o(n) = 0.
-2, 0, 1/4
Factor -1/2*r**2 - 4*r + 0.
-r*(r + 8)/2
Let i be 20*((-23)/5)/((-24)/30). Let k = i - 111. Determine b so that -1/3*b**5 + 1/3*b**3 + b**k + 4/3 - 7/3*b**2 + 0*b = 0.
-1, 1, 2
Suppose a = 1, 2*a + 0*a - 80 = -2*v. Let m be (-6)/v + 4/(-52)*-28. What is r in m*r**2 + 0 + 10/7*r**3 + 4/7*r = 0?
-1, -2/5, 0
Let j(f) be the third derivative of f**8/1008 - f**7/60 - 17*f**6/720 + 67*f**5/360 - f**4/16 - 11*f**3/18 + 172*f**2. Find k, given that j(k) = 0.
-2, -1/2, 1, 11
Suppose -2*p = -0*p + 4*c - 24, -31 = -2*p + 3*c. Factor -6*s - 33*s**4 + s**3 - 11*s**3 + 35*s**4 + p*s**2.
2*s*(s - 3)*(s - 1)**2
Let k(l) = 4*l**2 - 42*l + 42. Let r be k(1). Factor 16/7*u + 8/7*u**3 + 4/7*u**4 + 0 - r*u**2.
4*u*(u - 1)**2*(u + 4)/7
Find c such that 0 - 1/2*c**3 + 0*c + 2*c**2 = 0.
0, 4
Let y(a) = -2*a**2 - 5*a + 7. Let j be y(-3). Determine h so that -j*h**4 + 13*h**3 - 28*h**3 + 7*h**3 = 0.
-2, 0
Let f(h) be the second derivative of h**5/420 - h**4/21 + 8*h**3/21 + h**2 - 5*h. Let z(m) be the first derivative of f(m). What is c in z(c) = 0?
4
Let g(r) be the first derivative of 4*r**3/3 + 66*r**2 - 136*r + 296. Factor g(u).
4*(u - 1)*(u + 34)
Let h be 48/12*(-3)/(-4). Suppose -36*y**3 + 19*y**h - 3*y + 14*y**3 + 6*y**2 = 0. What is y?
0, 1
Let o(v) be the third derivative of -v**7/840 - v**6/80 + v**4/3 + 43*v**2 + 2*v. Factor o(d).
-d*(d - 2)*(d + 4)**2/4
Let j(p) be the third derivative of p**6/40 - 23*p**5/30 + 13*p**4/24 + 5*p**3 + 52*p**2. Determine k, given that j(k) = 0.
-2/3, 1, 15
Suppose -2*y + 2*s = 0, -s - 3 = -3*y + 3. Let i = y - -1. Let -8*p**3 - 12*p**2 - 4 + 5*p + 16*p**i + 9*p - 3*p**5 - 3*p**5 = 0. Calculate p.
-1, 2/3, 1
Let b(q) be the first derivative of -35/2*q**2 - 20/3*q**3 - 15*q + 7. Let b(l) = 0. What is l?
-1, -3/4
Let x(h) be the second derivative of h**4/60 - h**3/3 - 126*h. Factor x(s).
s*(s - 10)/5
Let c(y) be the first derivative of 2*y**6/27 - 4*y**5/9 + 2*y**4/9 + 56*y**3/27 - 2*y**2/3 - 4*y - 22. What is h in c(h) = 0?
-1, 1, 3
Let y(p) be the second derivative of -p**6/10 + 3*p**5/10 + 5*p**4/4 - 3*p**3 + 305*p. Let y(c) = 0. Calculate c.
-2, 0, 1, 3
Let y be 2/8 - (0 - 3/4). Let w be ((-2)/10)/(-5 - (-5 + y)). Factor -1/5*d + 0 + 0*d**2 + 0*d**4 + 2/5*d**3 - w*d**5.
-d*(d - 1)**2*(d + 1)**2/5
Suppose 44 = 7*x + 16. Suppose 0*h**2 + x*h**2 + 2 - 38*h + 14*h + 34 = 0. What is h?
3
Suppose -4*f = 39 + 1. Let p(n) = n**3 + 9*n**2 - 10*n + 3. Let t be p(f). Find h such that h**t + 0*h + h - 2*h**2 + 2 - 2*h = 0.
-1, 1, 2
Let j = 111 - 60. Suppose -j*g - 8 = -53*g. Solve 1/2*o**g - 3/2*o**3 + 3/2*o**2 + 0 - 1/2*o = 0.
0, 1
Let i(u) = -u**4 + 3*u**2 + u + 1. Let l(v) = -25*v**3 + 30*v**2 + 16*v + 7. Let r(k) = 21*i(k) - 3*l(k). Factor r(d).
-3*d*(d - 3)*(d - 1)*(7*d + 3)
Let q = -5 - -6. Let t(w) = -16*w**2 + 12*w - 20. Let s(m) = -m**2 + m - 1. Let g(f) = q*t(f) - 20*s(f). Factor g(b).
4*b*(b - 2)
Let h(m) be the third derivative of 1/15*m**5 + 0*m**3 + 15*m**2 + 0 + 0*m + 5/6*m**4. Find b, given that h(b) = 0.
-5, 0
Suppose 2*n - q - 10 = 0, 3*n - q - 30 = -13. Let w(a) be the first derivative of 1/3*a**2 + 8/9*a**3 - 4/3*a - 1/2*a**4 - n. Let w(k) = 0. Calculate k.
-2/3, 1
Let h(v) be the first derivative of 23*v**4/14 + 34*v**3/7 + 33*v**2/7 + 10*v/7 + 804. Factor h(d).
2*(d + 1)**2*(23*d + 5)/7
Let p(a) be the second derivative of a**6/30 + a**5/20 - 2*a**4/3 - 2*a**3 - 317*a. Factor p(l).
l*(l - 3)*(l + 2)**2
Let y = -54 + 53. Let c(t) = t**4 + t**3 - t + 1. Let d(z) = 22*z**4 - 82*z**3 + 108*z**2 - 56*z + 14. Let a(f) = y*d(f) + 6*c(f). Solve a(b) = 0.
1/2, 4
Let w(i) be the second derivative of i**5/5 - 5*i**4 + 42*i**3 - 98*i**2 + 266*i. Determine d so that w(d) = 0.
1, 7
Let i be 1/((3/1)/(-6)). Let f(v) = -7*v - 2 + 0*v + 6*v - 3*v. Let y(g) = -g**2 - 4*g - 3. Let z(h) = i*y(h) + 3*f(h). Solve z(p) = 0.
0, 2
Let c(i) be the second derivative of i**7/630 + 13*i**4/6 - 40*i. Let q(a) be the third derivative of c(a). Suppose q(r) = 0. Calculate r.
0
Let v(p) = -6*p**2 - 34*p + 4. Let g(j) be the first derivative of j - 2/3*j**3 - 11/2*j**2 - 4. Let s(m) = 16*g(m) - 5*v(m). Factor s(n).
-2*(n + 1)*(n + 2)
Let l(m) be the second derivative of -m**6/15 + 9*m**5/10 - 29*m**4/6 + 13*m**3 - 18*m**2 + 3*m + 2. Solve l(p) = 0 for p.
1, 2, 3
Factor -27/2 + 39/4*u**2 + 3/4*u**4 + 21/4*u**3 - 9/4*u.
3*(u - 1)*(u + 2)*(u + 3)**2/4
Suppose -5*a - 48 + 58 = 0. Let o be -1*1 + (a - 3 - -2). Factor 2/9*w**4 + 4/9*w**3 + o*w + 0*w**2 + 0.
2*w**3*(w + 2)/9
Let n(k) be the third derivative of -k**6/60 + k**5/5 + 13*k**4/12 - 14*k**3 - 3*k**2 - 53*k. Determine v so that n(v) = 0.
-3, 2, 7
Solve 6/23*u**3 - 12/23 - 8/23*u**2 - 26/23*u = 0.
-1, -2/3, 3
Let t(o) be the first derivative of -1/13*o**2 - 13 + 0*o - 2/39*o**3. Suppose t(g) = 0. Calculate g.
-1, 0
Suppose 8/5*u**2 - 6/5*u - 2/5*u**3 + 0 = 0. What is u?
0, 1, 3
Factor -5*i + i**2 + i**2 + i**2 + 50*i.
3*i*(i + 15)
Let z(n) = -2*n + 37. Let x be z(7). Suppose y + 20 = x. Solve y - 3/2*u**3 + 0*u**2 + 9/2*u = 0.
-1, 2
Let x(m) = -7*m**3 - m**2 - m - 1. Let c = 17 + -18. Let l be x(c). Let 4*r**3 - 4*r**5 + l*r**3 - 8*r**2 + 12*r**5 + 14*r**3 + 30*r**4 = 0. What is r?
-2, 0, 1/4
Let h = -12/11 - -654/55. Let u(b) be the first derivative of 12/5*b + 81/5*b**3 + h*b**2 - 2. Solve u(y) = 0 for y.
-2/9
Let q(f) be the third derivative of -f**7/105 - f**6/20 + f**5/30 + f**4/4 - 160*f**2. Factor q(j).
-2*j*(j - 1)*(j + 1)*(j + 3)
Let v(m) be the second derivative of -m**5/60 - 5*m**4/24 - 2*m**3/3 + 13*m**2/2 - 16*m. Let i(a) be the first derivative of v(a). Find h, given that i(h) = 0.
-4, -1
Let c(q) be the first derivative of -32/3*q**3 - 14/3*q**2 - 3 - 2/15*q**5 + 7/3*q**4 + 98/3*q. Suppose c(w) = 0. Calculate w.
-1, 1, 7
Suppose -157 = -6*o + 83. Suppose 0 = -4*q - 3*z + o - 10, -q = z - 8. Determine j so that -3*j + 0 - 15/4*j**3 + 3/4*j**4 + q*j**2 = 0.
0, 1, 2
Factor 5/4*r**2 - 15 - 5/4*r.
5*(r - 4)*(r + 3)/4
Suppose 2*t + t + 2*d + 34 = 0, 3*t - 5*d - 1 = 0. Let z(q) = q**3 + 7*q**2 - 11*q - 6. Let w be z(t). Factor -6 + 3*h**2 - 3*h + 15*h + w.
3*(h + 2)**2
Let w = -3 + 7. Suppose 0 = 3*s + i - 7, 11 = 4*s - i + w*i. Find r such that 4/7 + 2/7*r - 2/7*r**s = 0.
-1, 2
Let q be (14 - (-9 + 23))/2. Factor q - 1/4*m**3 - m**2 - 3/4*m.
-m*(m + 1)*(m + 3)/4
Determine u, given that 15 + 18*u**2 - 3/2*u**3 - 63/2*u = 0.
1, 10
Let b(o) = 15*o**3 + 1370*o**2 + 8640*o - 38880. Let n(x) = -2*x**3 - 171*x**2 - 1080*x + 4860. Let s(h) = -3*b(h) - 25*n(h). Factor s(g).
5*(g - 3)*(g + 18)**2
Suppose 173 = -14*j + 5. Let d be ((-260)/(-325))/(0 - j/10). Factor -d*w**3 + 4/3*w + 0 + 2/3*w**2.
-2*w*(w - 2)*(w + 1)/3
Suppose -10*a**2 + 463*a - 2*a**4 - 6 + 12*a**3 - 443*a - 14*a**2 = 0. Calculate a.
1, 3
Let q(k) be the first derivative of k**4/72 + k**3/3 + 11*k**2/12 + 45*k - 33. Let s(d) be the first derivative of q(d). Let s(t) = 0. What is t?
-11, -1
Solve 98 + 27*o**5 + 9*o**4 - 10458*o**3 + 24*o**2 + 46 + 336*o + 10218*o**3 = 0 for o.
-3, -2/3, 2
Factor -4 + 5/2*q**3 - 3*q**2 + q**4 - 10*q.
(q - 2)*(q + 2)**2*(2*q + 1)/2
Suppose 5*m = -4*h + 13, -m = 3*h - 4*m - 3. Factor 3/2*x + 1/2*x**h + 0.
x*(x + 3)/2
Factor 393*