(q) = 6*k(q) + 55*o(q). Solve s(d) = 0 for d.
-6, -1, 2
Factor 46/7*l + 88/7 + 1/7*l**2.
(l + 2)*(l + 44)/7
Let u(x) be the third derivative of -1/240*x**6 - 1/168*x**7 + 0*x + 0*x**3 + 0*x**5 + 0 + 0*x**4 + 6*x**2. Factor u(g).
-g**3*(5*g + 2)/4
Let r be (20/(-5))/(-12)*6. Suppose -5*n + 5*h - r*h = -109, -3*h = -2*n + 49. Determine m, given that 50*m**2 + 8/3 + 125/3*m**3 + n*m = 0.
-2/5
Determine m, given that -75/4*m + 15/2*m**2 + 0 - 3/4*m**3 = 0.
0, 5
Let c(q) be the third derivative of 3/25*q**6 + 8*q**2 + 0*q + 9/280*q**8 - 4/75*q**5 + 0*q**4 + 0*q**3 - 18/175*q**7 + 0. Find b such that c(b) = 0.
0, 2/3
Let k(r) be the second derivative of r**6/1620 + r**5/108 + r**4/18 + r**3/3 - 2*r. Let i(m) be the second derivative of k(m). What is w in i(w) = 0?
-3, -2
Let n(r) be the second derivative of 2*r - 5/6*r**3 + 0*r**2 + 0 + 3/28*r**4 + 1/70*r**5 + 1/1260*r**6. Let t(k) be the second derivative of n(k). Factor t(b).
2*(b + 3)**2/7
Let s = -88727 - -14551273/164. Let o = s - 1/41. Factor 1/4*y**2 + 0 + 0*y + o*y**3.
y**2*(y + 1)/4
Let i(f) be the first derivative of -f**4/6 + f**3/2 - f**2/2 - f - 11. Let u(g) be the first derivative of i(g). Factor u(n).
-(n - 1)*(2*n - 1)
Factor 276*l + 288*l + 5*l**2 - 49*l - 24*l + 38720 + 389*l.
5*(l + 88)**2
Let q be (3 - 26/8)/(2/(-4)). Factor 1/2*f**2 - 3 + q*f.
(f - 2)*(f + 3)/2
Factor -1 + 24*x**3 - 4 + 40*x - 4*x**3 - 30*x + 35*x**2.
5*(x + 1)**2*(4*x - 1)
Let v be (172/36 - (-16 - -21))*-24. Factor 8*y + 1/3*y**3 - v - 3*y**2.
(y - 4)**2*(y - 1)/3
Let y = -1297 - -1299. Let 0 + 0*s - 8/13*s**y - 8/13*s**3 - 2/13*s**4 = 0. Calculate s.
-2, 0
Let w(c) be the third derivative of c**5/20 + 61*c**4/4 + 3721*c**3/2 + 6*c**2 + 1. Solve w(l) = 0 for l.
-61
Let n = -1173 - -1177. Factor -4*g**3 + 0 - 16/3*g + 2/3*g**n + 8*g**2.
2*g*(g - 2)**3/3
Let k be ((-56)/(-70))/((-2)/(-5)). Let i be ((-1)/1)/((-4)/16). Factor -13 + m**2 + 3*m**k + 13 - i*m**4.
-4*m**2*(m - 1)*(m + 1)
Let w(f) be the first derivative of -5*f**6/9 - 4*f**5/15 + 5*f**4/2 - 8*f**3/9 - 4*f**2/3 - 200. What is x in w(x) = 0?
-2, -2/5, 0, 1
Let q be (8/(-2))/(-1) - 29. Let v = -28 - q. Let c(u) = u**3 + 1. Let d(n) = 8*n**3 + 15*n**2 + 10*n + 3. Let z(w) = v*c(w) + d(w). Solve z(r) = 0 for r.
-2, -1, 0
Let s(h) be the first derivative of h**4/20 - 6*h**2/5 + 16*h/5 - 298. Let s(z) = 0. Calculate z.
-4, 2
Let z(y) be the first derivative of 2*y**5/15 + 8*y**4/3 + 46*y**3/3 + 30*y**2 - 271. Solve z(u) = 0 for u.
-10, -3, 0
Factor 32/5*r + 16/5*r**2 - 4/5*r**4 - 8/5*r**3 + 0.
-4*r*(r - 2)*(r + 2)**2/5
Let f(d) be the second derivative of 1/240*d**6 + 2*d**2 + 0 - 1/3*d**3 + 2*d + 1/6*d**4 - 1/24*d**5. Let p(t) be the first derivative of f(t). Factor p(b).
(b - 2)**2*(b - 1)/2
Let d(t) be the third derivative of t**7/525 + t**6/60 - 2*t**5/25 - 3*t**4/5 + 141*t**2 - t. Solve d(v) = 0.
-6, -2, 0, 3
Factor 5484*w**2 + 725*w**4 - 8 + 1135*w**4 - 1836*w + 72*w**2 - 5572*w**3.
4*(w - 1)**3*(465*w + 2)
Let f(p) = -p**2 - 14*p - 11. Let x be f(-13). What is b in 26*b**3 + 30*b**2 + 2*b**4 - 23*b**4 + 22*b**3 - 48*b + 12 - 21*b**x = 0?
-1, 2/7, 1, 2
Suppose -10*c + 7*c - 24 = -5*s, -3*s = 3*c. Let d(v) be the second derivative of 0*v**2 - 7*v + 0 - 1/24*v**4 + 1/12*v**s. Factor d(g).
-g*(g - 1)/2
Let a(h) be the first derivative of -5/3*h**3 - 20*h - 12 - 25/2*h**2. Find u, given that a(u) = 0.
-4, -1
Let j be (-19 - -19)/(2 + -1). Let w(t) be the first derivative of 0*t**3 + 0*t + j*t**5 + 3/14*t**4 - 3/14*t**2 - 1/14*t**6 - 5. Factor w(n).
-3*n*(n - 1)**2*(n + 1)**2/7
Let v(c) be the third derivative of c**7/210 + 23*c**6/30 + 529*c**5/10 + 12167*c**4/6 + 279841*c**3/6 + 35*c**2. Factor v(u).
(u + 23)**4
Let c(o) be the third derivative of -2*o**7/105 - o**6/15 - o**5/15 - 7*o**2 + 9*o. Find w, given that c(w) = 0.
-1, 0
Let a(g) = 8*g**2 + 8*g. Let k(h) be the first derivative of -7*h**3/3 - 4*h**2 - 3. Let d(u) = 3*a(u) + 4*k(u). Let d(y) = 0. What is y?
-2, 0
Let b(p) be the third derivative of -p**5/210 + 5*p**4/84 + 2*p**3/3 + 2*p**2 - 27*p. Let b(y) = 0. What is y?
-2, 7
Let b(i) = -i**3 + i - 1. Let h(u) = 8*u**3 - 6*u**2 - 77*u + 5. Let w(p) = 5*b(p) + h(p). Suppose w(l) = 0. What is l?
-4, 0, 6
Suppose 6144 + 128*y + 2/3*y**2 = 0. Calculate y.
-96
Factor 0*p + 22/3*p**2 + 1/3*p**4 - 32/3 - 3*p**3.
(p - 4)**2*(p - 2)*(p + 1)/3
Let l(g) be the third derivative of -g**6/120 + g**5/18 + g**4/8 - 2*g**3/9 + 2*g**2 + 161. Factor l(w).
-(w - 4)*(w + 1)*(3*w - 1)/3
Let b = -7398/5 - -1480. Factor 2/15 - 4/15*y**3 + 2/5*y - 2/15*y**5 + 4/15*y**2 - b*y**4.
-2*(y - 1)*(y + 1)**4/15
Let f(z) = 2*z**2 - 16*z - 24. Let u(m) = 2*m - 1. Let n(i) = 2*f(i) - 4*u(i). Determine r, given that n(r) = 0.
-1, 11
Let y(r) be the second derivative of 0 + 39/2*r**4 + 56*r**3 + 147/2*r**2 + 16*r + 1/10*r**6 + 12/5*r**5. Suppose y(g) = 0. What is g?
-7, -1
Let x(q) be the first derivative of q**4/12 + 7*q**3/3 - q**2/6 - 7*q + 647. Find z, given that x(z) = 0.
-21, -1, 1
Let a = -4335/74 - -3/37. Let f = 60 + a. Factor 0*y - 3/2*y**3 + f*y**2 + 0.
-3*y**2*(y - 1)/2
Suppose 0 = -3*x + 40 - 46. Let z be x*(-3 + (-32)/(-12)). Determine i so that 0 - z*i**2 - 2/3*i = 0.
-1, 0
Let m be 6/2 - (3 - (4 - 39)). Let x = 38 + m. Find t such that 2*t**2 - 5/3*t + 1/2 + 1/6*t**4 - t**x = 0.
1, 3
Suppose 0 = -6*c + 4*c - 34. Let v be 4/(20/(-15)) - c/4. Factor -9/4 + 1/4*p**3 + 3/4*p + v*p**2.
(p - 1)*(p + 3)**2/4
Let g(z) = 3. Let r(k) = -4*k**2 - 348*k - 9. Let x(c) = 3*g(c) + r(c). What is v in x(v) = 0?
-87, 0
Factor -131*u**3 - 10*u**2 - 12*u + 3*u + 64*u**3 + 66*u**3.
-u*(u + 1)*(u + 9)
Suppose -4*m = 7*n - 6*n + 22, 0 = 2*m - 2*n + 6. Let p(k) = 5*k**3 - 4*k**2 - 6*k. Let u(s) = -5*s**3 + 5*s**2 + 5*s. Let v(q) = m*p(q) - 6*u(q). Factor v(l).
5*l**2*(l - 2)
Suppose 20 + 85 = 3*i. Solve 30*d + 30*d + 1 + 19*d**3 + i - 15*d**3 + 28*d**2 = 0 for d.
-3, -1
Let t(w) be the first derivative of -2*w - 5/6*w**3 + 1/8*w**4 - 11 + 2*w**2. Factor t(z).
(z - 2)**2*(z - 1)/2
Factor 0 - 4/13*t**2 - 2/13*t**3 + 6/13*t.
-2*t*(t - 1)*(t + 3)/13
Let w(z) = -7*z**3 + 6*z - 1. Suppose 17 = -3*p + 2. Let b(j) = 11*j**3 - 9*j + 2. Let c(y) = p*b(y) - 8*w(y). Suppose c(o) = 0. What is o?
-1, 2
Suppose -5*g = -26 + 11. Suppose -g*y = 4*y - 14. Determine p, given that 10/3*p**4 + 80/3*p + 80/3*p**y + 40/3*p**3 + 32/3 + 1/3*p**5 = 0.
-2
Let g be (-24)/27 + (-2)/18 + 1. Let k(b) be the third derivative of 0 + 1/16*b**4 + g*b - 1/24*b**3 - 1/48*b**5 - 2*b**2. Suppose k(t) = 0. What is t?
1/5, 1
Solve -16 - 1/2*w**2 - 9*w = 0 for w.
-16, -2
Let y = -60 + 65. Find j, given that 9*j**y + 0*j**4 - 12*j**4 + 28*j**3 - 3*j**5 - 4*j**5 - 4 + 18*j - 32*j**2 = 0.
1, 2
Suppose 2*r + 5 = -5*n + 16, 4*r - 34 = 2*n. Suppose -6*j + r = -2*j. Suppose -2/3*c**j + 2/3 + 0*c = 0. What is c?
-1, 1
Let k(m) be the first derivative of -3*m**4/2 - 15*m**3 - 36*m**2 + 48*m + 79. Factor k(f).
-3*(f + 4)**2*(2*f - 1)
Let u(c) be the first derivative of 27/8*c**4 - 7*c**3 + 18 + 27/4*c**2 - 3*c - 3/5*c**5. Let u(z) = 0. Calculate z.
1/2, 1, 2
Find b, given that -125*b**3 + 126*b**3 + 2*b - 2*b = 0.
0
Let p be 2 - (0 - (7 - 4)). Suppose 7 = 2*v - 1. Factor v*j**2 - j**3 + 4*j - j**4 - 3*j**3 - 5*j**4 + 2 - 2*j**p + 2*j.
-2*(j - 1)*(j + 1)**4
Suppose 1 = a - 2*v, -5*v - 2 + 10 = a. Let f be 3*5/20*8/a. Factor -14/15*m**f + 32/15*m - 8/15.
-2*(m - 2)*(7*m - 2)/15
Let s = -571/4 + 143. Factor 3/2*r**2 + s*r**4 + 1/4 - r**3 - r.
(r - 1)**4/4
Let s(t) be the first derivative of 5*t**7/42 - t**6/3 - t**5/4 + 5*t**4/6 - 32*t + 46. Let p(m) be the first derivative of s(m). Suppose p(r) = 0. Calculate r.
-1, 0, 1, 2
Suppose 6*x**2 + 15 - 12*x**2 - 3*x**2 + 187*x + 32 + 5*x**2 = 0. What is x?
-1/4, 47
Determine s so that -1/3*s - 2/3*s**2 + 0 - 1/3*s**3 = 0.
-1, 0
Let t = -6 - -9. Suppose -15 = 4*g - 7*g. Let -8*v**5 - 72*v**g - 5*v**2 + 172*v**4 + 42*v**t + 8*v + v**2 - 138*v**3 = 0. Calculate v.
-1/4, 0, 2/5, 1
Find k, given that 1374*k**4 - 1384*k**4 + k**3 + 3*k**5 + 7*k**2 - k**2 = 0.
-2/3, 0, 1, 3
Suppose -p + 46 = -5*i, i + 39 = -3*i + 3*p. Let z = 13 + i. Factor 4*m**3 + 25*m**4 - 4*m - 3 + 1 - 23*m**z.
2*(m - 1)*(m + 1)**3
Factor 457 + 220*i + 125*i**3 + 350*i**2 - 847 + 430.
5*(i + 2)*(5*i + 2)**2
Let o(x) = 2*x - 12. Let