(l) be the third derivative of l**9/12096 + l**8/448 + 3*l**7/112 + 3*l**6/16 - 7*l**5/60 - 6*l**2. Let a(k) be the third derivative of h(k). Factor a(c).
5*(c + 3)**3
Let u(r) = -118*r - 472. Let w be u(-4). Solve w*o + 0*o**2 + 0 + 3/5*o**3 = 0.
0
Let q(w) be the third derivative of -w**5/330 + w**4/132 + 2*w**3/11 + 59*w**2. Factor q(j).
-2*(j - 3)*(j + 2)/11
Suppose -5*z - 8*z = 0. Let s be (-15 - -16)*(0 + z). Determine q, given that s*q**2 + 66/7*q**3 - 8/7*q + 0 - 100/7*q**4 + 6*q**5 = 0.
-2/7, 0, 2/3, 1
Let v be 36/42 - (-6)/42. Factor v + 5/4*p + 1/4*p**2.
(p + 1)*(p + 4)/4
Let s(z) be the first derivative of 4*z**5/5 + 4*z**4 + 16*z**3/3 - 38. Factor s(f).
4*f**2*(f + 2)**2
Let m be 30/(-26) + (-4)/(-26). Let d be 6 - (m - -2)*3. Factor -4*r - 48*r**d - 6*r**5 - 9*r**5 - 54*r**4 - 24*r**2 + 3*r**5 + 14*r**4.
-4*r*(r + 1)**3*(3*r + 1)
Let y = 125 + -121. Factor -29*n**3 - 6 + 53*n**3 - 26*n**2 + 23*n - 8*n**y + n**5 - 8*n**2.
(n - 3)*(n - 2)*(n - 1)**3
Let s be 10*(108/160 + (-1)/(-8)). Let h be (s/14)/((-90)/(-63)). What is j in h - 3/5*j**3 + 1/5*j - 4/5*j**2 = 0?
-1, 2/3
Let q(n) be the second derivative of -5*n**4/12 - 325*n**3/12 + 165*n**2/4 + 68*n + 2. Let q(m) = 0. Calculate m.
-33, 1/2
Factor -1/10*u**3 + 1/5*u**2 + 0 - 1/10*u.
-u*(u - 1)**2/10
Let d(c) = 6*c**2 + 12*c - 1. Let l be d(3). Let u = l - 87. Factor 0 - 1/4*j**3 - 1/2*j**u + 0*j.
-j**2*(j + 2)/4
Let q be (6 - 6)*(3/6)/(-1). Let x(d) be the third derivative of q*d + 0*d**3 + 0 + 1/30*d**6 + 0*d**5 + 0*d**4 - 5*d**2. Suppose x(z) = 0. What is z?
0
Let k be (-6050)/(-2904) - (-3)/(-4). Determine h, given that 2/3 - k*h + 2/3*h**2 = 0.
1
Let p(z) be the third derivative of 5*z**8/336 - z**7/84 - 5*z**6/8 - 8*z**5/3 - 65*z**4/12 - 25*z**3/4 - 3*z**2 - 25. Solve p(q) = 0 for q.
-3/2, -1, 5
Suppose 5/3*k**2 - 20*k + 100/3 = 0. What is k?
2, 10
Let n = -78639/13 + 6051. Find r, given that -2/13*r**2 - 72/13 + n*r = 0.
6
Let l = 128 - 128. Let g(y) be the second derivative of l*y**2 + 1/12*y**4 + 0 + 1/3*y**3 - 3*y - 1/20*y**5. Let g(t) = 0. Calculate t.
-1, 0, 2
Let q(b) be the first derivative of 0*b + 6 - 1/8*b**6 - 3/20*b**5 + 1/4*b**3 + 3/16*b**4 + 0*b**2. What is i in q(i) = 0?
-1, 0, 1
Suppose -14*x - 53*x = -15*x. Let 0*n**3 + x - 5/2*n**2 + 5/2*n**4 + 0*n = 0. What is n?
-1, 0, 1
Let c = -8 - -11. Factor 1 - 6 + u**2 + 5 + c*u.
u*(u + 3)
Let u(b) be the second derivative of b**7/168 + b**6/40 + 3*b**5/80 + b**4/48 - 96*b. Solve u(r) = 0.
-1, 0
Suppose -28*a - 24 = -36*a. Determine d, given that -1/4*d**2 + 1/4*d**4 + 1/4*d - 1/4*d**a + 0 = 0.
-1, 0, 1
Let g(k) be the third derivative of 0*k**7 + 0 + 0*k**5 - 1/840*k**8 + 0*k + 0*k**4 + 1/300*k**6 - 12*k**2 + 0*k**3. Solve g(r) = 0 for r.
-1, 0, 1
Let c be (-36)/(-72) + 0/1. Suppose -2*n - 16 = -6*n. Find f, given that 0 + 0*f**2 + 0*f - c*f**n + 1/6*f**3 = 0.
0, 1/3
Let y be ((-9)/(-54) + (-2)/12)/(-1). Let s(u) be the first derivative of 3/4*u**2 + 3 - 1/2*u**3 + 3/10*u**5 - 3/8*u**4 + y*u. Factor s(j).
3*j*(j - 1)**2*(j + 1)/2
Let n(h) = -h**3 - 77*h**2 + 165*h + 29. Let j(o) = -o**3 - 229*o**2 + 495*o + 86. Let s(a) = -4*j(a) + 11*n(a). Determine v so that s(v) = 0.
-1/7, 5
Let s(k) = -25*k**2 + 1435*k - 105125. Let a(t) = 4*t**2 + 3*t. Let z(v) = 5*a(v) + s(v). Factor z(g).
-5*(g - 145)**2
Suppose -9*y = -4*y - 15. Suppose -9 = h - 4*h. Factor -2*m + 5*m**2 + 0*m**y + 9*m**3 - 2*m**h + 0*m**2.
m*(m + 1)*(7*m - 2)
Factor -49*d - 24*d + 11*d**4 + 87*d**2 + 91*d + 90*d**3 + 10*d**4.
3*d*(d + 1)*(d + 3)*(7*d + 2)
Let c(l) be the first derivative of -4/7*l - 3 + 2/7*l**2 - 1/7*l**4 + 4/21*l**3. Determine i, given that c(i) = 0.
-1, 1
Suppose 7*o - 4*u - 21 = 4*o, 15 = 3*o - 2*u. Let v = 4 + -2. Factor -5/4*z - 5/4 + 5/4*z**v + 5/4*z**o.
5*(z - 1)*(z + 1)**2/4
Suppose -4*l + 2*z + 4 = 0, -219 = 3*l - 4*z - 227. Determine x, given that 24 + 0*x - 12*x**2 + 3/2*x**4 + l*x**3 = 0.
-2, 2
Suppose 3*u - 9 = u + g, 5*g + 25 = 5*u. Suppose -v + 1 = f - 0*v, -5*f - 4*v + u = 0. Factor f*y + 2/7*y**2 - 2/7.
2*(y - 1)*(y + 1)/7
Let f(k) = -k**2 + 3*k + 3. Let r be f(-3). Let b be ((-9)/45)/(9/r). Determine n so that 0*n**4 + n - 4/3*n**3 + b*n**5 - 2/3 + 2/3*n**2 = 0.
-2, -1, 1
Let w(h) = -h**3 - 3*h - 2. Let u be w(-1). What is j in 60*j - 5*j**3 + 196*j**2 - 196*j**u - 80 = 0?
-4, 2
Find x, given that 3/7 - 1/7*x**2 - 2/7*x = 0.
-3, 1
Let m be (-9)/630*-5*1. Let q(o) be the third derivative of 0*o**3 - 4*o**2 + 0 - m*o**7 - 1/10*o**5 - 7/40*o**6 + 0*o**4 + 0*o. Determine r so that q(r) = 0.
-1, -2/5, 0
Let k(w) = w**2 - 82*w + 1058. Let j be k(16). Find o such that -15/4*o - 1/4*o**3 - 7/4*o**j - 9/4 = 0.
-3, -1
Suppose -q + 6*q = -10, -5*i - q = -13. Suppose -18250 - 7701*n + 95*n**i - 14555 - 5*n**4 - 6879*n - 2430*n**2 - 275*n**3 = 0. Calculate n.
-9
Let g(s) be the third derivative of 0 + 1/10*s**6 + 0*s - 1/350*s**7 - 10*s**2 + 49/10*s**4 - 63/50*s**5 + 343/10*s**3. Factor g(w).
-3*(w - 7)**3*(w + 1)/5
Let q = 11540/17301 + -2/5767. Factor -2/9*u**5 + 0*u + 0 + q*u**3 + 0*u**4 - 4/9*u**2.
-2*u**2*(u - 1)**2*(u + 2)/9
Suppose 23*i = 10*i + 26. Let n(w) be the third derivative of 0 + 0*w**3 + 6*w**i + 0*w**4 - 1/30*w**5 - 1/24*w**6 + 0*w. Factor n(c).
-c**2*(5*c + 2)
Solve 178 + 111*p - 15*p**2 - 375 + 155 = 0.
2/5, 7
Let c(u) be the second derivative of u**6/15 - 31*u**5/40 + 5*u**4/6 + 7*u**3/12 - 170*u. Find a such that c(a) = 0.
-1/4, 0, 1, 7
Let r(z) be the first derivative of z**3/6 + 11*z**2/2 - 23*z/2 + 366. Factor r(b).
(b - 1)*(b + 23)/2
Let g be ((5 - 2) + -4)/((-13)/39). Factor 0*p + 3/2*p**4 + 3/2 + 0*p**g - 3*p**2.
3*(p - 1)**2*(p + 1)**2/2
Let v(f) be the third derivative of -f**6/60 - f**5/6 + 7*f**2 + 2. Factor v(h).
-2*h**2*(h + 5)
Let p(o) be the third derivative of -o**9/211680 - o**8/70560 + o**7/2940 - 3*o**5/20 - 2*o**2. Let h(m) be the third derivative of p(m). Factor h(z).
-2*z*(z - 2)*(z + 3)/7
Let y be ((110/(-33))/5)/(-5). Let 4/3*n - y*n**2 - 10/3 = 0. Calculate n.
5
Let o(m) = 10*m**2 + 64*m - 91. Let y(u) = -u**2 - 4*u. Let w(h) = -5*o(h) - 55*y(h). Determine j, given that w(j) = 0.
7, 13
Let a(r) = 85 + 7*r - 85 + 10*r**2. Let h(p) = -2*p + 0*p + 3*p + p**2. Let j(x) = 2*a(x) - 18*h(x). Factor j(n).
2*n*(n - 2)
Let d(n) = -354*n - 1. Let t be d(-3). Factor 7*b**3 + 12*b + b**3 - 1079*b**2 - 2 + t*b**2.
2*(b - 1)**2*(4*b - 1)
Find q, given that -168*q**2 + 2/3*q**3 - 395136 + 14112*q = 0.
84
Let i = -738 - -738. Let z = -597/5 + 6657/55. Factor -16/11*d**3 - 6/11*d**4 + i + 8/11*d**2 + 0*d + z*d**5.
2*d**2*(d + 1)*(3*d - 2)**2/11
Let m = 12894/5 + -2578. Factor m + 4/5*y**2 + 8/5*y.
4*(y + 1)**2/5
Let i(z) be the third derivative of 31/2*z**4 + 153/5*z**5 + 3*z**2 + 3 + 0*z + 243/20*z**6 - 32805/448*z**8 - 8019/140*z**7 + 4*z**3. Factor i(l).
-3*(5*l - 2)*(9*l + 2)**4/4
Let z(d) = 2*d**3 - 19*d**2 - 122*d - 86. Let n(c) = -3*c**3 + 28*c**2 + 183*c + 128. Let u(r) = -5*n(r) - 8*z(r). Factor u(i).
-(i - 16)*(i + 1)*(i + 3)
Let x(u) be the second derivative of 0 - 9/20*u**5 - 19*u + 1/10*u**6 + 0*u**3 + 0*u**2 + 1/2*u**4. What is z in x(z) = 0?
0, 1, 2
Let a(f) be the first derivative of 3*f + 16 + 7/4*f**3 - 6*f**2. What is m in a(m) = 0?
2/7, 2
Let a = -4060/9 + 1354/3. Find y such that 2/9*y**2 + 2/9*y - 2/9*y**3 - a = 0.
-1, 1
Let h(k) be the first derivative of k**5/2 - 9*k**4/8 + k**3/2 + k**2/4 + 736. Suppose h(t) = 0. Calculate t.
-1/5, 0, 1
Let i be 2/7 - 48/(-28). Suppose -5 = -2*z + 1. Factor c**2 - c**z + 28*c**4 - i + 2 - 29*c**4 + c.
-c*(c - 1)*(c + 1)**2
Factor 38/5*l - 8/5*l**2 - 2/5*l**3 - 28/5.
-2*(l - 2)*(l - 1)*(l + 7)/5
Let y(a) be the first derivative of -a**4/36 - 11*a**3/9 - 121*a**2/6 + 15*a - 2. Let m(q) be the first derivative of y(q). Solve m(g) = 0 for g.
-11
Let j be (-70)/(-12) + 1/6. Let 4*g**3 + j*g**2 - 13*g**3 - 10*g**4 + 25*g**5 - 16*g**3 + 4*g**2 = 0. What is g?
-1, 0, 2/5, 1
Let w be (-10)/(160/(-24)) - ((-15)/18 - -1). Find y, given that 0 - 1/3*y**2 - w*y + 4/3*y**3 + 1/3*y**4 = 0.
-4, -1, 0, 1
Suppose 238*t - 242*t = -8. Let j(x) be the first derivative of -t - 3/2*x**2 - 4*x**3 + 9*x. Find q such that j(q) = 0.
-1, 3/4
Suppose -6*d - 8*d - 2*d**2 + 33*d + 17*d - 112 = 0. What is d?
4, 14
Let o be 242/5 - 1/15*6. Let u = 50 - o. Find w, given that 2