4
Let u be (54/(-160))/(18/(-24)). Let v(b) be the second derivative of -u*b**4 + 3/100*b**5 + 0 - 81/10*b**2 + 27/10*b**3 + 5*b. Suppose v(x) = 0. Calculate x.
3
Let d = -18 - -12. Let w be (8/d)/(14/(-21)). Factor -18*y**w + 2*y + 33*y**2 - 16*y**2.
-y*(y - 2)
Let b(s) be the first derivative of 5*s**6/24 - s**5 - 55*s**4/16 - 5*s**3/2 - 301. Find f such that b(f) = 0.
-1, 0, 6
Let y(d) be the third derivative of 5*d**8/84 + d**7/14 - 7*d**6/6 - 15*d**5/4 - 15*d**4/4 - 6*d**2 + 56*d. Suppose y(z) = 0. What is z?
-2, -1, -3/4, 0, 3
Let g(p) be the first derivative of 4*p**5/5 + 21*p**4 + 357. Factor g(r).
4*r**3*(r + 21)
Let h = -6766/33 - -205. Let m = 61/165 - h. Determine v so that 2/5*v + 2/5 - 4/5*v**2 + 2/5*v**5 + m*v**4 - 4/5*v**3 = 0.
-1, 1
Let w = 61 + -66. Let h(a) = 4*a**2 + 4*a - 5. Let t(q) be the third derivative of q**5/30 + q**4/12 - q**3/2 + 2*q**2. Let m(v) = w*t(v) + 3*h(v). Factor m(p).
2*p*(p + 1)
Solve 0*g - 1/3*g**3 + 44/3*g**2 + 0 = 0.
0, 44
Let o(z) be the first derivative of 0*z - 18 - 5/9*z**3 + 0*z**2. Factor o(v).
-5*v**2/3
Let k be 2/(80/46)*20/4 - 4. Factor 2*g + 1/4*g**3 + k*g**2 - 4.
(g - 1)*(g + 4)**2/4
Let w(x) be the first derivative of -x**4/3 - 10*x**3/3 - 8*x**2 - 14*x - 12. Let t(n) be the first derivative of w(n). Factor t(a).
-4*(a + 1)*(a + 4)
Let p = 69344/13 - 5334. Find f such that -4/13*f - 14/13*f**2 + p - 8/13*f**3 = 0.
-1, 1/4
Let t(s) be the third derivative of 25/2*s**3 + 0 + 10*s**2 + 0*s + 5/4*s**4 + 1/20*s**5. Let t(q) = 0. What is q?
-5
Let y(k) be the first derivative of 2*k**3 + 48*k**2/7 + 24*k/7 + 54. Let y(s) = 0. Calculate s.
-2, -2/7
Let h(d) be the third derivative of 49/9*d**3 + 0 + 0*d - 39*d**2 - 7/18*d**4 + 1/90*d**5. Factor h(o).
2*(o - 7)**2/3
Let c(n) be the first derivative of 3*n**5/5 + 9*n**4/4 - 9*n**3 - 69*n**2/2 - 36*n + 57. Factor c(r).
3*(r - 3)*(r + 1)**2*(r + 4)
Let u(i) = 63*i**2 - 69*i - 132. Let g(j) = -j**3 + j. Let y(w) = 3*g(w) - u(w). Factor y(c).
-3*(c - 2)*(c + 1)*(c + 22)
Suppose n = h - 1 - 2, -3*h + 9 = -n. Let b(u) be the second derivative of n + 1/9*u**7 + 1/10*u**5 + 1/9*u**4 + 5*u + 0*u**3 + 0*u**2 - 4/15*u**6. Factor b(c).
2*c**2*(c - 1)**2*(7*c + 2)/3
Let u(p) = -p**3 + p**2 + p + 1. Let g(m) be the second derivative of -2*m**5/5 + m**4/4 + m**3/3 + 5*m**2/2 - 4*m. Let z(a) = -5*g(a) + 35*u(a). Factor z(t).
5*(t + 1)**2*(t + 2)
Let c(i) be the second derivative of -i**5/10 - 3*i**4 - 32*i**3 - 128*i**2 - 9*i + 9. Find g, given that c(g) = 0.
-8, -2
Let c = 12 + -8. Suppose c*b - 8*b = -32. Solve b - 10 + 2*u**3 - 2*u**2 + 2 = 0 for u.
0, 1
Let b(k) = -k**3 - 102*k**2 + 103*k + 21. Let p(o) = -o**3 - 51*o**2 + 52*o + 12. Let j(f) = 4*b(f) - 7*p(f). Factor j(w).
3*w*(w - 16)*(w - 1)
Let x be (64/16)/(1 - -1). Factor -5*j + 4 + 3*j**2 + 0*j - j**x - j.
2*(j - 2)*(j - 1)
Let w(k) = -k**2 - k - 1. Let c(l) = -123*l**2 - 113*l + 12. Let p(j) = -c(j) - 2*w(j). Find v such that p(v) = 0.
-1, 2/25
Let b(t) be the third derivative of 1/50*t**5 - 1/100*t**6 + 0*t + 16*t**2 + 1/525*t**7 + 0 - 1/60*t**4 + 0*t**3. Factor b(m).
2*m*(m - 1)**3/5
Let i(u) = -8*u**3 - 76*u**2 - 800*u - 722. Let d(g) = -11*g**3 - 75*g**2 - 801*g - 722. Let x(m) = -4*d(m) + 6*i(m). What is l in x(l) = 0?
-19, -1
Let y(w) be the third derivative of -w**6/120 + w**5/40 + 3*w**4/4 - 4*w**3 + w**2. Let r(d) be the first derivative of y(d). Suppose r(f) = 0. What is f?
-2, 3
Let g(a) = -a**2 - 7*a + 3. Let u(b) = -4*b**2 + b - 4. Let s(l) = l**2 + 1. Let r(j) = -3*s(j) - u(j). Let f(x) = g(x) + 5*r(x). Suppose f(w) = 0. Calculate w.
1, 2
Let p(m) = 5*m + 83. Let k be p(-16). Suppose -z + i - 4 = -3*i, 3*i - k = 5*z. Find u, given that z*u + 0 - 4/3*u**2 + 2/3*u**4 + 2/3*u**3 = 0.
-2, 0, 1
Let r(d) be the third derivative of 7/12*d**4 - 2/105*d**7 + 1/5*d**5 - 25*d**2 + 2/3*d**3 + 0*d + 0 - 1/60*d**6. Suppose r(n) = 0. Calculate n.
-1, -1/2, 2
Let x(r) = 15*r**4 - 105*r**3 - 245*r**2 + 2395*r + 5755. Let w(s) = -23*s**4 + 158*s**3 + 369*s**2 - 3592*s - 8632. Let n(c) = 5*w(c) + 8*x(c). Factor n(p).
5*(p - 8)**2*(p + 3)**2
Factor -52/3*x - 2/3*x**2 - 16 + 2/3*x**3.
2*(x - 6)*(x + 1)*(x + 4)/3
What is o in 3 + 3*o**2 - 21 - 2220*o + 2205*o = 0?
-1, 6
Let j(f) = -9*f**4 - 39*f**3 + 12*f**2 + 66*f - 30. Let s(w) = w**4 - w**2 + w - 1. Let z(t) = -j(t) + 6*s(t). Solve z(c) = 0 for c.
-2, 2/5, 1
Let i(o) = 844*o + 2. Let x be i(1). What is h in 1610*h**5 + 675*h + 105*h**5 - 15 + 150 - 2596*h**3 + 450*h**2 + x*h**3 - 1225*h**4 = 0?
-3/7, 1
Let b(t) = -9*t**4 - 15*t**3 + 32*t**2 - 13*t - 5. Let y(a) = -2*a**4 + a**2 - 1. Let j(h) = -3*b(h) + 15*y(h). Factor j(v).
-3*v*(v - 13)*(v - 1)**2
Let v be (2 + (-12)/7)*3556/635. Let -4/5*j**3 + 4/5*j - 8/5 + v*j**2 = 0. Calculate j.
-1, 1, 2
Let t(x) = -2*x**3 - 4*x**2 - 6*x. Let i(c) = 8*c**3 + 15*c**2 + 25*c. Suppose 23*g - 27*g - 72 = 0. Let k(s) = g*t(s) - 4*i(s). Factor k(o).
4*o*(o + 1)*(o + 2)
Let t(j) = -8*j**2 - 13*j - 100. Let n(p) = p**2 - p. Let x(i) = 14*n(i) + 2*t(i). Factor x(k).
-2*(k + 10)**2
Suppose -l + 200 = l. Let v be l/28 - (-4)/(-7). Factor 17*d - 2*d + 15*d**2 + 6*d**3 - d**v + 5.
5*(d + 1)**3
Let w = -4879/80 - -61. Let q(a) be the third derivative of -1/160*a**6 + 0*a**3 - w*a**5 + 3*a**2 + 0 + 0*a**4 + 0*a. Determine r, given that q(r) = 0.
-1, 0
Factor 2/3*w**4 - 8/3*w**2 + 2 + 4/3*w - 4/3*w**3.
2*(w - 3)*(w - 1)*(w + 1)**2/3
Factor -345*w**2 - 3803 - 28*w**3 + 423 - 5*w**4 + 138*w**3 - 2860*w.
-5*(w - 13)**2*(w + 2)**2
Let v(z) be the third derivative of -z**7/70 + z**5/20 - 293*z**2 + 2. Factor v(p).
-3*p**2*(p - 1)*(p + 1)
Let h(z) be the second derivative of 0*z**4 + 2*z - 1/5*z**5 + 0 - 4/15*z**6 + 0*z**2 - 2/21*z**7 + 0*z**3. Factor h(g).
-4*g**3*(g + 1)**2
Let b(y) = y**2 - 12*y + 15. Let k be b(11). Let z be ((-12)/14 + 0)*k/(-6). Determine p, given that -6/7*p + 4/7 - 2/7*p**5 + 8/7*p**3 + 0*p**4 - z*p**2 = 0.
-2, -1, 1
Let m(a) = -24*a**3 - 127*a**2 - 190*a - 42. Let v(p) = 50*p**3 + 255*p**2 + 380*p + 85. Let k(o) = -5*m(o) - 2*v(o). Factor k(q).
5*(q + 2)*(q + 4)*(4*q + 1)
Let f(w) be the second derivative of w**7/2520 + w**6/180 + w**5/40 - 11*w**4/12 - 7*w. Let g(r) be the third derivative of f(r). Factor g(h).
(h + 1)*(h + 3)
Let q(w) be the first derivative of 22 - 1/20*w**4 + 1/25*w**5 + 0*w**2 + 0*w + 0*w**3. Solve q(j) = 0 for j.
0, 1
Let z = -22 - -25. Factor 3*u**3 + u - 3*u**z - 2*u**2 + 2*u - u**3.
-u*(u - 1)*(u + 3)
Let d be -1 - (1/(-2))/(2010/(-260) + 8). Determine l so that -9/7*l**2 + d - 3/7*l = 0.
-1, 2/3
Suppose -23 + 23 = -10*i. Let y(z) be the second derivative of -z + z**3 - 9/20*z**5 - 1/10*z**6 + 1/4*z**4 + 1/14*z**7 + i + 0*z**2. Factor y(o).
3*o*(o - 2)*(o - 1)*(o + 1)**2
Let u(i) be the second derivative of -i**4/36 + i**3/2 - 182*i. Determine a so that u(a) = 0.
0, 9
Let y(d) = -2*d**3 + 10*d**2 + d - 1. Let h = 225 - 220. Let s be y(h). Suppose 76/9*b**2 - 50/3*b**s + 130/9*b**3 - 40/9*b - 16/9 = 0. Calculate b.
-2/5, 2/3, 1
Let a(r) be the third derivative of r**6/24 + 35*r**5/12 - 15*r**4/2 + 6*r**2 - 6*r. Factor a(h).
5*h*(h - 1)*(h + 36)
Let j be (-6)/12 - (-54)/(-4). Let r be (-3)/j*5/((-15)/(-4)). Find b such that 2/7*b + r*b**2 - 4/7 = 0.
-2, 1
Let p be 0 - (-4 - (4 + -6)). Find y such that 4*y**p - 3 + 1 - 3 + y**2 = 0.
-1, 1
Suppose -46/3*d**4 + 0*d**2 + 2/3*d**5 + 0*d + 0 + 44/3*d**3 = 0. What is d?
0, 1, 22
Let h(s) be the second derivative of -8*s + 0 - 6*s**2 - 1/6*s**4 - 5/3*s**3. Determine n, given that h(n) = 0.
-3, -2
Let d(c) be the first derivative of 3*c**4/2 - 26*c**3/3 + 16*c**2 - 8*c - 35. Factor d(g).
2*(g - 2)**2*(3*g - 1)
Suppose -g + 21 + 71 = 0. Suppose 3*x - 98 + g = 0. Factor -2/7*q**x - 1/7*q**3 + 1/7*q + 2/7.
-(q - 1)*(q + 1)*(q + 2)/7
Let w = 15743/3 - 5247. Determine h, given that 2/3*h**3 - 2/3*h + w*h**2 - 2/3 = 0.
-1, 1
Let x = 36 + -46. Let i(j) = 6*j**3 - 21*j**2 + 6*j + 9. Let w(u) = 3*u**3 - 10*u**2 + 3*u + 4. Let f(m) = x*w(m) + 4*i(m). Solve f(b) = 0.
-1/3, 1, 2
Let s be (-22)/(-7) - 15/105. Let y(m) = m**2 + 5*m + 5. Let r be y(-5). Factor 4*q**3 - s*q**3 - r*q**3 - 4*q**2 + 8*q.
-4*q*(q - 1)*(q + 2)
Suppose -4*d + 16 = -5*d. Let b = -12 - d. Determine w so that -2/5*w**2 + 0 - 2*w**b + 4/5*w - 16/5*w**3 = 0.
-1, 0, 2/5
Suppose -4050*v 