 - 325*d**2 + 5*d**4 + 835*d**3 - 444*d**3 - 446*d**3.
5*d*(d - 15)*(d - 1)*(d + 5)
Let o(m) be the third derivative of -11*m**2 - 3/160*m**6 - 1/32*m**4 + 1/280*m**7 + 0 + 3/80*m**5 + 0*m**3 + 0*m. Let o(k) = 0. Calculate k.
0, 1
Factor -80*h - 1/5*h**5 + 0 - 42/5*h**4 - 481/5*h**3 - 168*h**2.
-h*(h + 1)**2*(h + 20)**2/5
Let n be (6/(-4))/(3/30). Let f be n/3*4*(-3)/30. Suppose 0 - 4/3*r - 14/3*r**f = 0. Calculate r.
-2/7, 0
Let f(s) = s**2 - 18*s - 35. Let u be f(20). Let n(i) be the first derivative of -1 + 0*i**2 - 2/35*i**u + 0*i - 2/21*i**3 - 1/7*i**4. Factor n(y).
-2*y**2*(y + 1)**2/7
Let o(c) = -12*c**4 - 63*c**3 - 84*c**2 - 27*c + 6. Let s(x) = -x**3 - 2*x**2 - x. Let a(t) = -2*o(t) + 10*s(t). Factor a(m).
4*(m + 1)**2*(m + 3)*(6*m - 1)
Suppose 0 = -5*o + 3027*z - 3031*z + 14, -2*z + 2 = 0. Factor 0 + 2/7*w**o + 6/7*w**4 + 0*w - 8/7*w**3.
2*w**2*(w - 1)*(3*w - 1)/7
Let z(y) be the second derivative of y**7/840 - y**6/360 - y**5/24 - y**4/8 + y**3/2 - 5*y. Let p(m) be the second derivative of z(m). Let p(l) = 0. What is l?
-1, 3
Let y(c) = -6*c - 38. Let f be y(-7). Let r(d) be the second derivative of -1/4*d**2 - 2*d + 0 + 1/24*d**3 + 1/48*d**f. Factor r(h).
(h - 1)*(h + 2)/4
Determine x so that 3*x + 1/2*x**3 - 7/2*x**2 + 0 = 0.
0, 1, 6
Let h(b) = b**3 - 19*b**2 - 20*b - 20. Let k be h(20). Let z be k*2/(-16) - (2 + -1). Factor 3*q + z + 3/2*q**2.
3*(q + 1)**2/2
Let k(c) be the first derivative of -c**4/6 + 28*c**3/9 - 25*c**2/3 + 8*c + 91. Factor k(b).
-2*(b - 12)*(b - 1)**2/3
Let x(a) be the second derivative of -a**6/15 - 41*a**5/10 - 220*a**4/3 - 400*a**3/3 + 110*a + 3. Factor x(c).
-2*c*(c + 1)*(c + 20)**2
Let r(m) = -51*m**2 + 42*m**2 - 8*m + 0 + 4 - m**3. Let a be r(-8). Factor -i**2 + 5*i**2 + a*i**2 + 4*i.
4*i*(2*i + 1)
Solve -17/5*x**2 - 1/5*x**3 + 17/5 + 1/5*x = 0 for x.
-17, -1, 1
Let m(o) = -28*o**4 - 104*o**3 - 80*o**2 + 48*o + 8. Let u(v) = -2*v - 1. Let r(c) = m(c) + 8*u(c). Let r(k) = 0. Calculate k.
-2, 0, 2/7
Find a such that -44 - 335*a + 45*a**3 - 196 - 100*a**2 + 63*a**3 - 113*a**3 = 0.
-16, -3, -1
Let a(x) = 30*x**4 + 10*x**3 - 25*x**2. Let p = 37 - 33. Let l(q) = 29*q**4 + 9*q**3 - 25*q**2 - q. Let m(o) = p*a(o) - 5*l(o). Let m(c) = 0. What is c?
-1, -1/5, 0, 1
Let r(t) be the first derivative of -t**3/2 - 117*t**2/4 - 198. Factor r(j).
-3*j*(j + 39)/2
Let v(n) be the second derivative of 2*n**5/85 + 14*n**4/51 + 25*n**3/51 + 6*n**2/17 - 88*n. Let v(q) = 0. Calculate q.
-6, -1/2
Suppose 0 = 2*i - g - 11, -8*i - g = -7*i - 7. Let h(z) be the first derivative of -9/2*z**2 - z**3 - i*z - 5. Factor h(t).
-3*(t + 1)*(t + 2)
Let r(p) = -p**4 + p**3 + 2*p**2 + p + 1. Let y(k) = k**5 + 2*k**4 - 16*k**3 - 7*k**2 + 5*k - 5. Let n(f) = 5*r(f) + y(f). Determine q so that n(q) = 0.
-2, -1, 0, 1, 5
Let y = -315 + 318. Let z(q) be the first derivative of 8/15*q**3 + 0*q + 0*q**2 + 6/5*q**4 - y - 14/25*q**5. Factor z(w).
-2*w**2*(w - 2)*(7*w + 2)/5
Let c(i) be the first derivative of -2*i**5/25 + 3*i**4/5 - 14*i**3/15 - 6*i**2/5 + 16*i/5 - 142. Solve c(j) = 0 for j.
-1, 1, 2, 4
Suppose -5*l = 3*t - t + 40, 3*t = -3*l - 24. Let x be (-1)/(-4) + (44/l)/(-11). Factor 0 + x*h**2 - 9/4*h.
3*h*(h - 3)/4
Let m(g) be the third derivative of 0*g - 28*g**2 + 1/110*g**6 + 0 - 1/385*g**7 + 0*g**3 - 1/110*g**5 + 0*g**4. Determine p, given that m(p) = 0.
0, 1
Suppose 44*q - 12*q = 64. Factor -20/7*d**3 - 8/7*d**q + 0 + 0*d.
-4*d**2*(5*d + 2)/7
Suppose -4*y = -4*n - 80, 4*y - 3 - 65 = -2*n. What is x in -3*x - 3*x**5 - 17*x**2 - y*x**3 + 29*x**2 + 7*x**4 + 5*x**4 = 0?
0, 1
Let j(n) be the first derivative of 0*n + 1/4*n**4 + 0*n**2 - 1/12*n**6 - 1/10*n**5 - 29 + 0*n**3. Factor j(a).
-a**3*(a - 1)*(a + 2)/2
Let u(t) be the second derivative of -t**8/336 - t**7/56 + t**5/6 - 5*t**3/3 + 4*t. Let m(p) be the second derivative of u(p). What is o in m(o) = 0?
-2, 0, 1
Suppose -3*w - 3*x + 6 = 0, w - 3*x - 6 = -2*w. Let g be (6/(-14) - 66/(-105))*w. Factor 0 + g*k + 2/5*k**3 - 4/5*k**2.
2*k*(k - 1)**2/5
Let v(t) be the first derivative of -9/4*t**4 + 6 + 9/2*t**2 - 6*t + t**3 + 3/5*t**5. Factor v(j).
3*(j - 2)*(j - 1)**2*(j + 1)
Solve -75/2*r**3 + 5/4*r**4 + 2025*r + 585/4*r**2 + 3645 = 0.
-3, 18
Let p be (-110)/(-176)*72/50. Let u(c) be the first derivative of -c + p*c**5 - 11/4*c**2 - 7/6*c**3 + 11/8*c**4 + 10. Factor u(z).
(z - 1)*(z + 1)**2*(9*z + 2)/2
Let t(i) be the first derivative of -5*i**3/3 + 5*i**2 + 15*i + 130. Determine a, given that t(a) = 0.
-1, 3
Factor -2 + 42/11*w - 18/11*w**2 - 2/11*w**3.
-2*(w - 1)**2*(w + 11)/11
Let y(u) be the first derivative of -3/4*u**4 + 0*u - 9/5*u**5 + 39 - 1/2*u**2 + 5/3*u**3. Find c such that y(c) = 0.
-1, 0, 1/3
Let h = -35 - -37. Factor 0*u - 10*u + 2*u**h + 2*u**2 + 6*u.
4*u*(u - 1)
Let t = 28704 - 315740/11. Let r be (-64)/(-77) + (-2)/7. Suppose t*l + 2/11*l**3 + 0 + r*l**2 = 0. What is l?
-2, -1, 0
Let q(a) = -a**2 + 12*a + 6. Let i be q(12). Let z(b) = -5*b**2 + 8. Let f(s) = 19*s**2 - 32. Let v(l) = i*f(l) + 22*z(l). Factor v(k).
4*(k - 2)*(k + 2)
Let w(n) = n**3 + 1. Let d(i) = 8*i**3 - 10*i**2 - 5*i + 13. Suppose s - 2*k = -2*s + 3, -5*s + 4*k + 3 = 0. Let g(r) = s*w(r) - d(r). What is l in g(l) = 0?
-1, 1, 2
Let i = 43 + 24. Let -15*q**2 + 5*q + 5*q**4 + 69 - 126 - 5*q**3 + i = 0. Calculate q.
-1, 1, 2
Let c(i) be the second derivative of i**6/90 - i**5/6 - i**4/3 + 52*i**3/9 + 80*i**2/3 + 282*i. What is p in c(p) = 0?
-2, 4, 10
Let r(g) = -2*g**3 + 6*g**2 - 8. Let x be 90/27 - (-4)/6. Suppose 2 = x*z - 10. Let w(s) = -s**3 + 3*s**2 - 4. Let q(i) = z*r(i) - 5*w(i). Factor q(o).
-(o - 2)**2*(o + 1)
What is g in 169*g - 160*g + 0*g**2 - 3*g**2 = 0?
0, 3
Let c(r) = -46*r - 2. Let m be c(-1). Factor 47*s**4 - m*s**4 - s**2 - 3*s**3 + s**2.
3*s**3*(s - 1)
Let g(f) = -2*f - 7. Let x be g(-5). Suppose -4*u = -3*k + 22, u - 4 = 2*u. Factor -m**4 + x*m**4 + 16*m**k - 18*m**2.
2*m**2*(m - 1)*(m + 1)
Let k(g) = -g**3 + 7*g**2 - 10*g - 8. Let t be k(6). Let n = t + 32. Factor n*l**2 + 3*l**3 + l**2 - 4*l**2.
3*l**2*(l - 1)
Suppose -2/3*a**3 + 32/3*a + 20/3 - 17/3*a**2 = 0. What is a?
-10, -1/2, 2
Suppose -13*w + 54 = -50. Suppose 5*j = -5*r, 2*j = 3*r + j - w. Factor 6/5*z**3 - 3/5*z**r - 3/5*z**4 + 0*z + 0.
-3*z**2*(z - 1)**2/5
Factor -52/5*g**2 + 0 + 4/5*g**3 + 24*g.
4*g*(g - 10)*(g - 3)/5
Let x(f) be the third derivative of -f**5/60 - f**4/6 + 2*f**2 - 79*f. Suppose x(d) = 0. Calculate d.
-4, 0
Suppose g = -g - 8. Let f(t) be the second derivative of t**4/6 - t**3 - 4*t**2 + 2*t. Let h(z) = -z**2 + 1. Let x(i) = g*h(i) - f(i). Factor x(y).
2*(y + 1)*(y + 2)
Let q(c) be the second derivative of -c**6/300 - c**5/150 + c**4/30 + 5*c**2 - 4*c. Let m(u) be the first derivative of q(u). Solve m(j) = 0 for j.
-2, 0, 1
What is i in 72/7 + 102/7*i + 33/7*i**2 + 3/7*i**3 = 0?
-6, -4, -1
Let k(y) be the first derivative of -4*y**3/3 + 28*y**2 + 60*y + 216. Factor k(b).
-4*(b - 15)*(b + 1)
Let 1/3*i**3 + 6348 + 6256*i - 275/3*i**2 = 0. What is i?
-1, 138
Let x(r) be the second derivative of -5/2*r**2 + 0 + 23*r + 35/36*r**3 + 25/72*r**4. Factor x(t).
5*(t + 2)*(5*t - 3)/6
Suppose -3*x = 9*m - 4*m - 11, -m + 7 = 3*x. Suppose -14*j**3 + j**4 - j**x - 9*j**3 + 3*j + 20*j**3 = 0. What is j?
-1, 0, 1, 3
Let p(i) = i**4 - i**3 - i**2 + i. Let d(z) = 11*z**4 - 8*z**3 - 14*z**2 + 8*z + 3. Let l = -19 + 20. Let w(u) = l*d(u) - 5*p(u). Solve w(t) = 0.
-1, -1/2, 1
Let y(a) be the first derivative of 1/7*a**4 - 4/7*a**3 + 6/7*a**2 - 4/7*a - 2. Factor y(s).
4*(s - 1)**3/7
Suppose 0 = 3*s - 2*s + 5*i + 95, 0 = -2*s + 5*i - 115. Let p = -279/4 - s. Factor -p*j**3 - 1/4*j + 0 + 1/2*j**2.
-j*(j - 1)**2/4
Let y be (0/10)/((-6)/(-2)). Let z(h) be the second derivative of -1/6*h**4 + 0 + 0*h**2 + y*h**3 - 3*h. Factor z(t).
-2*t**2
Let t(j) = -9*j**2 - 712*j - 14392. Let s(l) = -6*l**2 - 475*l - 9595. Let g(m) = 8*s(m) - 5*t(m). Let g(h) = 0. What is h?
-40
Suppose -2*g = 3*g - 15. Suppose 0 = 4*v + 4*d + 24, -5*d - 23 - 7 = 0. Factor 0 + v*q**4 + 0*q**2 + 1/2*q**5 + 0*q - 1/2*q**g.
q**3*(q - 1)*(q + 1)/2
Let j(v) be the second derivative of -v**7/42 + v**6/30 + v**5/4 - v**4/12 - 4*v**3/3 - 2*v**2 + v + 25. Factor j(n).
-(n - 2)**2*(n + 1)**3
Find u, given that 288/5*u - 1036*u**2 + 5184/5 - 288/5*u**3 - 4/5*u**4 = 0.
-36, -