w = 40. Let u(n) be the second derivative of 0 + 2*n - 3/100*n**5 + 1/10*n**3 - 1/50*n**6 + 0*n**2 + 1/20*n**w. Factor u(q).
-3*q*(q - 1)*(q + 1)**2/5
Let h(c) be the third derivative of 2*c**7/105 + 13*c**6/10 - 3*c**2 - 58. Determine o, given that h(o) = 0.
-39, 0
Let z(i) be the third derivative of 0*i**3 - 5*i**2 + 1/36*i**4 - 1/90*i**5 - 1/105*i**7 - 1/36*i**6 + 0*i + 0. Solve z(m) = 0.
-1, 0, 1/3
Suppose n - 12 = 5*r, 2*r = 4*r + 6. Let v be -1*32/3*n. Factor 2*p + 4 - 30*p**2 + v*p**2 + 4*p.
2*(p + 1)*(p + 2)
Let l(x) = -5*x**2 - x - 3. Let u(c) = 1 + 2*c + c**2 - 3*c + 0. Let o(t) = t**3 + 20*t**2 + 3. Let m be o(-20). Let r(f) = m*u(f) + l(f). Solve r(s) = 0.
-2, 0
Factor 1/8*q**2 + 1/8*q - 3/4.
(q - 2)*(q + 3)/8
Let j = -51037/30 + 8512/5. Factor -1/6*g**3 - j*g**2 - g + 0.
-g*(g + 1)*(g + 6)/6
Find h such that -3/8*h**2 - 153/4 + 69/8*h = 0.
6, 17
Let w be 2 + -2 - 1 - 106/(-24). Let q = w - 8/3. Solve -q*g**4 + 3/2 - 3/4*g**3 + 9/4*g**2 + 15/4*g = 0.
-1, 2
Let v(b) = b + 4. Let a be v(-2). Let k be 0*a*(0 - (-1)/2). Factor k*u**3 + 1/4*u**5 - 1/4*u - 1/2*u**2 + 0 + 1/2*u**4.
u*(u - 1)*(u + 1)**3/4
Suppose -z + 25 = 4*m, 8*z - 4*z - 40 = -4*m. Let c be (z/((-35)/(-3)))/((-5)/(-10)). Let 4/7*o + 2/7 - c*o**2 = 0. Calculate o.
-1/3, 1
Let p(m) be the first derivative of 2/3*m - 5/6*m**5 - 5/6*m**4 + 5/3*m**2 + 11 + 7/6*m**3. Determine s so that p(s) = 0.
-1, -2/5, 1
Let q be ((-234)/243 + -2)*(-60)/80. Factor 220/9*m + 26/3*m**2 + 121/9 + 1/9*m**4 - q*m**3.
(m - 11)**2*(m + 1)**2/9
Let b(a) be the first derivative of -1/5*a**5 + 2 + 1/3*a**4 - 3*a + 6*a**2 + 10/3*a**3. Let h(o) be the first derivative of b(o). Factor h(y).
-4*(y - 3)*(y + 1)**2
Let c be (0 + -3)/(-10 + 36/4). Factor 8/15*z**2 + 2/3*z**4 + 0*z - 8/5*z**c + 0.
2*z**2*(z - 2)*(5*z - 2)/15
Let l(z) be the first derivative of -z**4/4 - 8*z**3/3 - 21*z**2/2 - 18*z - 232. Suppose l(i) = 0. What is i?
-3, -2
Let c(r) = 17*r + 631. Let s be c(-37). Let j(i) be the first derivative of -i**3 - 9 - 3/4*i**4 + 0*i + 3/2*i**s + 3/5*i**5. Determine q, given that j(q) = 0.
-1, 0, 1
What is q in -q**2 - 9*q**2 + 38 + 118 - 152*q + 6*q**2 = 0?
-39, 1
Let p(b) = -b. Let h = 50 + -51. Let a(l) = -4*l**2 + 4*l + 16. Let m(s) = h*a(s) - 4*p(s). Factor m(x).
4*(x - 2)*(x + 2)
Let f(u) = -11*u**2 + 93*u + 104. Let g(w) = -4*w**2 + 31*w + 35. Let x(b) = 3*f(b) - 8*g(b). Let x(l) = 0. What is l?
-1, 32
Let f(h) be the third derivative of -h**5/450 - 29*h**4/45 - 3364*h**3/45 - 50*h**2 + 4*h. Solve f(n) = 0 for n.
-58
Let z be -12 + 18/(-24) + 13. What is h in 3/4*h**4 - h**3 + 0 + z*h**2 + 0*h = 0?
0, 1/3, 1
Let r(k) be the first derivative of k**3/6 + 59*k**2/4 - 30*k + 779. Factor r(m).
(m - 1)*(m + 60)/2
Let n(u) = u**2 + 92*u + 1950. Let t be n(-59). Factor 1/2*j**2 + 9/2*j**4 + 0*j + 3*j**t + 0.
j**2*(3*j + 1)**2/2
Suppose 8*h - 5*h = -6, 5*x - 2 = h. Let m(v) be the second derivative of 0*v**3 - 2/15*v**4 + x*v**2 + 1/15*v**6 - 11*v + 0 + 4/25*v**5. Factor m(q).
2*q**2*(q + 2)*(5*q - 2)/5
Suppose -1/4*b**3 - 3/4*b + 0 + b**2 = 0. Calculate b.
0, 1, 3
Let p = 16186 - 80926/5. Factor 1/5*k**2 - p*k + 4/5.
(k - 2)**2/5
Let q(s) = -7*s**2 + 16*s + 8. Suppose 4*p + 24 = 3*p. Let a(d) = d**2 - d + 1. Let u(f) = p*a(f) - 3*q(f). Determine z, given that u(z) = 0.
-4
Let r = 20931 - 20931. Determine p, given that 14/5*p**3 + r + 16/5*p + 6/5*p**4 - 36/5*p**2 = 0.
-4, 0, 2/3, 1
Let i be (-2 + 3)/((-2 - -3)/2). Let l be (8/(-72))/(i/(-24) + 0). Determine t so that 2/3 + 1/2*t**2 - l*t = 0.
2/3, 2
Let g(n) be the second derivative of 5*n**8/336 + n**7/7 + n**6/2 + 5*n**5/6 + 5*n**4/8 + 3*n**2 + n. Let q(u) be the first derivative of g(u). Factor q(x).
5*x*(x + 1)**3*(x + 3)
Suppose 0 + 5/4*r - 7/8*r**2 + 1/8*r**3 = 0. What is r?
0, 2, 5
Let u(k) be the first derivative of -2*k**3/3 - 15*k**2 - 52*k - 164. Let u(n) = 0. Calculate n.
-13, -2
Let u(d) be the third derivative of -d**5/100 - 11*d**4/40 - 9*d**3/5 + 35*d**2. Determine t so that u(t) = 0.
-9, -2
Let z(i) be the third derivative of -i**7/420 - i**6/80 - i**5/120 + i**4/16 + i**3/6 + 3*i**2 + 5*i. Suppose z(b) = 0. Calculate b.
-2, -1, 1
Let j(h) = -8*h**2 + 48*h - 135. Let f(q) = q**2 + 4*q. Let w(g) = 3*f(g) + j(g). Factor w(n).
-5*(n - 9)*(n - 3)
Let q(v) be the third derivative of 1/12*v**4 + 23*v**2 + 0*v + 1/10*v**5 + 0*v**3 + 1/30*v**6 + 0. Let q(m) = 0. What is m?
-1, -1/2, 0
Let n(u) be the third derivative of 0 + 0*u - 1/15*u**4 + 1/450*u**5 - 3*u**2 + 4/5*u**3. Factor n(q).
2*(q - 6)**2/15
Let x(p) = -p**2 - 5*p + 10. Suppose -3*g = -3*l - 12, 2*l - g - 3*g = -4. Let n be x(l). Solve -2 - 16*v**2 + n + 7 - 44*v + 3 = 0.
-3, 1/4
Let x be (4 - (-93)/(-21))/(9/(-6)). Let i = 25/6 - 163/42. Factor -x*o - 4/7*o**2 - i*o**3 + 0.
-2*o*(o + 1)**2/7
Let p(h) = 4*h**3 - 36*h**2 - 44*h + 20. Let o(b) = 2*b**2 + b - 1. Let m(f) = -20*o(f) - p(f). Factor m(s).
-4*s*(s - 2)*(s + 3)
Let q(p) be the third derivative of 5*p**8/168 + p**7/35 - p**6/5 + 2*p**5/15 - 5*p**2 + 3. Suppose q(i) = 0. Calculate i.
-2, 0, 2/5, 1
Suppose 0*o + 0*o**3 + 2/3*o**4 - 8/3*o**2 + 0 = 0. Calculate o.
-2, 0, 2
Let n(z) be the first derivative of -2*z**2 + 8 + 0*z + 1/20*z**5 + 9/2*z**3 + 3/4*z**4. Let r(k) be the second derivative of n(k). Factor r(d).
3*(d + 3)**2
Suppose 2*k = 4*k, -5*n + 5*k + 15 = 0. Let -4*x - x**4 + n*x - x - x**3 + 3*x + x**2 = 0. Calculate x.
-1, 0, 1
Let l = 106 + -102. Let j(m) be the first derivative of 1/6*m**l + 1/15*m**5 + 0*m + 5 + 1/9*m**3 + 0*m**2. Factor j(u).
u**2*(u + 1)**2/3
Suppose -18 = u - 5*w, 7*u - 10 = 10*u - 4*w. Solve -1/3*c**u - 10/3 - 7/3*c = 0.
-5, -2
Let d = -83 - -86. Let r = -2 - -4. Find w such that -3*w**2 - 6*w**2 - 7*w**3 + 12*w**4 + 3*w**d + w**r = 0.
-2/3, 0, 1
What is c in 124/9 + 1502/3*c**2 + 18*c**4 + 1306/9*c + 574*c**3 = 0?
-31, -1/3, -2/9
Let v(i) be the first derivative of i**3 + 29*i**2/2 + 18*i - 127. What is h in v(h) = 0?
-9, -2/3
Let -248/5*r + 224/5 + 2/5*r**3 + 72/5*r**2 - 2/5*r**4 = 0. Calculate r.
-7, 2, 4
Let g(b) = -46*b**3 + b**2 - 1. Let w be g(-1). Suppose 5 - 25 = -4*y. Determine f, given that w + 8*f**4 - 4*f**y - 46 = 0.
0, 2
Factor -18/7*c + 12/7*c**3 + 18/7*c**4 - 12/7*c**2 + 6/7*c**5 - 6/7.
6*(c - 1)*(c + 1)**4/7
Let b(d) be the second derivative of 2*d - 1/6*d**4 - 4/3*d**3 - 3*d**2 + 11. Factor b(n).
-2*(n + 1)*(n + 3)
Let 1 - 7 - 5*q**4 + 10*q**2 + 1 = 0. Calculate q.
-1, 1
Let o(m) be the third derivative of -m**8/112 - 3*m**7/35 - 9*m**6/40 - m**5/5 + 86*m**2. Let o(t) = 0. Calculate t.
-4, -1, 0
Let a(f) be the first derivative of f**4/16 - 3*f**3/4 - 13. Factor a(n).
n**2*(n - 9)/4
Let q(y) be the third derivative of y**7/30 + 121*y**6/120 + 99*y**5/10 + 76*y**4/3 + 64*y**3/3 - 4*y**2 + 23. Find n such that q(n) = 0.
-8, -1, -2/7
Let q(j) be the second derivative of 15/4*j**4 + 5*j**2 - 5/4*j**5 + 0 + 11*j + 1/6*j**6 - 35/6*j**3. Factor q(g).
5*(g - 2)*(g - 1)**3
Let u be (-2)/(-2)*(-236 + 236). Factor 4/7*d - 2/7*d**2 + u.
-2*d*(d - 2)/7
Let x(j) = -11*j**2 + 7*j**4 + 12*j + 0*j**4 - 8 + 0*j**2 - 23*j - j**3. Let z(y) = 3*y**4 - 5*y**2 - 6*y - 4. Let c(u) = 2*x(u) - 5*z(u). Factor c(s).
-(s - 2)*(s + 1)**2*(s + 2)
Suppose i - 3*q = 6, 0 = -i - 5*q - 7 + 5. Factor 3/2*d**4 + 9/2*d**i - 9 + 51/2*d - 45/2*d**2.
3*(d - 1)**3*(d + 6)/2
Suppose -5*k = 3*x - 5, 3*x = 1679*k - 1675*k + 50. Factor -1/5*o**4 + 0 - 9*o**2 + x*o + 12/5*o**3.
-o*(o - 5)**2*(o - 2)/5
Let u = 767 - 764. Find k such that 4/5 - 4/5*k**2 + 2/5*k**5 - 8/5*k**u + 6/5*k + 0*k**4 = 0.
-1, 1, 2
Solve 0*z**3 + 0 - 4/7*z**2 + 1/7*z**4 + 0*z = 0 for z.
-2, 0, 2
Let u(w) be the first derivative of -w**4/24 + 10*w + 1. Let p(r) be the first derivative of u(r). Factor p(q).
-q**2/2
Suppose 56*r - 908*r**4 + 10*r**5 - 32 - 11*r**5 - 10*r**3 + 915*r**4 - 20*r**2 = 0. Calculate r.
-2, 1, 2, 4
Let j(n) be the first derivative of 1 - 52*n**3 - 2 + 152*n**3 + 27*n + 90*n**2. Determine x, given that j(x) = 0.
-3/10
Let d(a) be the third derivative of 2*a**7/315 + 61*a**6/360 + 239*a**5/180 + 7*a**4/9 - 6*a**2 + 26*a. Factor d(u).
u*(u + 7)*(u + 8)*(4*u + 1)/3
Let x(i) = 5*i**2 - 3*i - 2. Let d be (21/(-9)*3)/(-1). Let q(p) = -6*p**2 + 4*p + 2. Let t(v) = d*x(v) + 6*q(v). Let t(g) = 0. What is g?
1, 2
Let q be (-3)/4*(-17