 52)/17
Suppose 0*t + 3*t - 12 = 0. Suppose -3*r + 4*o = -10, -2*r - 4*o = -t*r + 8. Factor 4*k**3 - 8 + 4*k**2 + 4*k**2 - r*k**2 - 6*k**3.
-2*(k - 2)**2*(k + 1)
Let g = -90 - -94. Suppose 0 = -g*k + 8*k - 12. Factor k*t**2 + 9/2*t + 3/2.
3*(t + 1)*(2*t + 1)/2
Let y(v) be the first derivative of -v**4 - 13*v**3 - 27*v**2 + 16*v + 586. Factor y(b).
-(b + 2)*(b + 8)*(4*b - 1)
Let w be (9/(-54)*0)/1. Let r(q) be the third derivative of w*q + 9*q**2 - 1/90*q**5 - 1/540*q**6 + 0 + 0*q**4 + 4/27*q**3. Find p, given that r(p) = 0.
-2, 1
Let z(n) be the third derivative of -11/60*n**6 + 0*n**4 + 0*n - 4*n**2 + 16/105*n**7 - 1/24*n**8 + 1/15*n**5 + 0*n**3 + 0. Factor z(s).
-2*s**2*(s - 1)**2*(7*s - 2)
Let c(k) = -k**3 + 10*k**2 + 7*k - 22. Let i be c(9). Let b = i - 122. Factor 2*y**2 + b - 1/2*y.
y*(4*y - 1)/2
Suppose 0 = -4*u - 2*i + 42, -u + 5*i + 5 = -0. Suppose -11 + 4*o - 2*o**2 + 7 + u = 0. What is o?
-1, 3
Let z be (-262)/30*(3990/18)/(-19) - -3. Find a, given that 32/9 + 320/9*a + 18*a**4 + 80*a**3 + z*a**2 = 0.
-2, -2/9
Let c(q) be the first derivative of -q**6/6 + 4*q**5/5 - q**4 - 2*q**3/3 + 5*q**2/2 - 2*q - 151. Let c(y) = 0. Calculate y.
-1, 1, 2
Let w(s) be the second derivative of s**7/189 - 4*s**6/135 + 2*s**5/45 + 214*s. Solve w(j) = 0 for j.
0, 2
Let m be 2*15/(-6)*(-8)/20. Determine d so that 2*d + 435*d**3 - 4*d - 441*d**3 + 6*d**2 + m*d**4 = 0.
0, 1
Let r(s) be the third derivative of s**8/2016 + 53*s**7/630 + 231*s**6/40 + 972*s**5/5 + 41553*s**4/16 - 59049*s**3/2 + s**2 - 89. Factor r(g).
(g - 2)*(g + 27)**4/6
Let q(p) be the second derivative of -4*p**2 + 0 - 2/3*p**3 + 9*p + 1/3*p**4. Factor q(h).
4*(h - 2)*(h + 1)
Let n(d) be the second derivative of -d**7/147 + 2*d**6/5 - 276*d**5/35 + 1192*d**4/21 - 1392*d**3/7 + 2592*d**2/7 + d + 126. Factor n(x).
-2*(x - 18)**2*(x - 2)**3/7
Determine t so that 2/9*t**2 + 124/9*t + 1922/9 = 0.
-31
Let l(t) = -t + 1. Let f(g) = g + 2*g**2 - 2*g - 4*g**2 + 7. Let s(o) = -2*f(o) + 14*l(o). Factor s(n).
4*n*(n - 3)
Let y(h) = 27*h**4 + 35*h**3 - 42*h**2 - 22*h - 2. Let n(u) = 28*u**4 + 35*u**3 - 43*u**2 - 23*u - 3. Let b(m) = -2*n(m) + 3*y(m). Solve b(a) = 0 for a.
-2, -2/5, 0, 1
Let j(s) be the third derivative of 1/8*s**3 + 3/80*s**5 - 1/70*s**7 - 7*s**2 - 1/32*s**6 + 0*s + 5/32*s**4 + 0. Suppose j(w) = 0. Calculate w.
-1, -1/4, 1
Let u(v) be the third derivative of -8*v**7/105 + 73*v**6/30 + 226*v**5/15 + 107*v**4/6 - 28*v**3 + 86*v**2 + 4*v. Solve u(k) = 0 for k.
-2, -1, 1/4, 21
Let i be 147/(-14)*(-4)/6. Let l be (i + -7)*2/2. Factor -8/3*c**2 - 2/3*c - 4/3*c**4 + l - 10/3*c**3.
-2*c*(c + 1)**2*(2*c + 1)/3
Let i = -201 - -235. Let n be ((-3)/10)/(i/(-136)). Factor 8/5*z**2 - 1/5*z**5 + n*z**3 + 0 + 0*z**4 + 3/5*z.
-z*(z - 3)*(z + 1)**3/5
Factor -2*m**2 - 12*m**3 + 19*m**3 - 12*m**3 + 22*m**2.
-5*m**2*(m - 4)
Let i(d) be the first derivative of -3*d**4/16 - 5*d**3/8 - 3*d**2/4 + 17*d - 16. Let k(r) be the first derivative of i(r). Suppose k(a) = 0. Calculate a.
-1, -2/3
Let t(g) be the third derivative of -g**8/672 + g**7/70 - g**6/20 + g**5/12 - g**4/16 + 93*g**2. Factor t(n).
-n*(n - 3)*(n - 1)**3/2
Suppose 0 - 1/3*k + 1/3*k**2 = 0. What is k?
0, 1
Let w**2 + 3605 + 2*w - 89*w - 3605 = 0. What is w?
0, 87
Let p = -52/335 - -826/1005. Factor -16/3 + 4*o - p*o**2.
-2*(o - 4)*(o - 2)/3
Let x(c) = 18*c. Let g be x(0). Let j(i) be the second derivative of -3/20*i**5 + 0*i**2 + g*i**3 + 1/10*i**6 - 1/4*i**4 + 1/14*i**7 + 0 - 4*i. Factor j(z).
3*z**2*(z - 1)*(z + 1)**2
Let f(t) be the second derivative of 3*t**5/100 - t**4/10 - t**3/10 + 3*t**2/5 - 55*t. Factor f(l).
3*(l - 2)*(l - 1)*(l + 1)/5
Let h = 2821/6 - 470. Let q(j) be the first derivative of -3/2*j + h*j**3 + 4 + 1/2*j**2. Factor q(g).
(g - 1)*(g + 3)/2
Let l(g) be the second derivative of 0 - 40/3*g**3 + 0*g**2 + 4/3*g**6 - 10/3*g**4 + 4*g + 15/4*g**5 + 5/42*g**7. Solve l(i) = 0.
-4, -1, 0, 1
Let g(z) = -3*z + 42. Let j be g(14). Suppose -21*h + 7*h = j. Find t such that h*t**2 - 4/5*t**3 + 12/5*t + 8/5 = 0.
-1, 2
Let v = -11/104 - -1697/312. Factor 2/3*x**2 + 32/3 - v*x.
2*(x - 4)**2/3
Let t(z) = 7*z**2 - 25*z + 18. Let c(o) = -o**2 + 1. Let y(v) = -2*c(v) - t(v). Let y(k) = 0. What is k?
1, 4
Let y(l) be the third derivative of l**8/90720 - l**7/5670 + l**6/1080 + l**5/5 + 10*l**2. Let o(g) be the third derivative of y(g). Factor o(m).
2*(m - 3)*(m - 1)/9
Let d(j) be the third derivative of j**8/90720 - j**7/5670 + j**6/1080 + 7*j**5/60 - 13*j**2. Let g(l) be the third derivative of d(l). Factor g(h).
2*(h - 3)*(h - 1)/9
Let t(o) = -6*o**4 + 6*o**3 + 3*o**2 - 3*o + 6. Let b(h) = -7*h**4 + 5*h**3 + 4*h**2 - 3*h + 5. Let u(c) = -6*b(c) + 5*t(c). Factor u(p).
3*p*(p + 1)*(2*p - 1)**2
Let w be 174/11 + (-2)/(-11). Let -4*n - 2*n**2 + 0*n + 38*n**2 + w*n**4 - 4*n - 48*n**3 = 0. Calculate n.
0, 1/2, 2
Let u(o) = -o**2 + 7*o + 8. Let z be u(6). Suppose z*d = 10*d. Suppose -2/7*l**3 + d - 4/7*l + 6/7*l**2 = 0. Calculate l.
0, 1, 2
Let j(b) = 3*b + 10. Let m(h) = -h - 3. Let s(r) = 2*j(r) + 7*m(r). Let u be (2 - 0)*3/6. Let d(y) = 3*y**2 - 7*y + 8. Let c(t) = u*d(t) + 2*s(t). Factor c(f).
3*(f - 2)*(f - 1)
Suppose 2*f - 4 - 14 = -g, 3*f + 5*g = 20. Factor -v**2 + f*v + 4*v + v + 36*v**2 + 25*v**3 + 5*v**4.
5*v*(v + 1)**2*(v + 3)
Let v(q) = -9*q**3 + 3*q**2 - 12*q + 6. Let p(n) = -4*n**3 + n**2 - n. Let b(g) = 3*p(g) - v(g). Solve b(h) = 0 for h.
-2, 1
Let c(r) be the first derivative of -7*r**4 - 19 - 16*r + 56*r**2 - 64*r**3 + 49/5*r**5. Determine a so that c(a) = 0.
-2, 2/7, 2
Factor -25*t**2 + 0*t**5 + 1634*t**4 + 4*t**5 + t**2 - 1610*t**4 - 4*t**3.
4*t**2*(t - 1)*(t + 1)*(t + 6)
Let f = -1469/22 - -751/11. Factor 9/2 + 15/2*k - 3/2*k**3 + f*k**2.
-3*(k - 3)*(k + 1)**2/2
Let v = 4106/13429 - -2/1033. Let n(i) be the second derivative of -16/39*i**3 + 0 + 7/78*i**4 - 5*i + v*i**2. Factor n(x).
2*(x - 2)*(7*x - 2)/13
Let u(a) be the first derivative of -14*a**3/39 - 12*a**2/13 + 8*a/13 + 206. Factor u(n).
-2*(n + 2)*(7*n - 2)/13
Let j(s) be the third derivative of -5*s**8/336 + 5*s**7/42 - 7*s**6/24 + s**5/4 + 200*s**2. Factor j(w).
-5*w**2*(w - 3)*(w - 1)**2
Let f(v) be the first derivative of -5*v**4/12 - 10*v**3/3 - 15*v**2/2 - 22*v + 51. Let m(u) be the first derivative of f(u). Factor m(p).
-5*(p + 1)*(p + 3)
Let h(a) = -a**3 + 10*a**2 + 38*a + 17. Let l be h(13). Let i be 33/(-11)*(-14)/l. Factor -13/2*b**3 + i*b**4 + 0 + b**2 + 0*b.
b**2*(3*b - 1)*(7*b - 2)/2
Let z(k) be the first derivative of -k**6/21 + 24*k**5/35 - 26*k**4/7 + 64*k**3/7 - 64*k**2/7 + 201. Determine b, given that z(b) = 0.
0, 2, 4
Let j(l) be the second derivative of -l**5/100 - l**4/12 - l**3/5 + 8*l. Factor j(u).
-u*(u + 2)*(u + 3)/5
Let b(q) = q**4 + q**2 - q. Let d(g) = 9*g**4 + 20*g**3 + 21*g**2 - 5*g. Suppose -a + 10 = -3*a. Let l(s) = a*b(s) + d(s). Find o such that l(o) = 0.
-4, -1, 0
Let i(r) be the second derivative of -r**4/20 - 3*r**3/10 + 6*r**2/5 - 84*r. Factor i(j).
-3*(j - 1)*(j + 4)/5
Let m(p) be the third derivative of -1/15*p**5 + 0 - 1/6*p**4 + 0*p**3 + 1/120*p**6 + 0*p + p**2 + 1/210*p**7. Factor m(z).
z*(z - 2)*(z + 1)*(z + 2)
Let c(g) be the third derivative of -5*g**7/14 + 29*g**6/24 - 13*g**5/12 - 5*g**4/24 - g**2 - 19. Factor c(b).
-5*b*(b - 1)**2*(15*b + 1)
Let h(a) be the second derivative of 0*a**3 + 0*a**2 + 1/168*a**7 + 16*a - 1/30*a**6 + 0 + 1/16*a**5 - 1/24*a**4. Solve h(u) = 0.
0, 1, 2
Let v(n) be the first derivative of n**3/12 - 11*n**2/8 - 3*n - 79. Factor v(u).
(u - 12)*(u + 1)/4
Factor 37*z**4 - 12*z**2 - 10*z + 10*z + 19*z**3 + z**5 - 45*z**4.
z**2*(z - 4)*(z - 3)*(z - 1)
Factor -9/7*s**2 - 3/7*s**3 + 48/7*s - 36/7.
-3*(s - 2)*(s - 1)*(s + 6)/7
Let w be 0*((-2)/20 - 2/5). Let n(v) be the third derivative of 1/30*v**5 - 1/3*v**3 + w + 0*v + 5*v**2 + 1/60*v**6 - 1/12*v**4. Factor n(z).
2*(z - 1)*(z + 1)**2
Let b(v) be the second derivative of -1/24*v**6 - 5/24*v**3 + 5*v + 0 + 5/48*v**4 + 1/16*v**5 + 0*v**2. Let b(a) = 0. Calculate a.
-1, 0, 1
Factor -10*c + 15*c**3 + 13*c**3 - 15*c**2 - 30*c**3 + 24 + 3*c**2.
-2*(c - 1)*(c + 3)*(c + 4)
Let u(r) be the third derivative of -r**8/504 - r**7/105 + r**6/180 + 7*r**5/90 - 4*r**3/9 - 90*r**2. Let u(h) = 0. Calculate h.
-2, -1, 1
Suppose 0 = -5*z - o + 44, 3*z - 2*o - 32 = -2*z.