t f = 5964/10081 - 2/593. Factor -f*s - 2/17*s**3 + 8/17*s**2 + 4/17.
-2*(s - 2)*(s - 1)**2/17
Let j(x) be the first derivative of 5*x**4/16 - 21*x**3/4 - 13*x**2/4 - 153. Solve j(b) = 0.
-2/5, 0, 13
Find p such that -12*p**2 - 200 - 90*p - 1/2*p**3 = 0.
-10, -4
Let z(y) be the second derivative of 1/42*y**7 - 1/12*y**4 + 3/20*y**5 + 0*y**3 - 21*y - 1/10*y**6 + 0 + 0*y**2. Factor z(g).
g**2*(g - 1)**3
Let w(f) = 3*f**2 - 4*f + 1. Let o = -8 - -8. Let t = 3 - o. Let n(g) = -4*g**2 + 5*g - 1. Let q(m) = t*w(m) + 2*n(m). Factor q(s).
(s - 1)**2
Let n(d) be the second derivative of d**10/15120 + d**9/3780 - d**8/1120 - 7*d**4/12 + 2*d. Let a(f) be the third derivative of n(f). Factor a(s).
2*s**3*(s - 1)*(s + 3)
Factor -3/2 + 32*r**5 + 16*r + 6*r**3 - 97/2*r**2 + 104*r**4.
(r + 1)*(r + 3)*(4*r - 1)**3/2
Let v = 56 - 52. Let -5*l**2 - 14*l - 11*l**4 + 15*l**3 + 6*l**v + 10 - l = 0. What is l?
-1, 1, 2
Let c be (-132)/110*(-5)/10. Factor c*z**4 + 33/5*z**2 + 3*z + 21/5*z**3 + 0.
3*z*(z + 1)**2*(z + 5)/5
Let k(h) be the second derivative of -h**6/60 - 3*h**5/40 + h**4/6 + h**3 - 234*h. Let k(y) = 0. What is y?
-3, -2, 0, 2
Let y be (2/(-3))/(4/(-12)). Factor y*m**5 - 2*m + 2*m - m**5.
m**5
Let a(u) be the first derivative of u**3 + 123*u**2/2 + 500. Find k such that a(k) = 0.
-41, 0
Let y(m) be the second derivative of -4/3*m**3 - 5*m + 5 + 1/6*m**4 + 3*m**2. Factor y(b).
2*(b - 3)*(b - 1)
Let c(t) be the first derivative of -3/20*t**5 + 0*t - 5 + 0*t**3 - 1/24*t**6 + 0*t**2 - 1/8*t**4. Factor c(s).
-s**3*(s + 1)*(s + 2)/4
Let i(j) be the first derivative of -j**3 + 1/360*j**6 - 1/120*j**5 + 0*j**4 + 0*j**2 + 4 + 0*j. Let p(w) be the third derivative of i(w). Factor p(d).
d*(d - 1)
Suppose -5*p + 4*f + 79 = 99, 3*p + 10 = 2*f. Factor 6/11*l**2 - 6/11*l**4 + 0*l**3 + 0*l + p.
-6*l**2*(l - 1)*(l + 1)/11
Let v(t) be the first derivative of t**6/24 + t**5/10 - 3*t**4/16 - 2*t**3/3 - t**2/2 - 2. Factor v(k).
k*(k - 2)*(k + 1)**2*(k + 2)/4
What is d in 190/7*d**2 - 2/7*d**5 + 58/7*d**4 + 186/7*d**3 + 64/7*d + 0 = 0?
-1, 0, 32
Let p(q) = q**3 - 11*q**2 + 3*q - 29. Let i be p(11). Let r(y) be the second derivative of -7*y + 1/21*y**i + 0 - 1/35*y**5 + 4/21*y**3 + 0*y**2. Factor r(c).
-4*c*(c - 2)*(c + 1)/7
Suppose 29*k - 28*k - 2 = 0. Determine w, given that -3*w + 4*w**3 - 9*w**2 - 4*w**3 + 13*w**k - w**3 = 0.
0, 1, 3
Let i(v) = -3*v**3 + 3*v + 4. Let b(o) = -2 + 7*o**3 - 7 - 6*o + 2 - 2. Let y(p) = -2*b(p) - 5*i(p). Factor y(l).
(l - 2)*(l + 1)**2
Let o be (10 + (-7 - 3))*1. Factor 2/9*r**3 + o*r + 8/9 - 2/3*r**2.
2*(r - 2)**2*(r + 1)/9
Let x(r) = -124*r - 124. Let g be x(-1). Factor -3/2*z - 6*z**2 - 3/2*z**5 - 9*z**3 + g - 6*z**4.
-3*z*(z + 1)**4/2
Suppose -2*j - 4*o = 15 + 109, 5*o = -j - 77. Let d = 52 + j. Factor 0*k**2 + 0 - 2/15*k**5 - 2/15*k**3 + 4/15*k**4 + d*k.
-2*k**3*(k - 1)**2/15
Determine z, given that 2/7*z**2 + 8/7*z - 10/7 = 0.
-5, 1
Let x(a) be the third derivative of -1/8*a**4 + 0*a**3 + 23*a**2 + 0 + 0*a - 1/60*a**5. Factor x(d).
-d*(d + 3)
Suppose f = -f + 82. Factor 6*b**3 - f*b**2 - 32 - 79*b**2 + 112*b - 5*b**3 + 35*b**3.
4*(b - 2)*(3*b - 2)**2
Let 233 + 344 + 5*o**2 + 73 + 336 - 120*o - 266 = 0. Calculate o.
12
Let h = 40385/19 - 2125. Let l = 68/57 - h. Factor 0*q**2 - 2*q + l*q**3 + 4/3.
2*(q - 1)**2*(q + 2)/3
Let a(z) = -3*z**4 - 21*z**3 - 42*z**2 + 237*z - 153. Let t(h) = -h**4 - 11*h**3 - 21*h**2 + 119*h - 78. Let b(y) = -4*a(y) + 9*t(y). Let b(k) = 0. Calculate k.
-3, 1, 2, 5
Let d(v) be the second derivative of -v**10/10080 - v**9/5040 + v**8/1120 - 3*v**4/4 - 7*v. Let f(c) be the third derivative of d(c). Factor f(r).
-3*r**3*(r - 1)*(r + 2)
Let b be (-24)/30 - (-659)/460. Let z = b + -3/92. Factor 1/5*j**3 + j**2 - 9/5 + z*j.
(j - 1)*(j + 3)**2/5
Suppose i - 39 + 14 = 0. Let v(r) = -20*r**5 - 45*r**4 + 155*r**3 - 100*r**2 - 120*r + 160. Let t(p) = p**5 - p**3. Let j(m) = i*t(m) + v(m). Factor j(w).
5*(w - 4)*(w - 2)**3*(w + 1)
Let l(j) = -8*j**3 + 17*j**2 - 2*j - 17. Let k(t) = -4*t**3 + 9*t**2 - 2*t - 9. Let q(o) = -5*k(o) + 3*l(o). Solve q(g) = 0.
-1, 1, 3/2
Let d(a) be the second derivative of -a**8/4032 + a**7/756 - a**6/432 - 11*a**4/6 - 16*a. Let g(w) be the third derivative of d(w). Factor g(s).
-5*s*(s - 1)**2/3
Let w(c) be the first derivative of -c**6/540 - c**5/60 - c**4/18 - 10*c**3/3 + 1. Let z(i) be the third derivative of w(i). Factor z(f).
-2*(f + 1)*(f + 2)/3
Suppose 0 = -0*b + 2*b. Let d(x) be the second derivative of 0*x**2 + 1/2*x**4 - 1/5*x**6 + 1/3*x**3 - 1/10*x**5 + b - 2*x. Suppose d(j) = 0. Calculate j.
-1, -1/3, 0, 1
Factor 2*p**3 + 1/5*p**4 - 5 - 2*p + 24/5*p**2.
(p - 1)*(p + 1)*(p + 5)**2/5
Let c be (18/33)/(-3) + (2 - 790/495). Suppose -2/9*g + 0 - c*g**2 = 0. What is g?
-1, 0
Let z(a) = a - 7. Let s be z(10). Suppose -2*c - c + 9 = s*y, 2 = -2*y. What is d in -d**5 + 5*d**4 - 7*d**c + 3*d**4 + 2*d**2 + 1 + 2*d**3 - 4*d**2 - d = 0?
-1, 1
Suppose -3*v - 5*j - 6 = 0, 2*j + 2 = 4*v - 16. Let s(b) be the first derivative of 0*b - 1/10*b**2 + v - 1/5*b**3. Find x, given that s(x) = 0.
-1/3, 0
Let s(k) = 2*k - 13. Let x be s(10). Suppose 4*u - x = 21. Let 5*d - 5*d**2 + 2*d**2 - 2*d**3 + 7*d**3 - u*d**2 = 0. What is d?
0, 1
Suppose 58 = 9*m - 212. Determine s so that 0*s**2 - 4 + 2*s**2 - 28*s**2 + m*s = 0.
2/13, 1
Let c(v) be the second derivative of v**4/12 + 94*v**3/3 + 4418*v**2 + 183*v. Find s such that c(s) = 0.
-94
Let j(i) = 11*i**2 - 1. Let s be ((-2)/6)/(2/(-108)). Let w(u) = -39*u**2 + 3. Let m(h) = s*j(h) + 5*w(h). Solve m(n) = 0.
-1, 1
Let q(u) be the third derivative of -3*u**3 - 1/105*u**7 - 5*u**2 - 2*u**4 - 2/15*u**6 + 0 + 0*u - 11/15*u**5. Let q(f) = 0. What is f?
-3, -1
Let c = -856/3 - -286. Let r(l) be the first derivative of 3 + 0*l**2 + 2*l - c*l**3. Solve r(m) = 0 for m.
-1, 1
Let r(u) be the second derivative of u**5/14 - 11*u**4/21 + 23*u**3/21 - 6*u**2/7 - 38*u - 4. Factor r(a).
2*(a - 3)*(a - 1)*(5*a - 2)/7
Let a(z) be the first derivative of -z**3/3 + 6*z**2 - 74. Factor a(q).
-q*(q - 12)
Let b(y) = -y**5 + y**4 - y**3 - y - 1. Let v(p) = 14*p**5 + 37*p**4 + 29*p**3 + 5*p + 5. Let w(g) = -5*b(g) - v(g). Factor w(l).
-3*l**3*(l + 4)*(3*l + 2)
Let d = -2 - -7. Factor -4*s**2 - 10*s + 3*s - d*s.
-4*s*(s + 3)
Factor 77*n**2 + 4*n**3 + 4 - 17*n**2 - 4*n - 20 - 30 - 14.
4*(n - 1)*(n + 1)*(n + 15)
Suppose 7 + 14 + 17 = 19*s. Let 0 - 3/2*u + 9/4*u**s - 3/4*u**3 = 0. Calculate u.
0, 1, 2
Let -1/9*c**4 + 13/9*c**2 + 7/9*c + 5/9*c**3 + 0 = 0. Calculate c.
-1, 0, 7
Let i(q) be the second derivative of -q**7/630 - q**6/120 - q**5/60 - q**4/72 + 5*q**2/2 - 9*q. Let l(f) be the first derivative of i(f). Factor l(p).
-p*(p + 1)**3/3
Factor 27/2 - 225/4*n**3 + 99/4*n - 30*n**2.
-3*(3*n - 2)*(5*n + 3)**2/4
Let s(p) be the first derivative of -p**4/4 + p**3 + 3*p**2 - 8*p - 662. Factor s(n).
-(n - 4)*(n - 1)*(n + 2)
Suppose 0 = -13*y + 6854 - 6841. Suppose y - 4/3*j**2 + 1/3*j**4 - 2/3*j + 2/3*j**3 = 0. Calculate j.
-3, -1, 1
Suppose -4*c - 2*r + 110 = -52, 0 = 3*c + 3*r - 120. Find m such that -15*m**5 - 121*m + c*m + 68*m**3 + 46*m**2 - m**2 - 13*m**3 - 25*m**4 + 20 = 0.
-2, 1/3, 1
Let j(v) be the third derivative of 0 - 1/20*v**5 + 0*v + 1/12*v**4 + 0*v**3 + 1/120*v**6 + 4*v**2. Factor j(k).
k*(k - 2)*(k - 1)
Let f(d) = d**2 + 30*d + 178. Let g be f(-8). Factor 1/2*s**4 - 2*s + 0*s**g + 0 + 3/2*s**3.
s*(s - 1)*(s + 2)**2/2
Let f(d) = d**2 + d + 4. Let m(t) = 4*t - 3*t**2 + 6*t**2 - 1242 - 1226 + 2480. Let x = -1 + 4. Let a(b) = x*m(b) - 8*f(b). Factor a(q).
(q + 2)**2
Let y(n) be the first derivative of n**6/70 + 9*n**5/140 + n**4/28 + 11*n**2 - 15. Let c(k) be the second derivative of y(k). What is a in c(a) = 0?
-2, -1/4, 0
Let c(u) be the second derivative of u**4/3 + 16*u**3/3 - 40*u**2 - 213*u. Factor c(r).
4*(r - 2)*(r + 10)
Suppose 20 = 5*t, -4*t = 5*a + t + 400. Let c be a/(-24) + 1/2. Factor -4 + 9*s**3 - 13*s**3 + 4*s**2 + 0 + c*s.
-4*(s - 1)**2*(s + 1)
Let d(k) be the first derivative of k**6/2 - 48*k**5/5 - 27*k**4 - 2*k**3 + 105*k**2/2 + 54*k + 33. Solve d(b) = 0.
-1, 1, 18
Determine n, given that -16*n**3 + 16*n - 28*n**4 + 16/7 + 180/7*n**2 = 0.
-1, -2/7, 1
Let o be (-128)/448*21*(-4 - -2). Factor -3 + 9/2*g**3 + 21/2*g - o*g**2.
3*(g - 1)**2*(3*g - 2)/2
Suppose -234/