ivative of x**8/7560 - x**6/1620 + 3*x**3 - 5. Let f(r) be the third derivative of s(r). Determine z, given that f(z) = 0.
-1, 0, 1
Let d(n) be the second derivative of -n**7/280 + n**6/120 + n**5/20 + n**3/2 - 3*n. Let r(t) be the second derivative of d(t). Solve r(y) = 0.
-1, 0, 2
Let q(b) = b**2 + b + 2. Suppose -3*p + p = 0. Let h be q(p). Factor 1/2*d**h + 0*d + 1/2*d**3 + 0.
d**2*(d + 1)/2
Let w(b) = -7*b**2 + 23*b - 42. Let m(j) = j**2 + j. Let t(s) = -4*m(s) - w(s). Find a, given that t(a) = 0.
2, 7
Suppose 0*n = -x - 5*n, -2*x = -n. Let i(s) = x*s + 4*s - s**2 - 5*s. Let b(r) = -3*r**2. Let v(o) = b(o) - 2*i(o). What is c in v(c) = 0?
0, 2
Let d = -739 - -2218/3. Factor -d*j**3 + j**2 + 0 - 2/3*j.
-j*(j - 2)*(j - 1)/3
Factor -r**5 - r**2 - 5*r**3 + 0*r**4 + 6*r**3 + r**4.
-r**2*(r - 1)**2*(r + 1)
Factor -2/7*o**3 - 18/7*o**2 - 54/7 - 54/7*o.
-2*(o + 3)**3/7
Suppose 0 = -3*t - 0*t + 18. Find b such that -b + 3*b**4 - 5*b**3 + t*b - 2 - b**2 + 0*b = 0.
-1, 2/3, 1
Factor 12*a**2 + 20*a**3 - 5*a**4 - 18*a**2 - 14*a**2.
-5*a**2*(a - 2)**2
Let u be 40/78 + ((-4)/(-26))/1. Determine r so that 0 - u*r**3 + 0*r**2 + 2/3*r**4 + 0*r = 0.
0, 1
Let k(i) be the first derivative of 2*i**5/5 + i**4/2 - 10*i**3/3 + 3*i**2 + 9. Factor k(c).
2*c*(c - 1)**2*(c + 3)
Let z = 1 + -1/2. Let v(q) = q**2 + 11*q + 2. Let f be v(0). Factor -1/4*m**3 + 0 - 1/4*m + z*m**f.
-m*(m - 1)**2/4
Let v(q) be the first derivative of -q**4/21 - 8*q**3/21 - 8*q**2/7 + 4*q + 5. Let m(j) be the first derivative of v(j). Factor m(c).
-4*(c + 2)**2/7
Let z(d) = -d**3 + 10*d**2 + 2*d - 15. Let u be z(10). Let y(f) be the first derivative of 2 + 4/9*f**3 - 2/15*f**u + 0*f**2 - 2/3*f + 0*f**4. Factor y(h).
-2*(h - 1)**2*(h + 1)**2/3
Factor 26/19*x**2 + 24/19*x + 2/19*x**4 + 12/19*x**3 + 8/19.
2*(x + 1)**2*(x + 2)**2/19
Factor 3*u**2 + u**4 + 2*u**2 - 6*u**4.
-5*u**2*(u - 1)*(u + 1)
Factor p + 44*p**2 - 47*p**2 + 11*p.
-3*p*(p - 4)
Suppose q - 13*q = -2*q. Factor -2/3*d + q + 2/3*d**2.
2*d*(d - 1)/3
Let q be 0*6/(-54)*3. Factor -2/11*y**2 - 4/11*y + q + 2/11*y**3.
2*y*(y - 2)*(y + 1)/11
Suppose 2*q + 6 = 5*q. Factor q*y**4 + 0*y**4 + 0*y**3 - 8*y**3 + 3*y**2 - 4*y + 7*y**2.
2*y*(y - 2)*(y - 1)**2
Let y(l) be the first derivative of -l**6/15 + l**4/10 + 14. Factor y(g).
-2*g**3*(g - 1)*(g + 1)/5
What is r in 14/3*r**4 - 2/3*r**5 + 0 - 12*r**3 - 16/3*r + 40/3*r**2 = 0?
0, 1, 2
Let z be 68/10*40/16. Let i = z - 14. What is q in -2*q**5 - 20/9*q**i + 2/3*q + 2/9 - 4/3*q**2 + 14/3*q**4 = 0?
-1/3, 1
Factor 2/9*n**3 + 10/9*n**2 - 2 + 2/3*n.
2*(n - 1)*(n + 3)**2/9
Suppose -21*g**3 - 8*g**2 + 23*g**5 - 70*g**4 + 2*g**5 + 65*g**3 = 0. What is g?
0, 2/5, 2
Let y(h) be the first derivative of -h**9/3528 - h**8/1470 - h**7/2940 + 2*h**3 + 2. Let n(a) be the third derivative of y(a). Find j, given that n(j) = 0.
-1, -1/3, 0
Let z = 4 - -2. Let y(r) = -z*r + 0*r**2 + 4*r + 2*r**2. Let x(w) = 4*w**2 - 4*w. Let q(m) = -6*x(m) + 11*y(m). Let q(n) = 0. Calculate n.
0, 1
Let y(d) be the second derivative of d**6/6 - d**5/4 - 5*d**4/12 + 5*d**3/6 + 4*d. Suppose y(h) = 0. What is h?
-1, 0, 1
Let o = 0 + 1. Let h be 6 + o/(1/(-2)). Find g such that 0*g**2 + 2*g**2 + 2*g - 2*g**3 - 2*g**h + 0*g**2 = 0.
-1, 0, 1
Let l = -296/9 + 33. Let y(r) be the third derivative of -r**2 + 1/90*r**5 - l*r**3 - 1/24*r**4 + 0*r**7 + 0 + 0*r - 1/1008*r**8 + 1/90*r**6. Factor y(v).
-(v - 2)*(v - 1)*(v + 1)**3/3
Factor -3*q**4 + 6*q - 3 - 4*q - 18*q**2 + 8*q**3 + 4*q**3 + 10*q.
-3*(q - 1)**4
Find k such that -16/3*k + 16/3 + 1/3*k**5 + 16/3*k**3 - 7/3*k**4 - 8/3*k**2 = 0.
-1, 2
Suppose 2*v + 0 = 4. Let f(l) be the first derivative of -11/10*l**4 - 7/15*l**6 + 0*l**v - 1 - 32/25*l**5 + 0*l - 4/15*l**3. What is y in f(y) = 0?
-1, -2/7, 0
What is t in 5*t**4 + t**5 - 4*t - 2*t**4 + 5*t**4 + 3*t**5 - 8*t**2 = 0?
-1, 0, 1
Suppose 32/11*z**3 + 0*z + 14/11*z**4 + 0 + 8/11*z**2 = 0. Calculate z.
-2, -2/7, 0
Let f be (-3)/(-8) - (-169)/104. Let o(t) be the second derivative of 0*t**4 + t**3 + 2*t**2 - 1/10*t**5 - f*t + 0. Solve o(k) = 0.
-1, 2
Let i(v) be the second derivative of -v**6/15 + 9*v**5/40 - v**4/4 + v**3/12 + 40*v. Factor i(u).
-u*(u - 1)**2*(4*u - 1)/2
Suppose 2*j - 5*n = -12, -5*n = -3*j + 4 - 12. Suppose j + 11 = 5*m. Factor -2*y**2 + 3*y - m*y.
-2*y**2
Suppose 5*j + v = j + 8, -5*j = 4*v - 10. Let h = j + 0. Factor -3/2*o**h - 5/2*o - 1.
-(o + 1)*(3*o + 2)/2
Suppose -k = 105 - 108. Let q(b) be the second derivative of 0 + b + 0*b**k - 1/5*b**5 + 0*b**2 + 1/15*b**6 + 0*b**4. Find c, given that q(c) = 0.
0, 2
Suppose -3*y + 25 = -2*y. Let k be (-32)/(-10) + (-5)/y. Determine w, given that -3*w**2 - w - 1 + 3 - 3*w - k = 0.
-1, -1/3
Let w(h) be the second derivative of h**5/4 + 5*h**4/6 - 35*h**3/6 + 10*h**2 + 3*h - 1. Factor w(i).
5*(i - 1)**2*(i + 4)
Let t be (6/(-5))/(8/(-20)). Factor 5*k**4 - 16*k**5 - 57*k**4 - 28*k**2 - 4*k - 32*k**3 - 28*k**t.
-4*k*(k + 1)**3*(4*k + 1)
Suppose -2*r + 8 = 0, -29 + 3 = -2*j - 4*r. Factor y**5 - 2*y**4 - 3*y**5 + y**5 + 0*y**j - y**3.
-y**3*(y + 1)**2
Suppose 0 = 5*h - 11 - 9. Let 56*s**2 + 7*s + 54*s**h - 39*s**3 + 141*s**3 + s = 0. What is s?
-1, -2/3, -2/9, 0
Let f(d) be the third derivative of d**7/1470 + d**6/420 - d**5/140 - d**4/42 + 2*d**3/21 + 2*d**2 - 36. Determine t so that f(t) = 0.
-2, 1
Let t(g) = 4*g**2 - 1. Let r be t(1). Let 132*y - 20 - 284*y**r - 4 + 80*y**3 - 147*y**4 - 54*y**2 - 153*y**3 = 0. What is y?
-2, -1, 2/7
Let r(m) be the third derivative of m**8/616 + 2*m**7/1155 - m**6/660 - 20*m**2. Factor r(u).
2*u**3*(u + 1)*(3*u - 1)/11
Suppose 0 = 3*p - 4*p. Suppose -2*f - a + 3 = -2*a, 3*f - 15 = 5*a. Solve f*z - 1/3*z**2 + p = 0.
0
Let s(a) = -a**2 + 25*a - 100. Let u be s(20). Factor -3/2*l**5 + 3/2*l**4 + 0*l**2 + u*l + 0 + 0*l**3.
-3*l**4*(l - 1)/2
Let y(h) = h**2 - 19*h - 17. Let f be y(20). Let v(t) be the first derivative of 1/12*t**f + 1/4*t - 1/4*t**2 - 3. Factor v(d).
(d - 1)**2/4
Let v = -1 + 3. Let i = 1 + v. Suppose 7*j**2 - 7*j**2 - 2*j**i + 0*j**2 + 2*j**5 = 0. Calculate j.
-1, 0, 1
Let f(b) be the second derivative of -1/120*b**5 - 1/36*b**4 + 0*b**2 + 0*b**3 + 0 + 1/180*b**6 - b. Factor f(m).
m**2*(m - 2)*(m + 1)/6
Let w(r) be the third derivative of -r**9/30240 + r**8/2520 - r**7/630 - r**5/10 - 9*r**2. Let m(t) be the third derivative of w(t). Solve m(f) = 0.
0, 2
Suppose 4 = -5*x + 9. Let w be (1/(-3))/(x/(-12)). Let -4*o**2 + o - o**3 + w*o**2 = 0. What is o?
-1, 0, 1
Let y be (-2)/(-5) + (-15)/100. Factor -y*t**4 + 0*t**2 - 1/2*t + 1/2*t**3 + 1/4.
-(t - 1)**3*(t + 1)/4
Let t = 31633/48 - 659. Let c(v) be the second derivative of 0 + 4*v + 0*v**2 - 1/24*v**3 + t*v**4. Factor c(n).
n*(n - 1)/4
Let n(s) be the first derivative of s**7/1260 - s**5/180 + 2*s**3/3 + 1. Let w(x) be the third derivative of n(x). Find l such that w(l) = 0.
-1, 0, 1
Let f = 101/24 - 7/8. Let a = 13/12 + 1/4. Factor f*d**2 - a + 2*d.
2*(d + 1)*(5*d - 2)/3
Suppose 0 = -3*o - 2*h + 14, 2*o - 4 - 7 = -3*h. Let v = 13 + -9. Let -3*c + 1 + v*c + 3*c**3 - o*c - 5*c**2 + 4*c**4 = 0. Calculate c.
-1, 1/4, 1
Let i be -1 + 1 - 3/(-1). Suppose -p + 13 = -4*v, i*p + 5*v - 15 = -2*p. Factor 5*c**2 + 4*c - 6*c**2 - 7*c**3 + 9*c**2 - p*c**4.
-c*(c - 1)*(c + 2)*(5*c + 2)
Let p = 4 - 1. Factor 1/5*u**p - 1/5*u**2 + 0 + 0*u.
u**2*(u - 1)/5
Factor 5 - 2*n**4 + 2*n - 4*n - 4 + 2*n**3 + n**4.
-(n - 1)**3*(n + 1)
Let p(g) be the second derivative of 3*g + 0 - 5/24*g**4 - 2/3*g**3 + g**2. Find a, given that p(a) = 0.
-2, 2/5
Factor 24/5 - 6/5*z**2 - 3/5*z**3 + 12/5*z.
-3*(z - 2)*(z + 2)**2/5
Let u be 8/(-10)*(-15)/6. What is o in -2/7*o**u - 8/7*o - 8/7 = 0?
-2
Let y be 2/(-2)*(-1 + 3). Let i be y/(-7) + (-104)/(-28). Find h, given that 0 + 4/5*h - 2/5*h**i - 4/5*h**3 + 2/5*h**2 = 0.
-2, -1, 0, 1
Suppose -4*f + 6*f - 8 = 0. Let w(t) be the third derivative of 1/80*t**5 + 5/96*t**f + 1/12*t**3 + t**2 + 0*t + 0. Factor w(x).
(x + 1)*(3*x + 2)/4
Let 11*h**3 + 2 + 12*h - 10 - 15*h**3 = 0. Calculate h.
-2, 1
Let w(t) be the first derivative of -t**6/12 - 3*t**5/10 + 9. Solve w(a) = 0 for a.
-3, 0
Let u be (-1)/(-4) + (-70)/(-40). Factor 2 + 2*y**4 + 8*y**3 + 10*y**u + 8*y + 0*y**2 + 2*y**2.
2*(y + 1)**4
Let w(u) be the first derivative of -1/4*u**2 - 1/4*u - 1/12*u**3 + 4. Find r such that w(