f + c*f**2.
-4*(f - 2)**3
Let v(k) be the second derivative of -k**9/5040 + k**8/560 - k**7/210 + 17*k**4/6 - 31*k. Let h(a) be the third derivative of v(a). Suppose h(t) = 0. What is t?
0, 2
Let l(n) be the third derivative of n**7/140 + n**6/80 - 3*n**5/8 + 23*n**4/16 - 5*n**3/2 + 10*n**2 + 3. What is f in l(f) = 0?
-5, 1, 2
Suppose -7*d + 4*d + 6 = 0. Factor p**2 + 3 + 33 + 24*p + p**2 + 2*p**d.
4*(p + 3)**2
Let j(m) be the first derivative of 0*m + 1/13*m**4 + 0*m**3 + 2/65*m**5 + 0*m**2 - 10 - 1/39*m**6. Solve j(g) = 0 for g.
-1, 0, 2
Solve -8/3*i - 2/3*i**2 + 8 = 0.
-6, 2
Let u(j) be the first derivative of -5*j**3/3 - 5*j**2/2 + 19. Solve u(s) = 0 for s.
-1, 0
Let t(i) be the second derivative of -i**6/180 - i**5/30 - 8*i**2 - 12*i. Let d(g) be the first derivative of t(g). Suppose d(l) = 0. Calculate l.
-3, 0
Let s(r) be the third derivative of -r**6/200 - 3*r**5/100 + r**4/10 + 65*r**2. Let s(a) = 0. What is a?
-4, 0, 1
Suppose 0 = -5*v - 5*g + 40, 4*g - 6 = v + 11. Factor -v*q + q**2 - q**2 + q**3 + q**2 + q**2.
q*(q - 1)*(q + 3)
Let v(g) be the second derivative of 0 + 0*g**4 + g + 1/60*g**6 - 1/10*g**5 + 4/3*g**3 - 2*g**2. Let l(p) be the first derivative of v(p). Factor l(t).
2*(t - 2)**2*(t + 1)
Suppose -28 = -4*m - 0. Suppose 0 = -5*c + m*c. Determine i so that -1/2*i**5 + 3/2*i**3 - 5/2*i**2 + c + i + 1/2*i**4 = 0.
-2, 0, 1
Factor -9408/5*t**2 - 48*t**4 + 0 + 32928/5*t - 3024/5*t**3 - 6/5*t**5.
-6*t*(t - 2)*(t + 14)**3/5
Let k(y) = -35*y**2 - 9*y - 44*y + 18*y**3 + 5*y + 11*y**3 - 18. Let o(v) = -5*v**3 + 6*v**2 + 8*v + 3. Let j(s) = 6*k(s) + 34*o(s). Factor j(c).
2*(c - 3)*(c + 1)*(2*c + 1)
Let j(f) be the second derivative of -f**4/3 - 2*f**3/3 + 4*f**2 + 61*f. Factor j(w).
-4*(w - 1)*(w + 2)
Let i(j) = -j**2 + 12*j - 13. Let f be i(11). Let n be 1/f*(-5 + 8/2). Factor -3*g - n*g**2 - 9/2.
-(g + 3)**2/2
Let p(r) be the first derivative of -4*r**5/5 + r**4 + 8*r**3/3 - 54. Let p(q) = 0. Calculate q.
-1, 0, 2
Let p(c) = c**3 - 15*c**2 + 34*c + 24. Let f be p(12). Let z(t) be the first derivative of 4/3*t**3 + f*t - 4*t**2 + 7. Suppose z(o) = 0. What is o?
0, 2
Let s(d) be the first derivative of d**3/3 - 27*d**2/2 - 202. Factor s(m).
m*(m - 27)
Suppose 87*i + 280*i - 340 = 761. Let h = 60 + -298/5. Factor 0*o + 0 - h*o**2 - 2/5*o**i.
-2*o**2*(o + 1)/5
Let a be ((-112)/(-2156))/((-4)/(-44)). Find k such that -a*k**4 + 16/7*k**2 + 0 + 0*k + 12/7*k**3 = 0.
-1, 0, 4
Let l(n) be the second derivative of -3/4*n**2 + 1/4*n**4 - 9/80*n**5 - 35*n + 5/8*n**3 + 0. Suppose l(c) = 0. Calculate c.
-1, 1/3, 2
Determine y, given that -3/4*y**3 + 0 - 12*y**2 + 0*y = 0.
-16, 0
Let p(r) be the second derivative of -r**5/120 - r**4/12 - 11*r**3/36 - r**2/2 + 159*r. Find x such that p(x) = 0.
-3, -2, -1
Let c(n) be the first derivative of -4*n**3/27 + 7*n**2/9 - 2*n/3 - 96. Factor c(z).
-2*(z - 3)*(2*z - 1)/9
Let p = 6469 + -6469. Solve p*q**2 + 0 - 10/9*q**3 + 0*q - 2/9*q**4 = 0.
-5, 0
Let d(t) be the first derivative of -t**6/2 + 6*t**5/5 - 3*t**4/4 + 24. Factor d(k).
-3*k**3*(k - 1)**2
Let t = -581/30 - -207/10. Solve 0*n**3 + 1/3*n**5 + 0*n + 0 + n**4 - t*n**2 = 0 for n.
-2, 0, 1
Factor 17*k**3 - 18*k**3 + 288 - 96*k - 48*k**2 + 26*k**2.
-(k - 2)*(k + 12)**2
Let r = 1614/74503 + -4/521. Let y = 157/1001 - r. Factor -1/7*a - 2/7*a**4 + y*a**5 + 2/7*a**2 + 0 + 0*a**3.
a*(a - 1)**3*(a + 1)/7
Let w = 19141/2 + -9569. Factor 7/8*b**4 + w*b**3 + 3/8*b**2 + 0 - 1/4*b.
b*(b + 1)**2*(7*b - 2)/8
Let c(z) be the first derivative of z**4/2 + 410*z**3/3 + 10403*z**2 - 21218*z - 371. Find p, given that c(p) = 0.
-103, 1
Let q(t) be the first derivative of -3*t**4/4 - 43*t**3 - 63*t**2 - 73. Factor q(p).
-3*p*(p + 1)*(p + 42)
Let x(f) = -15*f**2 + 35*f + 10. Let q(h) = h**2 - h - 1. Let d(l) = -2*l**2 + 3*l + 4. Let p(m) = d(m) + 3*q(m). Let g(b) = 20*p(b) + x(b). Solve g(z) = 0.
-6, -1
Suppose 398*s - 5*y - 40 = 399*s, 16 = 2*s - 2*y. Factor s + 0*v + v**3 + 1/4*v**5 + v**4 + 0*v**2.
v**3*(v + 2)**2/4
Suppose -4*o + 6*o - 26 = 0. Let d = 16 - o. Solve y**d + 0 + 3*y**2 + 0 + 1 + y + 2*y = 0.
-1
Let u(r) = -352*r - 10910. Let n be u(-31). Solve -128/11 + 96/11*c + 2/11*c**3 - 24/11*c**n = 0.
4
Let i(z) be the third derivative of 0 + 1/3*z**5 - 1/21*z**7 - 1/4*z**6 + 5/8*z**4 + 8*z**2 - 5/3*z**3 + 5/112*z**8 + 0*z. Let i(q) = 0. What is q?
-1, 2/3, 1
Let o(t) be the third derivative of -19/20*t**5 + 0*t - 1/2*t**3 - 8/35*t**7 - 5/8*t**6 + 0 - 7/8*t**4 - 1/28*t**8 + 20*t**2. Factor o(p).
-3*(p + 1)**3*(2*p + 1)**2
Let o(n) be the first derivative of -1/9*n**3 + 2 - 1/3*n**2 - 1/3*n. Suppose o(d) = 0. What is d?
-1
Let r(u) be the second derivative of 0 + 0*u**2 + 3*u + 5/6*u**3 + 1/6*u**4 - 1/45*u**6 + 1/30*u**5. Let a(m) be the second derivative of r(m). Factor a(f).
-4*(f - 1)*(2*f + 1)
Let f = 13 - -6. What is x in -4*x**4 + 10*x + 25*x**5 - 11*x**4 - 16*x**3 - f*x**3 + 15*x**2 = 0?
-1, -2/5, 0, 1
Let b(x) = -x**2 + 22*x + 11. Let w be b(23). Let l be w/(-7) - 22/(-77). Determine u so that 0 + 2*u**4 + l*u**2 - 3*u**3 - 1/2*u - 1/2*u**5 = 0.
0, 1
Let y(a) be the first derivative of a**4/72 - 5*a**3/36 - a**2/2 + 20*a - 16. Let q(s) be the first derivative of y(s). Factor q(b).
(b - 6)*(b + 1)/6
Solve -2116*f**3 + 4*f**4 + 6*f**2 + 10*f**4 - 3*f**5 + 2099*f**3 = 0.
0, 2/3, 1, 3
Let s = 10361 + -52017/5. Let t = 44 + s. Solve 2*o - 2*o**3 + 6/5*o**2 - t*o**4 + 2/5 = 0.
-1, -1/4, 1
Let p = 3162 + -3160. Suppose -2/3*l**4 + 0*l - 4/3*l**3 + 0 - 2/3*l**p = 0. Calculate l.
-1, 0
Suppose 4*x + 2 = 2*h, 9 = -257*h + 261*h - 3*x. Suppose -4/5 - 12/5*w**2 - 12/5*w - 4/5*w**h = 0. What is w?
-1
Let v(f) be the second derivative of f**4/4 + 71*f**3/2 - 400*f. Solve v(g) = 0 for g.
-71, 0
Let k = 15/383 - -9087/2681. Let h = -254 + 1784/7. Solve 4*x**2 + h*x - 4/7 - k*x**4 - 2*x**5 + 8/7*x**3 = 0.
-1, 2/7, 1
Find l, given that -1/9*l**3 + 343/9 + 7/3*l**2 - 49/3*l = 0.
7
Let g(u) be the first derivative of u**5/2 - 29*u**4/4 - 89*u**3/6 - 13*u**2/2 + 213. Let g(j) = 0. What is j?
-1, -2/5, 0, 13
Let y be -1 + 3 + 1/1. Suppose -10 = -y*c - 1. Suppose -81*f**2 + 18*f + 1 + 9*f - 4 + 81*f**c = 0. What is f?
1/3
Find w such that 250*w**5 - 147*w**3 + 42*w**4 + 5 - 253*w**5 + 1 - 6 = 0.
0, 7
Factor 0 - x**3 - 15/7*x**2 - 2/7*x.
-x*(x + 2)*(7*x + 1)/7
Let p = -1/4250 - -4257/29750. Suppose -4/7*h - p*h**2 - 4/7 = 0. Calculate h.
-2
Let w(y) = -y**3 - 15*y**2 - 13*y + 17. Let a(b) = -14*b**3 - b**2 + b. Let t be a(1). Let o be w(t). Factor -8*m**3 + 6*m**2 + 8*m - 5 - 3*m**4 + 5*m**4 - o.
2*(m - 2)**2*(m - 1)*(m + 1)
Let u(d) be the second derivative of 1/18*d**4 - 1/120*d**5 + 0 - 20*d - 5/36*d**3 + 1/6*d**2. Factor u(t).
-(t - 2)*(t - 1)**2/6
Let x(p) be the second derivative of p**4/8 + 5*p**3/2 + 27*p**2/4 + 82*p + 1. Suppose x(o) = 0. Calculate o.
-9, -1
Let c(h) be the third derivative of -1/120*h**5 + 1/12*h**4 + 0 + 1/3*h**3 + 0*h - 9*h**2 - 1/240*h**6. Suppose c(d) = 0. What is d?
-2, -1, 2
Let g(a) be the first derivative of -a**5/30 - a**4/4 - 4*a**3/9 + 232. What is b in g(b) = 0?
-4, -2, 0
Let i(t) be the third derivative of -t**4/24 - t**3/6 + 3*t**2. Let q be i(-3). Suppose -q + 12*u**2 + 2*u**2 + 8*u**3 - u**3 + 4*u + u**3 = 0. Calculate u.
-1, 1/4
Suppose -32*z - 428/3*z**2 + 192 - 24*z**3 - 1/3*z**5 + 7*z**4 = 0. Calculate z.
-2, 1, 12
Factor -1/3*x**2 - 12 - 37/3*x.
-(x + 1)*(x + 36)/3
Factor -147 + 107*g + 96*g - 63*g + 11 - 4*g**2.
-4*(g - 34)*(g - 1)
Factor -z - 1/4*z**2 + 0.
-z*(z + 4)/4
Let y(g) be the third derivative of g**7/42 - 13*g**6/12 + 47*g**5/4 + 455*g**4/6 + 490*g**3/3 - 409*g**2. Factor y(p).
5*(p - 14)**2*(p + 1)**2
Let -4*r**2 + 4*r**4 + 3*r**3 + 2*r**4 - 2*r**4 + r**3 - 4*r**5 = 0. What is r?
-1, 0, 1
Let x(q) = -54*q**4 + 12*q**3 + 4*q. Let b be (12/10)/((-9)/45). Let u(k) = 54*k**4 - 13*k**3 - k**2 - 3*k. Let p(o) = b*u(o) - 5*x(o). Factor p(i).
-2*i*(3*i - 1)**2*(3*i + 1)
Let f(j) = j**3 - 5*j**2 + 3*j + 4. Let z be f(4). Let t be (-4)/(-3)*(-36)/(-24). Factor 3*l + z*l**t + 6*l**2 - l.
2*l*(3*l + 1)
Factor 0 + c**3 + 1/6*c**2 + 0*c.
c**2*(6*c + 1)/6
Let d be (1 + 1*3)/7. Let l be (-736)/(-1449) - 6/27. Suppose -d*v**3 - l*v**2 + 0 + 0*v - 2/7*v**4 = 0. What is v?
-1, 0
Let b = -1/24 + 3/8. Let z(n) be the second derivative of 1/24