(f + 1)*(f + 4)/5
Let s(k) be the first derivative of -k**5 - 25*k**4/2 + 85*k**3 - 170*k**2 + 140*k - 446. Determine d, given that s(d) = 0.
-14, 1, 2
Let i = 21124 - 21122. Factor -3 - 9/2*k + 0*k**i + 3/2*k**3.
3*(k - 2)*(k + 1)**2/2
Let r(o) = 49*o**3 - 6*o**2 - 49*o + 10. Let g(c) = 540*c**3 - 65*c**2 - 540*c + 110. Let i = -94 + 98. Let u(m) = i*g(m) - 45*r(m). What is t in u(t) = 0?
-1, 2/9, 1
Let m(i) be the second derivative of i**4/30 + i**3 + 14*i**2/5 - 43*i. Find p such that m(p) = 0.
-14, -1
Let z(o) be the third derivative of -1/70*o**7 - 34*o**2 - 1/40*o**6 + 0 + 0*o + 1/4*o**5 + 0*o**3 - 3/8*o**4. Solve z(c) = 0.
-3, 0, 1
Let f(q) = -q**2 - 28*q + 48. Let z(c) = -3*c**2 - 54*c + 94. Let v(y) = -13*f(y) + 6*z(y). Determine s, given that v(s) = 0.
2, 6
Let t be 8 - (-1936)/(-240) - (-7)/30. Factor -t - 1/6*n**2 + 1/3*n.
-(n - 1)**2/6
Let b(q) be the third derivative of q**7/336 - 5*q**6/144 + q**5/8 - 7*q**3/3 - 30*q**2. Let u(s) be the first derivative of b(s). Factor u(t).
5*t*(t - 3)*(t - 2)/2
Let q(l) = 2*l**3 + 64*l**2 - 66*l + 2. Let a be q(-33). Let u(d) be the first derivative of 0*d**a + 1 + 0*d - 1/6*d**3. Factor u(k).
-k**2/2
Suppose 7*k + 590 = 590. Determine b, given that 0 + 3/2*b**3 + k*b + 3*b**2 = 0.
-2, 0
Let c(h) be the third derivative of 0*h**4 + 0 + 2/105*h**7 + 12*h**2 + 0*h**5 + 0*h - 1/168*h**8 + 0*h**6 + 0*h**3. Factor c(o).
-2*o**4*(o - 2)
Let u(q) be the first derivative of q**5 + 25*q**4/2 + 55*q**3 + 110*q**2 + 100*q + 85. Factor u(a).
5*(a + 1)*(a + 2)**2*(a + 5)
Suppose n = 2*w - 0*n - 11, -n - 17 = -4*w. Factor 7*d**2 - d**2 - 4*d + 2*d + 2*d**w - 6.
2*(d - 1)*(d + 1)*(d + 3)
Let j be (-11)/(-132) - 2/(-3). Let a(z) = -z**3 - 30*z**2 - 190*z - 18. Let h be a(-21). Factor 9/4*b**2 + 0 + j*b**h + 3/2*b.
3*b*(b + 1)*(b + 2)/4
Let k be (207/(-1932))/(6/(-16)). Factor -4/7 + 2/7*z**2 + k*z.
2*(z - 1)*(z + 2)/7
Let a(j) be the first derivative of j**4/36 + j**3/18 + 29*j - 9. Let p(t) be the first derivative of a(t). Find y such that p(y) = 0.
-1, 0
Let o(n) be the third derivative of n**8/2016 + 11*n**7/1260 + 3*n**6/80 + 5*n**5/72 + n**4/18 + 146*n**2. Factor o(w).
w*(w + 1)**3*(w + 8)/6
Let q(w) be the first derivative of 6*w**2 + 4/3*w**3 - 40*w + 25. Factor q(n).
4*(n - 2)*(n + 5)
Let u = -2 + 5. Let k be u + (4 + -3)/(2/(-2)). Solve 1/3*a**k - 1/3*a - 2/3 = 0.
-1, 2
Let a = -178 - -178. Let b(q) be the third derivative of 0 + a*q + 6*q**2 + 1/14*q**4 + 1/21*q**3 + 1/42*q**5. Solve b(c) = 0.
-1, -1/5
Let x = 1267 + -21515/17. Find b, given that x*b + 2/17*b**2 + 72/17 = 0.
-6
Let a = 7555 - 7552. Find l such that 9/7*l**a + 6/7*l**2 + 3/7*l**4 + 0 + 0*l = 0.
-2, -1, 0
Let d(y) be the third derivative of -y**7/2520 - y**6/540 + y**5/90 + y**4/9 + 5*y**3/3 + y**2. Let x(k) be the first derivative of d(k). Factor x(m).
-(m - 2)*(m + 2)**2/3
Let j(v) be the third derivative of -v**8/840 + v**7/420 + v**6/90 + 8*v**3/3 + 8*v**2. Let l(h) be the first derivative of j(h). Factor l(i).
-2*i**2*(i - 2)*(i + 1)
Suppose 3*h + 10 = -2*r, -11*h - 25 = -9*h + 5*r. Factor 2/9*w**2 + 8/9*w**3 + 0*w + h.
2*w**2*(4*w + 1)/9
Determine i so that 110/9*i + 14/3*i**3 - 38/3*i**2 - 4 - 2/9*i**4 = 0.
1, 18
Let g(j) be the first derivative of -1/20*j**4 + 2/5*j**2 + 2 - 8/5*j + 2/15*j**3. Factor g(o).
-(o - 2)**2*(o + 2)/5
Factor 33*a**4 + 27*a**2 + 245*a - 28*a**3 - 17*a**3 + 150 + 18*a**2 - 28*a**4.
5*(a - 6)*(a - 5)*(a + 1)**2
Let d = 18 - 14. Suppose -r + 3 = 0, -h - 3*h - d*r = -240. Solve -18*u + h*u - 292*u**3 + 41*u - 40*u**5 + 88*u**2 + 196*u**4 - 32 = 0 for u.
-1/2, 2/5, 1, 2
Let m = 90 - 42. Suppose 2*t - m*t**4 + 21*t**4 + 26*t**4 + 6*t**2 - 3*t**2 = 0. Calculate t.
-1, 0, 2
Let o(u) be the first derivative of 3*u**4/4 - 156*u**3 + 12168*u**2 - 421824*u - 239. Factor o(l).
3*(l - 52)**3
Solve i**3 - 3*i**4 + 6*i**4 + i**4 - 12*i**2 - 46*i**3 - 2*i**3 = 0.
-1/4, 0, 12
Let j(h) be the second derivative of h**5/130 + h**4/78 - 2*h**3/13 - 9*h - 3. What is y in j(y) = 0?
-3, 0, 2
Let g = -120/67 + 628/201. Factor 2/5*o**4 + g*o**3 + 4/5*o + 8/5*o**2 + 2/15.
2*(o + 1)**3*(3*o + 1)/15
Let m(c) be the third derivative of -c**7/2310 - c**6/1320 + 3*c**5/220 + 3*c**4/88 + 44*c**2. Factor m(k).
-k*(k - 3)*(k + 1)*(k + 3)/11
Let o(v) = v**3 - 3*v**2 + 4. Let c be o(3). Let x(s) = -4*s**4 + 3*s**2 + 11*s. Let u(m) = 5*m**4 - 2*m**2 - 12*m + 1. Let j(t) = c*x(t) + 3*u(t). Factor j(a).
-(a - 3)*(a + 1)**3
Let v be ((81/4)/(-3))/((-2275)/(-156) + -15). Factor -972/5*r - 24/5*r**5 - v*r**2 + 36/5*r**4 + 54*r**3 - 729/5.
-3*(r - 3)**2*(2*r + 3)**3/5
Suppose 23*i = 28*i. Let c be (-1)/(i + -1) - -4. Find l such that -3*l - 6*l**4 + 7*l - 3*l**c - l + 6*l**2 = 0.
-1, 0, 1
Let d be 2/(-39) + 7826/14196. What is t in 0*t - 1/8*t**3 + 3/8*t**2 - d = 0?
-1, 2
Let z(c) be the second derivative of 1/3*c**4 - 1/3*c**3 - 29*c + 0 + 0*c**2 + 1/60*c**6 - 1/8*c**5. Solve z(t) = 0.
0, 1, 2
Factor -9*h**2 + 3*h**3 + 3*h**4 + 3*h**2 + 0*h**4 - 9*h + 9*h.
3*h**2*(h - 1)*(h + 2)
Let r(g) be the second derivative of g**8/560 - g**7/70 + g**6/40 + g**5/10 - g**4/2 - 16*g**3/3 - 3*g. Let a(f) be the second derivative of r(f). Factor a(w).
3*(w - 2)**2*(w - 1)*(w + 1)
Let t(d) be the third derivative of -d**9/4536 - d**8/1008 - d**7/630 - d**6/1080 + 2*d**3/3 + 13*d**2. Let p(a) be the first derivative of t(a). Factor p(j).
-j**2*(j + 1)**2*(2*j + 1)/3
Suppose -5*b + 10 = -n, -4*b - 87*n + 91*n + 8 = 0. Factor 0 + 1/2*h**2 + 3/2*h**4 + 0*h - b*h**3.
h**2*(h - 1)*(3*h - 1)/2
Suppose 5313 - 5301 = 6*c. Find k such that 0 - 3/2*k**c + 3/2*k = 0.
0, 1
Let m(k) be the second derivative of -1/150*k**5 - 13*k + 0*k**2 + 1/90*k**4 + 0*k**3 + 1/315*k**7 - 1/225*k**6 + 0. Factor m(i).
2*i**2*(i - 1)**2*(i + 1)/15
Suppose -2*m = 2*l - 4, -5*m + 91*l - 94*l + 10 = 0. Solve 2/3*s**5 + 2/3*s**2 + 0 + m*s**3 + 2*s**4 + 0*s = 0 for s.
-1, 0
Factor -1/2*n**3 + 1/2*n**2 + 1/2*n - 1/2.
-(n - 1)**2*(n + 1)/2
Let i(l) = -35*l**3 + 35*l**2 + 75*l. Let o(w) = -3*w**3 + 3*w**2 + 6*w. Let k(r) = -2*i(r) + 25*o(r). What is m in k(m) = 0?
0, 1
Let y(s) be the second derivative of -s**5/20 + 5*s**4/6 - 16*s**3/3 + 16*s**2 + 464*s. Factor y(b).
-(b - 4)**2*(b - 2)
Let u(o) = o**2 + 65*o - 29. Let q(m) = -32*m + 14. Let s(d) = d**2 - 12*d - 15. Let w be s(14). Let g(t) = w*q(t) + 6*u(t). Determine l so that g(l) = 0.
1/3, 4
Factor -183 - 440*o - 224 - 162*o**3 + 455 + 1044*o**2.
-2*(o - 6)*(9*o - 2)**2
Suppose 5*y = 3*r + 15 + 1, 0 = 3*y - 15. Let b(n) be the second derivative of -1/18*n**4 + n - 4/9*n**r + 0 - 4/3*n**2. Solve b(l) = 0 for l.
-2
Let k be (-9)/(-15) + 0 + (-7)/70. Let m(g) be the second derivative of -4/3*g**3 + 0 + 0*g**2 + 4/3*g**4 + 1/15*g**6 - 2*g - k*g**5. Factor m(t).
2*t*(t - 2)**2*(t - 1)
Let a(m) be the first derivative of -5*m**6/6 + 14*m**5 + 40*m**4 + 10*m**3/3 - 155*m**2/2 - 80*m - 638. Factor a(f).
-5*(f - 16)*(f - 1)*(f + 1)**3
Suppose r - 5*p + 2 = -6, 4*r + 2 = 5*p. Let b(x) be the third derivative of 1/12*x**4 - 1/60*x**5 + 0*x**3 - 2*x**r + 0*x + 0. Factor b(j).
-j*(j - 2)
Let j be (-4)/26 + 28/13. Find h, given that 4*h**3 - 8 + h**2 - 2*h + 7*h**j - h - h = 0.
-2, -1, 1
Let g(k) be the second derivative of 1/3*k**2 - 7*k + 0 + 169/72*k**4 + 13/9*k**3. Suppose g(p) = 0. What is p?
-2/13
Let i be ((-132)/154)/(8/(-14)) - (-18)/(-20). Let i - 1/5*y**3 - 7/5*y + y**2 = 0. Calculate y.
1, 3
Suppose 9*k + 5*u - 24 = 6*k, 0 = 4*k - 4*u. Let f(p) be the second derivative of -1/16*p**4 + 0*p**2 - 3/80*p**5 + 1/40*p**6 + 1/8*p**k + 0 + p. Factor f(n).
3*n*(n - 1)**2*(n + 1)/4
Let y(k) be the second derivative of 3*k**5/80 - k**4/2 + 2*k**3 + 261*k. Factor y(d).
3*d*(d - 4)**2/4
Let c(s) be the second derivative of 2*s**6/75 + 12*s**5/25 + 13*s**4/5 + 56*s**3/15 + 286*s. Find b such that c(b) = 0.
-7, -4, -1, 0
Let s(y) be the first derivative of y**7/315 - y**6/180 - y**5/90 + y**4/36 - 8*y**2 + 24. Let r(p) be the second derivative of s(p). Factor r(g).
2*g*(g - 1)**2*(g + 1)/3
Let g(o) = 3249*o**2 - 360*o + 1. Let n(b) = -1624*b**2 + 180*b - 1. Let w(k) = 4*g(k) + 9*n(k). Let w(u) = 0. Calculate u.
1/18
Factor -8*b**2 + 55/2*b + 1/2*b**3 + 0.
b*(b - 11)*(b - 5)/2
Let l(j) be the first derivative of -1/14*j**6 + 0*j**3 - 3/14*j**2 + 3/14*j**4 + 