 = 184, 4*d + 0*p + 4*p = 408. Let k = d - 96. Factor 190/7*h**k + 24/7 + 50/7*h**3 + 128/7*h.
2*(h + 3)*(5*h + 2)**2/7
Let w(h) be the third derivative of -h + 10*h**2 + 0 - 1/24*h**3 - 1/192*h**4 + 1/240*h**5 + 1/960*h**6. Let w(a) = 0. Calculate a.
-2, -1, 1
Let b(x) be the first derivative of -x**4/4 - x**3/3 + x + 11. Let y(d) = 5*d**3 - 12*d**2 - 3*d + 3. Let p(g) = -2*b(g) + 2*y(g). Factor p(l).
2*(l - 2)*(2*l + 1)*(3*l - 1)
Let y(w) be the first derivative of -w**7/210 - w**6/90 - 13*w**3/3 - 8. Let k(z) be the third derivative of y(z). Solve k(v) = 0.
-1, 0
Let s(j) be the first derivative of -2 + 2/9*j + 2/9*j**3 - 1/3*j**2 - 1/18*j**4. Factor s(n).
-2*(n - 1)**3/9
Let c(q) be the first derivative of q**4/4 + q**3/3 - 2*q**2 - 4*q - 38. Factor c(o).
(o - 2)*(o + 1)*(o + 2)
Let m(u) = u**3 + u**2. Let t(a) = 9*a**3 + 6*a**2 - 3*a. Suppose 7 = 3*y + 1. Let x = y - 1. Let g(k) = x*t(k) - 12*m(k). Factor g(p).
-3*p*(p + 1)**2
Factor 36*t + 13*t + 39*t - 968 - 4*t**2 + 2*t**2.
-2*(t - 22)**2
Let r(d) be the third derivative of 0 + 0*d + 1/15*d**5 + 0*d**3 - 1/3*d**4 + d**2. Solve r(i) = 0.
0, 2
Let c(u) = u**3 - 12*u**2 + 10*u + 14. Let a be c(11). Factor 60*l - 7*l**3 + 7 + 2*l**a + 73.
-5*(l - 4)*(l + 2)**2
Factor 1315*t + 535*t + 2*t**3 + 18522 + 1000*t - 268*t + 126*t**2 + 64*t.
2*(t + 21)**3
Let f(q) be the third derivative of -q**6/480 + q**5/8 + 21*q**4/32 + 4*q**3/3 + 5*q**2. Let f(l) = 0. What is l?
-1, 32
Let b(i) = -i**2 - 5*i - 1. Let r be b(-4). Let o = 6 - 4. Factor 2*h - 3*h**3 - h + o*h + r - 3*h**2.
-3*(h - 1)*(h + 1)**2
Suppose -5*b + 12 = -4*k, 0 = 5*k - 2*b - 2. Suppose -5*a + 15*a**3 + 0*a**2 + 4*a**k + 10 - 24*a**2 = 0. Calculate a.
-2/3, 1
Factor -4205/3 - 290/3*g - 5/3*g**2.
-5*(g + 29)**2/3
Find a, given that -9*a**3 + 22*a**2 - 7994*a**4 + 7997*a**4 - 51*a - 67*a**2 - 18 = 0.
-1, 6
Let l(m) be the third derivative of 16*m**2 - 1/45*m**5 - 8/9*m**3 + 0*m - 2/9*m**4 + 0. Factor l(i).
-4*(i + 2)**2/3
Let p(t) be the second derivative of 3*t**5/20 - 13*t**4/4 + 11*t**3 - 5*t - 19. Factor p(n).
3*n*(n - 11)*(n - 2)
Determine q, given that 4/3*q**2 + 8/3 - 14/3*q + 2/3*q**3 = 0.
-4, 1
Let p be 144/(-32)*(-6)/9. Let a(l) be the second derivative of -1/55*l**6 + 3*l + 0*l**2 - 7/66*l**4 + 2/33*l**p + 0 + 4/55*l**5. Factor a(h).
-2*h*(h - 1)**2*(3*h - 2)/11
Let n(v) = v**3 - 7*v**2 - 6*v + 9. Let x be n(8). Factor -14*y**5 - y**2 + x*y**5 + y**3 - 12*y**5 + y**4.
-y**2*(y - 1)**2*(y + 1)
Let d(g) = 3*g**3 - 177*g**2 + 198*g + 210. Let c(x) = -x**3 - 2*x**2 + x + 1. Let m(s) = 6*c(s) - d(s). Find j such that m(j) = 0.
-2/3, 2, 17
Find u, given that 15/2*u**3 + 5 + 5*u**2 - 35/2*u = 0.
-2, 1/3, 1
Let b(l) = 69*l**2 - 12*l - 27. Let p(v) = 4*v**2 - v - 1. Let i(q) = -b(q) + 15*p(q). Determine h, given that i(h) = 0.
-4/3, 1
Let f(h) = 5*h**4 - 89*h**3 + 156*h**2 - 65*h + 14. Let m(s) = -2*s**4 + 30*s**3 - 52*s**2 + 22*s - 4. Let p(b) = -2*f(b) - 7*m(b). Factor p(c).
4*c*(c - 6)*(c - 1)**2
Let w be 16*(479/38 - 6/57). Let t = w - 599/3. Factor 1/6*r**2 + 1/6 + t*r.
(r + 1)**2/6
Find n, given that -84*n - 8*n**2 - 144 + 4/3*n**3 = 0.
-3, 12
Let c(m) be the first derivative of -m**6/24 + m**5/10 + m**4/2 + m**3/6 - 7*m**2/8 - m - 540. Factor c(r).
-(r - 4)*(r - 1)*(r + 1)**3/4
Suppose 3*o - 15 = 5*k + 2, 5*k + 1 = -o. Factor 4*w**3 - 4*w**2 + w - 3*w - 2*w + o*w**4.
4*w*(w - 1)*(w + 1)**2
Factor -3/4*x**2 + 9/4 - 3/2*x.
-3*(x - 1)*(x + 3)/4
Let g = 63021/17 - 3707. Factor -2/17*r + 0 + g*r**2.
2*r*(r - 1)/17
Suppose 1 = -5*m + 1. Let r(o) be the first derivative of 0*o**3 + m*o**2 - 3/20*o**5 + 0*o + 3/8*o**4 - 14. Factor r(k).
-3*k**3*(k - 2)/4
Suppose -3*d + 8 = d. Let 1 - 3*o - 11 + 12 - 5*o**d = 0. Calculate o.
-1, 2/5
Suppose 0 = 19*r - 15 - 23. Let k = -42 + 212/5. Factor 1/5*n - k + 3/5*n**r.
(n + 1)*(3*n - 2)/5
Suppose -3*c + 10 = 2*d, 0 = -4*c + 5*d - 3*d - 10. Determine y so that 3/2*y**2 - 3*y + c = 0.
0, 2
Let q(f) be the third derivative of 1/57*f**4 + 0 + 1/570*f**5 + 0*f + 4/57*f**3 + 6*f**2. Solve q(j) = 0 for j.
-2
Suppose 15*y - 88 = 17*y. Let k be (y/(-28) - -2) + -3. Determine d, given that -6/7*d + k*d**2 - 4/7 + 0*d**4 - 2/7*d**5 + 8/7*d**3 = 0.
-1, 1, 2
Let c(b) be the second derivative of -b**7/252 - 11*b**6/20 - 1681*b**5/60 - 5272*b**4/9 - 8704*b**3/3 - 16384*b**2/3 - 714*b. Factor c(p).
-(p + 1)*(p + 2)*(p + 32)**3/6
Let j(g) be the second derivative of g**4/138 - g**3/23 - 17*g - 2. Factor j(w).
2*w*(w - 3)/23
Let l(j) be the first derivative of j**4 - 2*j**2 + 58. Find c such that l(c) = 0.
-1, 0, 1
Let -2/7*u**5 + 48/7*u + 72/7 - 94/7*u**2 - 46/7*u**3 + 22/7*u**4 = 0. Calculate u.
-1, 1, 6
Let c = -19 - -11. Let l be 96/54*((-18)/c)/3. Factor 2*z**2 + 0 + 2/3*z**3 + l*z.
2*z*(z + 1)*(z + 2)/3
Suppose 3*j - 5*k + 1 + 0 = 0, 25 = -3*j - k. Let f = -5 - j. Factor 14*y - 24*y**f - 16 + 5*y**3 + 0*y**4 + 3*y**3 + 18*y - y**4.
-(y - 2)**4
Let b = -360 + 360. Let o(c) be the second derivative of 0*c**3 + 0*c**2 + b + 0*c**5 - 3*c - 1/15*c**6 + 1/6*c**4. Find f, given that o(f) = 0.
-1, 0, 1
Let y(t) be the first derivative of t**3/18 - 13*t**2/6 + 8*t - 39. Factor y(k).
(k - 24)*(k - 2)/6
Let v be (-8)/28 - (-8 + 75/10). Let o(q) be the second derivative of 0 + v*q**3 + 3/28*q**4 + 3/140*q**5 + 8*q + 3/14*q**2. Solve o(c) = 0 for c.
-1
Let z(r) be the third derivative of -1/1320*r**6 + 0*r + 0 + 0*r**4 + 0*r**3 + 15*r**2 - 1/220*r**5. Solve z(y) = 0.
-3, 0
Let c be (-9 - -2 - -1)/((-108)/8). Let l = -2/39 + 32/117. Factor -l*b**2 - 2/9 - c*b.
-2*(b + 1)**2/9
Let l = 294 - 294. Let t(y) be the third derivative of 1/9*y**3 - 1/180*y**5 - 2*y**2 + l*y - 1/72*y**4 + 0. Factor t(v).
-(v - 1)*(v + 2)/3
Let g(x) = x**5 - x**4 + x**3 - 2*x**2. Let w(k) = k**5 - 10*k**4 - 4*k**3 + 4*k**2 + 7*k. Let m(c) = -2*g(c) + w(c). Find a such that m(a) = 0.
-7, -1, 0, 1
Suppose -31*c + 2045 = 1983. Find n, given that 1/4 + 1/4*n**c - 1/2*n = 0.
1
Let r(h) be the second derivative of -2*h**5/5 + h**4/2 - h**3/6 + 26*h. Suppose r(p) = 0. Calculate p.
0, 1/4, 1/2
Let f(d) be the first derivative of 2*d**3/15 - 46*d**2/5 + 1058*d/5 - 175. Let f(z) = 0. Calculate z.
23
Let u be (27/90)/(30/80). Factor -2/5*x**2 + 2/5*x + u.
-2*(x - 2)*(x + 1)/5
Factor -w**4 + 3*w**4 - 57*w**3 + 167 - 290*w + 3*w**4 + 157*w**3 - 15*w**2 + 33.
5*(w - 1)**2*(w + 2)*(w + 20)
Let x(f) be the third derivative of 0*f + 2/3*f**4 + 1/42*f**8 + 0 + 7/15*f**6 - 11/15*f**5 - 17/105*f**7 - 1/3*f**3 + 15*f**2. Suppose x(j) = 0. What is j?
1/4, 1
Let y be (32/6)/(-747 - -757). Find w such that y*w**3 + 4/15*w**4 - 2/15*w - 2/5*w**5 - 4/15*w**2 + 0 = 0.
-1, -1/3, 0, 1
Let a(p) be the third derivative of p**9/3360 + p**8/480 - 17*p**7/2520 + p**6/120 + p**5/15 + 11*p**2. Let s(x) be the third derivative of a(x). Factor s(g).
2*(g + 3)*(3*g - 1)**2
Let o(g) = 2*g**2 - 94*g + 98. Let p(x) = 2*x**2 - 96*x + 99. Let t(v) = -5*o(v) + 6*p(v). Determine u so that t(u) = 0.
1, 52
Suppose 2*i + 3*i - 15 = 0. Factor -3*d**2 + 10*d**3 - 10*d - 5*d**4 - d**2 + i*d**2 + 6*d**2.
-5*d*(d - 2)*(d - 1)*(d + 1)
Suppose 3 = -3*t + 3*d, -8*t + 2*d = -7*t + 6. Let x(k) be the first derivative of -k**2 - 2/3*k - 2/3*k**3 - 1/6*k**t + 8. Solve x(v) = 0.
-1
Factor 3/2*k**2 + 15 + 33/2*k.
3*(k + 1)*(k + 10)/2
Let l(s) be the first derivative of s**4/16 - s**3/3 - 47. What is x in l(x) = 0?
0, 4
Let p(o) = 3*o**5 + 8*o**4 + 2*o**3 + 2*o**2. Let g(a) = -4*a**5 - 11*a**4 - 3*a**3 - 3*a**2. Let m(i) = -5*g(i) - 7*p(i). Find z, given that m(z) = 0.
-1, 0, 1
Let n(y) be the third derivative of -y**6/30 - 8*y**5/15 - 13*y**4/6 - 4*y**3 - y**2 - 80*y. Factor n(c).
-4*(c + 1)**2*(c + 6)
Let f(q) = -21 + 12*q - 8 - q**2 + 12. Let s be f(10). Solve -66/5*n**s - 8/5*n + 0 - 7/5*n**5 + 44/5*n**2 + 37/5*n**4 = 0 for n.
0, 2/7, 1, 2
Let f(q) be the third derivative of -q**8/112 - 3*q**7/35 + 9*q**6/20 + 28*q**5/5 - 105*q**4/8 - 225*q**3 + 99*q**2. Find p, given that f(p) = 0.
-5, -2, 3
Suppose 5*a = 7*m - 12*m - 10, 0 = -4*a - 3*m - 3. Let a*d**4 + 3968 - 9*d**3 - 3968 = 0. What is d?
0, 3
Let v(o) be the third derivative of -o**5/90 - o**4/4 + 22*o**3/9 - 13*o**2 - 7. Suppose v(k) = 0. What is k?
-11, 2
Let a be 0 - -3 - (-15)/(2 + -5). Let g be (-1100)/(-250) + ((-4)/(-5))/a. Factor 8/5*q**g - 