14 - 5/16*g**4 + 1/2*g**3 + 1/20*g**5. Factor f(h).
(h - 2)**3*(h + 1)/4
Let f(c) be the first derivative of c**4/16 + c**3/12 - 5*c**2/4 + 2*c - 688. Determine r, given that f(r) = 0.
-4, 1, 2
Let y(s) be the third derivative of -s**5/4 + 69*s**4/4 + 28*s**3 - 1148*s**2 - 2*s. Determine z so that y(z) = 0.
-2/5, 28
Let h(g) be the third derivative of g**7/840 + 3*g**6/160 + g**5/10 + g**4/6 + 2*g**2 - 359*g. Solve h(m) = 0 for m.
-4, -1, 0
Determine o, given that 99*o - 4848*o**2 + o + 4936*o**2 - 184 - 4*o**3 = 0.
-2, 1, 23
Let m(i) be the first derivative of -4/3*i**3 + 1/18*i**4 + 17*i + 11 + 12*i**2. Let s(a) be the first derivative of m(a). Factor s(c).
2*(c - 6)**2/3
Solve 319*w**4 - 322*w**4 - 1734*w**2 - 1878*w**2 - 35076*w - 290304 - 42684*w - 3084*w**2 - 237*w**3 = 0.
-24, -7
Let q be (-5)/(-25)*(-8 - -9) + 2/(-30). Let o(v) be the first derivative of 2/15*v**4 - 4/15*v**2 + 2/45*v**3 + 5 - q*v. Factor o(g).
2*(g - 1)*(g + 1)*(4*g + 1)/15
Let y(o) be the third derivative of o**7/12600 - o**5/600 + 11*o**4/24 + 121*o**2. Let v(d) be the second derivative of y(d). Suppose v(m) = 0. Calculate m.
-1, 1
Let h(j) be the first derivative of 5/6*j**3 + 5/6*j**4 - 1/6*j**6 - 1/12*j**5 - 38 + 31/2*j**2 + 0*j. Let k(s) be the second derivative of h(s). Factor k(l).
-5*(l - 1)*(l + 1)*(4*l + 1)
Let a = 57 - 64. Let p be 1/a + 18/126. What is f in -f**3 + 13*f**3 - 10*f**4 + 248*f**5 - 246*f**5 + p*f**4 = 0?
0, 2, 3
Let w(v) be the first derivative of v**4 - 2/5*v**5 + 0*v**2 - 2/3*v**3 + 0*v + 66. Factor w(k).
-2*k**2*(k - 1)**2
Let 1/6*t**3 + 2 + 3/2*t**2 + 10/3*t = 0. Calculate t.
-6, -2, -1
Let h(r) = 20*r**2 - 696*r - 2112. Let s(y) = -5*y**2 + 2*y - 1. Let z(j) = h(j) + 3*s(j). What is p in z(p) = 0?
-3, 141
Let b(s) be the first derivative of 19 - 1/28*s**4 + 3/7*s**2 - 1/14*s**3 - 35*s. Let a(w) be the first derivative of b(w). Suppose a(c) = 0. Calculate c.
-2, 1
Let p be ((-1)/7 - 154/294) + 11/3. Let j(t) be the third derivative of 0*t**4 + 0*t + 1/40*t**6 - 1/10*t**5 + 0*t**p - 5*t**2 + 0. Let j(g) = 0. Calculate g.
0, 2
Let l(f) be the second derivative of -f**4/21 + 16*f**3/7 + 350*f**2 - 322*f - 2. Solve l(j) = 0 for j.
-25, 49
Factor 734*h**2 - 331*h**2 + 507 - 406*h**2.
-3*(h - 13)*(h + 13)
Suppose 128/7 + 32*j + 2/7*j**4 + 26/7*j**3 + 120/7*j**2 = 0. What is j?
-4, -1
Factor 29310*f**2 - 29333*f**2 + 123 - 5*f**3 + 101*f - 4.
-(f + 1)*(f + 7)*(5*f - 17)
Suppose 80*l - 65 = 93*l. Let k be 7 + l - (-21)/(-14). Factor 1/4*n**3 - 1 - 7/4*n - k*n**2.
(n - 4)*(n + 1)**2/4
Let f(u) be the second derivative of 0*u**2 + 1/60*u**5 - 2*u + 0 - 1/420*u**7 - u**3 + 0*u**4 + 0*u**6. Let k(z) be the second derivative of f(z). Factor k(x).
-2*x*(x - 1)*(x + 1)
Let b be (-480)/(-230) + (-2)/23. Find w such that -4146*w**2 + w**3 + 9*w + 4158*w**b + 2*w**3 = 0.
-3, -1, 0
Suppose 4*q + 22 = -m - 10, 3*q + 49 = -2*m. Let w = m - -31. Factor n + 8*n + w*n - 4*n**2 - 18*n**3 - 6*n**3.
-4*n*(n + 1)*(6*n - 5)
Find k such that 1/4*k**3 - k**2 - 3/4*k + 9/2 = 0.
-2, 3
Let v(w) be the first derivative of -3*w**6/2 - 64*w**5/5 - 133*w**4/4 - 86*w**3/3 - 4*w**2 + 1907. Suppose v(t) = 0. What is t?
-4, -2, -1, -1/9, 0
Let p(s) = -17*s**3 + 26*s**2 + 43*s + 20. Let c(h) = 4*h**3 - h**2 + h + 1. Let a(t) = -4*c(t) - p(t). Find k, given that a(k) = 0.
-1, 24
Let q(t) be the third derivative of 3 + 0*t + 2/3*t**4 + 32/15*t**3 - 1/150*t**6 + 2/25*t**5 - 1/525*t**7 + 6*t**2. Suppose q(j) = 0. Calculate j.
-2, 4
Let c(i) be the first derivative of -i**6/1620 - 2*i**5/135 + i**4/12 - 2*i**3/3 - 19*i - 76. Let n(q) be the third derivative of c(q). Factor n(l).
-2*(l - 1)*(l + 9)/9
Suppose -14*v = 20*v - 32878. Let d = v + -967. Solve 0 - 4/5*n**3 + d*n - 1/5*n**4 - 4/5*n**2 = 0 for n.
-2, 0
Let y(r) = 265*r**3 + 1070*r**2 + 2070*r. Let a(z) = 29*z**3 + 119*z**2 + 230*z. Let h(j) = -55*a(j) + 6*y(j). Factor h(l).
-5*l*(l + 2)*(l + 23)
Let h = 6279 + -6277. Factor 0 + 1/2*b + 0*b**h - 1/2*b**3.
-b*(b - 1)*(b + 1)/2
Let n(t) be the second derivative of 3/5*t**5 - 7*t + 6 + 0*t**2 - 4*t**4 + 8/3*t**3 + 2/3*t**6. Suppose n(u) = 0. Calculate u.
-2, 0, 2/5, 1
Let z = 17995 + -71979/4. Let w(p) be the first derivative of 0*p - 4 - z*p**4 + 2/3*p**2 + 0*p**3 - 1/15*p**5. Factor w(o).
-o*(o - 1)*(o + 2)**2/3
Let f(w) = 3*w**3 - 2*w**2 + w - 1. Let r(g) = -65*g**3 + 60*g**2 + 40*g + 20. Let z(v) = -20*f(v) - r(v). Factor z(m).
5*m*(m - 6)*(m + 2)
Let r(v) be the first derivative of -1/3*v**6 - 69*v**4 - 33 - 645*v**2 + 450*v - 54/5*v**5 + 1172/3*v**3. Factor r(q).
-2*(q - 1)**3*(q + 15)**2
Let q(m) be the first derivative of 16*m**3/15 + 11*m**2/5 - 38*m/5 + 565. Solve q(y) = 0 for y.
-19/8, 1
Let i(g) = -g**2 + 3159*g - 3170. Let h(n) = -20*n**2 + 53700*n - 53890. Let l(x) = -2*h(x) + 35*i(x). Determine f, given that l(f) = 0.
-634, 1
Factor -344/3 + 94/3*c - 2/3*c**2.
-2*(c - 43)*(c - 4)/3
Let f be ((-57)/133)/(6 - (-96)/(-14)). Factor 74*y + f*y**2 + 2738.
(y + 74)**2/2
Let o(s) be the second derivative of -17/18*s**4 + 26/9*s**3 + 2*s + 28 + 7/60*s**5 - 4*s**2. Factor o(l).
(l - 2)**2*(7*l - 6)/3
Suppose -a + v + 39 = 8, -3*a = 4*v - 100. Solve -2*j + 26*j - 9*j**4 - a*j**2 + 36 - 24*j**3 + 5*j**4 = 0 for j.
-3, -1, 1
Let c = 11971/4 + -5637/2. Let n = c - 172. Find s such that 3/4*s**3 - 3/2*s + 3/4*s**5 + n*s**2 - 9/4*s**4 + 0 = 0.
-1, 0, 1, 2
Let t(i) = -65*i - 5. Let u(p) = 5*p**2 + 335*p + 63. Let o(m) = -m**2 - 67*m - 12. Let v(w) = -11*o(w) - 2*u(w). Let q(r) = 6*t(r) + 5*v(r). Factor q(j).
5*j*(j - 11)
Suppose 5*h + 5*k = -200, 10*k - 11*k - 122 = 3*h. Let u = h - -41. Solve 1/2*o**4 - o**3 + o + u - 1/2*o**2 = 0 for o.
-1, 0, 1, 2
Suppose 768/5 + 784/5*k - 52/5*k**2 - 64/5*k**3 + 4/5*k**4 = 0. Calculate k.
-3, -1, 4, 16
Let o(c) be the first derivative of c**4/16 + 7*c**3/4 - 11*c**2/4 - 5374. Factor o(p).
p*(p - 1)*(p + 22)/4
Let i(n) = -3*n**3 - 7*n**2 + 28*n + 6. Let v(f) = -8*f**3 - 12*f**2 + 56*f + 15. Let t(g) = -5*i(g) + 2*v(g). Factor t(r).
-r*(r - 7)*(r - 4)
Let y be (-14572370)/(-18235) + 0 + 34. Solve -2/7*k**2 - y - 216/7*k = 0.
-54
Let m = 3282036/17 - 66671081849/345338. Let b = m + -1/2902. Suppose -3/7*g + 1/7*g**2 - b = 0. What is g?
-1, 4
Suppose 24*c - 70 = 2. Factor 9*y - 15*y + 3*y + y**3 + c*y - y - 9 + 9*y**2.
(y - 1)*(y + 1)*(y + 9)
Suppose -6*f + 28 - 10 = 0. Factor -m**4 - 2*m**f + 2*m - 3*m**2 + 3*m**4 + 2 - 3*m**2 + 2.
2*(m - 2)*(m - 1)*(m + 1)**2
Let l(h) be the first derivative of 13*h**5/35 - 20*h**4/7 + 4*h**3/7 + 7207. Suppose l(c) = 0. Calculate c.
0, 2/13, 6
Let t = -23 - -19. Let n be 0 - (3 + t) - -3. Factor -35*o + 5*o**2 + 11 + 10*o**2 + n - 5*o**3 + 10*o**2.
-5*(o - 3)*(o - 1)**2
Let s(d) be the first derivative of -d**4/13 + 142*d**3/39 + 37*d**2/13 - 72*d/13 - 593. Determine n, given that s(n) = 0.
-1, 1/2, 36
Find j, given that 2/7*j**2 + 0 + 2944/7*j = 0.
-1472, 0
Factor -1 + 59*p**2 + 21*p**2 + 6 - 62*p + 17*p - 40*p.
5*(p - 1)*(16*p - 1)
Let l(f) be the third derivative of f**8/1344 - f**7/28 + 133*f**6/480 - 17*f**5/20 + 25*f**4/24 - 864*f**2 + 3. Suppose l(y) = 0. Calculate y.
0, 1, 2, 25
Suppose -2*l = 6 + 66. Let j(s) = s**2 - s. Let n(b) = 7*b - 2*b - 8*b**2 + 6*b + 0*b. Let d(x) = l*j(x) - 4*n(x). Find t, given that d(t) = 0.
-2, 0
Suppose 27 = 14*u - 1. Solve -85 + 96*a + u*a**2 + 661 + a**2 + a**2 = 0 for a.
-12
Let m(u) be the first derivative of u**4/24 + 401*u**3/18 - 403*u**2/6 + 9526. Factor m(c).
c*(c - 2)*(c + 403)/6
Let d(v) be the third derivative of -v**5/140 - 23*v**4/14 + 93*v**3/14 + 991*v**2. Factor d(k).
-3*(k - 1)*(k + 93)/7
Let z(g) be the second derivative of 1/360*g**5 - g - 7/72*g**4 - 7/2*g**2 + 49/36*g**3 + 0. Let f(i) be the first derivative of z(i). Factor f(q).
(q - 7)**2/6
Let x(g) be the first derivative of -g**3/3 - 4*g**2 - 7*g - 6852. Factor x(q).
-(q + 1)*(q + 7)
Let t be (-259)/(7770/320) - 16/(-1). Factor 2/3*d**5 + 14/3*d - t*d**3 - 4/3*d**4 + 8/3 - 4/3*d**2.
2*(d - 4)*(d - 1)*(d + 1)**3/3
Let g(o) be the first derivative of o**3/21 - 18*o**2/7 + 99*o/7 + 1275. Let g(k) = 0. Calculate k.
3, 33
Let b = 16829/5335 + 1329/1067. Factor 2/5*y**3 + 0 - b*y**2 + 0*y.
2*y**2*(y - 11)/5
Let h(i) = -47*i + 12*i**2 - 15*i**2 - 18*i. Let o(g) = 3*g**2 + 66*g. Let v(t) = 6*h(t) + 7*o(t