 0 + 1/4*a**4 + 1/20*a**5. Factor f(k).
3*(k - 2)*(k + 4)
Let h = -339 + 342. Factor 3*y**2 + 34*y**3 + 5*y**h - y - 38*y**3 - y**4 - 2.
-(y - 2)*(y - 1)*(y + 1)**2
Suppose -18*k = 6*k - 3*k + 9*k. Find c, given that 4/5*c + k*c**2 + 0 - 1/5*c**3 = 0.
-2, 0, 2
Let k(n) = -110*n**3 - 104*n**3 - 18*n - 5 - 13*n**2 + 230*n**3 - 4. Let i(u) = -7*u**3 + 6*u**2 + 8*u + 4. Let o(a) = 9*i(a) + 4*k(a). Factor o(b).
b**2*(b + 2)
Let b = -1910459/7 - -272923. Factor 36/7 - b*i**2 - 2*i.
-2*(i - 2)*(i + 9)/7
Let s be ((-414)/(-27))/((-4)/(-6)). Suppose -3*i = -98 + s. Factor -i*w + 25*w - 4 + w**2.
(w - 2)*(w + 2)
Let r(x) be the third derivative of -x**7/210 - x**6/15 - 7*x**5/20 - 3*x**4/4 - 2*x**2 - 1046*x + 2. Find u such that r(u) = 0.
-3, -2, 0
Let h(f) = f**4 + 428*f**3 - 2362*f**2 + 3468*f - 1583. Let r(i) = i**4 + 143*i**3 - 787*i**2 + 1153*i - 528. Let l(u) = -3*h(u) + 8*r(u). Factor l(j).
5*(j - 21)*(j - 5)*(j - 1)**2
Let y = -24398 - -243981/10. Let m(w) be the first derivative of 0*w + y*w**2 + 0*w**3 - 1/20*w**4 + 3. Solve m(b) = 0.
-1, 0, 1
Suppose 0 = 4*y - 48*y - 220. Let q be y - ((-110)/(-33) + -9). Factor q*h - 4 + 8/3*h**2 + 2/3*h**3.
2*(h - 1)*(h + 2)*(h + 3)/3
Let t(f) = -f**2 + 8*f + 51. Let k be t(12). Factor -25*j**4 - 10*j**k - 10*j**2 + 23*j**4 + 39*j + 36 + 8*j**2 + 3*j.
-2*(j - 2)*(j + 1)*(j + 3)**2
Let q = -4 - -6. Let h(v) = -8*v**2 + 4*v + 2*v + v**2 + q - 9. Let z(s) = s**2 - s + 1. Let g(l) = -5*h(l) - 40*z(l). Factor g(n).
-5*(n - 1)**2
Let i(x) be the second derivative of x**4/9 + 8*x**3/3 - 30*x**2 + 24*x + 1. Solve i(u) = 0.
-15, 3
Let p(f) be the third derivative of f**8/672 + f**7/210 - 19*f**6/12 - 571*f**5/60 - 1141*f**4/48 - 95*f**3/3 + 5*f**2 + 740*f. Factor p(h).
(h - 20)*(h + 1)**3*(h + 19)/2
Let k be 115/(-46) + 1193/2. Suppose k = -4*o + 602. Let -3/4*w**o - 1/4 - w = 0. What is w?
-1, -1/3
Let f(g) be the first derivative of -44*g**3/3 - 8*g**2 + 444*g - 6109. Factor f(t).
-4*(t - 3)*(11*t + 37)
Let o be (-24)/2*(-13)/26. Let u(g) = -6*g + 39. Let p be u(o). Factor 4*x**2 + 2*x - 2*x**2 + x**2 + x**p.
x*(x + 1)*(x + 2)
Let v = 497845 - 3484870/7. Solve -v - 39/7*o - 11/7*o**2 - 1/7*o**3 = 0 for o.
-5, -3
Let c(u) be the third derivative of 3*u**8/2240 - u**7/105 + u**6/80 + u**5/20 - 107*u**4/12 - 90*u**2. Let r(z) be the second derivative of c(z). Factor r(i).
3*(i - 2)*(i - 1)*(3*i + 1)
Let p(a) be the first derivative of -2*a**3/9 + 136*a**2/3 + 274*a/3 - 1503. Solve p(z) = 0 for z.
-1, 137
Let f(u) = -5*u**4 - 1595*u**3 + 4790*u**2 - 4810*u + 1600. Let j(q) = -q**3 - 2*q**2 - 1. Let a(n) = f(n) - 5*j(n). Let a(m) = 0. What is m?
-321, 1
Let k be (6864/(-396) + 0/(-1))*(-6)/16. Suppose -k*i**2 - 43/6*i**3 + 14/3*i**4 + 14/3*i - 2/3 = 0. Calculate i.
-1, 1/4, 2/7, 2
Let x(m) = -5*m + 5. Let y be x(-4). Let v = -23 + y. Let -12*q - 15*q**2 - 10*q**v + 22*q - 35*q**3 = 0. Calculate q.
-1, 0, 2/7
Let r(f) be the first derivative of -f**6/75 + 3*f**4/25 - 16*f**3/75 + 3*f**2/25 + 834. Factor r(b).
-2*b*(b - 1)**3*(b + 3)/25
Let l = 7122227/13 + -546953. Let d = -910 + l. Factor -12/13*k**3 - d - 24/13*k - 2/13*k**4 - 2*k**2.
-2*(k + 1)**2*(k + 2)**2/13
Let y(r) be the second derivative of -r**5/30 + r**4/12 + 20*r**3/3 + 53*r**2/2 + 103*r. Let g(a) be the first derivative of y(a). Factor g(d).
-2*(d - 5)*(d + 4)
Let n(y) be the third derivative of -11*y**8/216 + 43*y**7/105 + 221*y**6/540 - 1007*y**5/270 - 62*y**4/9 + 20*y**3/27 + 1447*y**2. Find i, given that n(i) = 0.
-1, 2/77, 2, 5
Suppose 13*j = -8*j + 147. Suppose 7 = -5*f + j. Factor 0*q**3 - 2*q**2 + f + 2/3*q**4 - 4/3*q.
2*q*(q - 2)*(q + 1)**2/3
Suppose 3*j = -14*j + j. Suppose 12*u + 5*u - 9*u = j. Factor u - 6/7*r**2 - 4/7*r - 2/7*r**3.
-2*r*(r + 1)*(r + 2)/7
Determine r, given that -580*r - r**3 - 4*r**2 - 2*r**2 - 3*r**2 + 640*r + 2*r**2 = 0.
-12, 0, 5
Let v(z) be the second derivative of -3*z - 1/3*z**4 - 2/15*z**6 + 7 - 4/5*z**5 + 1/21*z**7 + 7/3*z**3 + 4*z**2. Factor v(r).
2*(r - 4)*(r - 1)*(r + 1)**3
Let k(i) = -i**2 - 49*i + 42. Let f be k(-28). Let m = f - 628. Solve -2/11*z**4 - 10/11*z**3 - 14/11*z - 4/11 - 18/11*z**m = 0.
-2, -1
Factor 907926/11*h - 117727738/11 - 2334/11*h**2 + 2/11*h**3.
2*(h - 389)**3/11
Let o(q) be the second derivative of 0*q**2 + 0*q**3 + 1/28*q**4 - 1 + 3/140*q**5 + 9*q. Determine s so that o(s) = 0.
-1, 0
Let a(n) = 10*n**3 - 342*n**2 + 1652*n + 736. Let o(w) = 5*w**3 - 228*w**2 + 1102*w + 490. Let x(l) = 5*a(l) - 8*o(l). Find k such that x(k) = 0.
-15, -2/5, 4
Let v(f) = -f**2 + 29*f - 128. Let w be v(21). Let -1905*d**2 - w*d**3 + d**4 + 1943*d**2 + d**4 = 0. What is d?
0, 1, 19
Suppose 0 = -4*y + t + 2194 - 399, -4*y + 1799 = 3*t. Determine g, given that -346*g - 16 + y*g + 649*g - 8836*g**2 = 0.
2/47
Let m(d) be the first derivative of -5*d**6/6 + 90*d**5 + 925*d**4/4 - 150*d**3 - 460*d**2 + 2805. Let m(z) = 0. Calculate z.
-2, -1, 0, 1, 92
Suppose -14*k + 6 = -11*k + 3*d, -k = 3*d - 2. Factor 92/9*u - 2/9*u**k - 1058/9.
-2*(u - 23)**2/9
Let n be ((-146)/(-4))/(7/((-98)/7)). Let g = -70 - n. Solve -5*m + 6 - 10*m**4 + 20*m**2 + 10*m**g - 10 - 6 - 5*m**5 + 0 = 0 for m.
-2, -1, 1
Suppose -t - 2*p - 6 = 0, -61*p + 66*p + 22 = t. Let j be 6/(-60)*t*(-150)/105. Factor 1/7*g**5 + 3/7*g - 2/7*g**4 + j*g**2 - 4/7*g**3 + 0.
g*(g - 3)*(g - 1)*(g + 1)**2/7
Let q = -2/39235 + 78492/431585. Suppose 16/11*b**2 - 32/11*b + 14/11*b**4 + 32/11*b**3 + q*b**5 - 32/11 = 0. Calculate b.
-2, 1
Let s(h) = -h**3 + 15*h**2 + 9*h + 131. Let n be s(16). Let x(d) be the first derivative of 0*d**2 + 12*d - n - 3*d**3 + 3/4*d**4. Factor x(c).
3*(c - 2)**2*(c + 1)
Let a(n) = -n**3 - 7*n**2 - 3*n - 93. Let m be a(-8). Let t(k) = 4*k**2 - 11*k - 20. Let v(i) = 5*i**2 - 12*i - 23. Let z(j) = m*v(j) + 6*t(j). Factor z(o).
-(o + 1)*(o + 5)
Let n(h) = -h**3 + 51*h**2 - 344*h. Let c be n(8). Determine p, given that 2/5*p**3 - 18/5*p**2 + 0 + c*p = 0.
0, 9
Let k = -186 - -226. Suppose -28*s + k*s = 0. What is d in 6/19*d**4 + 0 + 2/19*d**2 - 6/19*d**3 + s*d - 2/19*d**5 = 0?
0, 1
Let i = -1/1107928 + 7755499/3323784. Solve -66*z + 56/3 + i*z**2 = 0.
2/7, 28
Suppose -155/3*o - 1/3*o**3 + 77/3 + 79/3*o**2 = 0. Calculate o.
1, 77
Let k(y) = -4*y**2 - 77*y + 77. Let p be k(-20). Let z(l) be the first derivative of p + 18/7*l**2 - 4/3*l**3 - 8/7*l. Factor z(g).
-4*(g - 1)*(7*g - 2)/7
Let z(r) be the second derivative of -r**5/15 + r**4/3 + 16*r**2 + 5*r + 2. Let u(w) be the first derivative of z(w). Factor u(s).
-4*s*(s - 2)
Let h(a) be the third derivative of a**6/240 + 731*a**5/120 - 61*a**4/4 + a**2 - 1906. Determine g, given that h(g) = 0.
-732, 0, 1
Factor -615/4*x + 619 - 1/4*x**2.
-(x - 4)*(x + 619)/4
Let k(y) be the third derivative of -3*y**7/385 - 3*y**6/110 + 31*y**5/330 + 2*y**4/33 - 4*y**3/11 - 1268*y**2. Let k(z) = 0. What is z?
-3, -2/3, 2/3, 1
Let k(b) be the third derivative of b**6/40 + b**5/5 - 5*b**4/2 - 24*b**3 + 1144*b**2 + b. Solve k(v) = 0 for v.
-6, -2, 4
Let q(w) be the third derivative of -w**8/448 - 17*w**7/280 - 63*w**6/160 + 81*w**5/80 - 2*w**2 - 207*w + 2. Find b, given that q(b) = 0.
-9, 0, 1
Solve 74163*l**4 - 2895*l**2 - 35 - 424*l**3 - 74353*l**4 - 1405*l - 1291*l**3 = 0.
-7, -1, -1/38
Let n(j) be the first derivative of 2*j**5/35 - j**4 - 34*j**3/21 + 30*j**2/7 + 556. Suppose n(t) = 0. Calculate t.
-2, 0, 1, 15
Let u(z) = 13*z - 18*z**3 - 5287 + 17*z - 5*z**4 + 5281 - z**2. Let h(t) = -5*t**4 - 20*t**3 + 30*t - 5. Let b(s) = 6*h(s) - 5*u(s). Factor b(n).
-5*n*(n - 1)*(n + 1)*(n + 6)
Find l such that 7416/5*l**2 + 15105858048/5 + 18332352/5*l + 1/5*l**3 = 0.
-2472
Let l = -1673 - -1676. Let s(b) be the second derivative of 5/14*b**4 - 4/7*b**2 + 0 + 13*b + 4/21*b**l. Solve s(m) = 0 for m.
-2/3, 2/5
Let g be (50/14 - 1) + (-291)/(-679). Suppose -5*m = -g*m - 4. Suppose -16*s**2 + 4*s**3 - 5*s**3 + 8*s**m + 19*s - 10 = 0. What is s?
-10, 1
Let m(f) = -25 - f + 22 + 47*f + 10 + 5*f**2. Let h(g) = 25*g**2 + 231*g + 43. Let x(d) = 6*h(d) - 33*m(d). Suppose x(b) = 0. Calculate b.
-9, 1/5
Let q = 88 - 93. Let x(r) = 5*r**2 - 7*r + 30. Let z(h) = -3*h**2 + 4*h - 20. Let k(n) = q*x(n) - 8*z(n). Factor k(p).
-(p - 5)*(p + 2)
Let y be 17 + 0 + 0/8. Let z(t) = y*t + 12*t**2 + 12 - 8 + 15. Let k(w) = -4*w**2 - 6*w - 6. Let g(o