2*c**3*(c + 1)/15
Factor -176*g**3 + 41*g**2 - 1080 + 756*g + 31*g**2 - 145*g**4 + 193*g**4 - 4*g**5.
-4*(g - 5)*(g - 3)**3*(g + 2)
Determine b so that -509*b**3 + 2358*b + 1628*b**3 - 2046*b**2 - 436*b - 2*b**4 - 543*b**3 - 450*b**3 = 0.
0, 1, 31
Let i(o) = -o**2 - 45*o - 50. Let j be i(-44). Let r(w) = -2*w**2 - 5*w. Let m(p) = -p**3 - 3*p**2 - 8*p + 1. Let c(d) = j*m(d) + 14*r(d). Solve c(k) = 0.
-1, -1/3, 3
Let l = 224 + -216. Factor -11*o**2 + 14*o**5 + 4*o**4 - 3*o**2 - 27*o**5 - l*o - 3*o**3 + 14*o**5.
o*(o - 2)*(o + 1)**2*(o + 4)
Let n(r) be the first derivative of -r**6/24 - r**5/5 + 3*r**4/16 + 5*r**3/6 - r**2 - 1075. Determine i so that n(i) = 0.
-4, -2, 0, 1
Let r(w) be the first derivative of -75*w**2 - 35/3*w**3 + 32 + 45*w. Let f(y) = -18*y**2 - 75*y + 22. Let t(g) = -5*f(g) + 2*r(g). Factor t(d).
5*(d + 4)*(4*d - 1)
Let p = -107 + 111. Let s(y) = -y**3 + 111*y**2 + 591*y + 1009. Let x(d) = -28*d**2 - 148*d - 252. Let i(h) = p*s(h) + 18*x(h). Factor i(u).
-4*(u + 5)**3
Let l(j) be the first derivative of 32 - 13/30*j**3 - 2/5*j - 1/50*j**5 - 3/20*j**4 - 3/5*j**2. Solve l(x) = 0 for x.
-2, -1
Suppose -4*w - 6*u + 8*u - 72 = 0, w + 4*u = -9. Let i = 88/5 + w. Factor 0*d**2 + 6/5*d**3 + 0*d**4 - 3/5*d + 0 - i*d**5.
-3*d*(d - 1)**2*(d + 1)**2/5
Let o(v) be the third derivative of 1/280*v**6 - 34*v**2 + 256000/7*v**3 + 2400/7*v**4 + 0 + 12/7*v**5 + 0*v. Factor o(m).
3*(m + 80)**3/7
Let v(c) be the second derivative of -c**5/4 + 25*c**4/6 + 85*c**3/6 - 165*c**2 - 2495*c. Factor v(d).
-5*(d - 11)*(d - 2)*(d + 3)
Let m(g) = 73*g + 4750. Let f be m(-65). Let x(r) be the third derivative of 8*r**3 + 0 - 4*r**2 + 0*r - 7/20*r**f - 27/4*r**4. Let x(i) = 0. What is i?
-8, 2/7
Let r(o) = 5*o**4 - 24*o**3 + 27*o**2 + 32*o + 12. Let x(w) = w**4 - w**3 + w**2 - w + 2. Let k(a) = -r(a) + 6*x(a). Solve k(u) = 0 for u.
-19, -1, 0, 2
Let o(f) be the second derivative of -f**5/20 + 2281*f**4/12 + 1141*f**3/3 + 2716*f. Determine q, given that o(q) = 0.
-1, 0, 2282
Factor 0 + 149/2*k - 1/2*k**2.
-k*(k - 149)/2
Suppose -p + 27 = 2*u, -189*u + 3 = -190*u + p. Solve 16/3*k + u + 2/3*k**2 = 0 for k.
-6, -2
Let g(y) be the first derivative of -y**5/40 + 3*y**4/8 + 115*y - 38. Let q(k) be the first derivative of g(k). Factor q(r).
-r**2*(r - 9)/2
Let p(i) be the first derivative of 1/10*i**5 - 3/2*i**4 - 118 - 21/2*i**2 + 8*i + 37/6*i**3. Suppose p(r) = 0. Calculate r.
1, 2, 8
Let d(n) be the third derivative of n**8/13440 + n**7/5040 - n**6/240 - 23*n**4/8 + 153*n**2. Let u(m) be the second derivative of d(m). Factor u(p).
p*(p - 2)*(p + 3)/2
Let y(j) be the second derivative of j**5/35 - 271*j**4/7 + 15776*j**3 - 47096*j**2 - 2218*j. Solve y(k) = 0.
1, 406
Let a = 103 - 80. Factor -19 + 139 - 27*r - a*r - 3*r**2 - 2*r**2.
-5*(r - 2)*(r + 12)
Let q = 74/5 + -14. Let g = -5105 - -25527/5. Factor q*u**2 + g*u + 0 + 2/5*u**3.
2*u*(u + 1)**2/5
Let w(z) be the first derivative of -z**4/8 + z**3/3 + 13*z**2/4 + 5*z - 728. Factor w(s).
-(s - 5)*(s + 1)*(s + 2)/2
Let -1/7*r**3 - 64*r**2 - 446/7 - 893/7*r = 0. What is r?
-446, -1
Let l(q) be the third derivative of 2*q**7/105 + 19*q**6/30 - 41*q**5/15 + 7*q**4/2 + 1188*q**2. Let l(j) = 0. Calculate j.
-21, 0, 1
Let f = 133819/92 + -33426/23. Factor 1/4*x**4 - 1/4*x**3 + 0 - f*x**2 - 3/4*x.
x*(x - 3)*(x + 1)**2/4
Factor 22500/7*b - 3/7*b**4 - 150/7*b**3 - 67500/7 - 975/7*b**2.
-3*(b - 5)**2*(b + 30)**2/7
Let l(k) be the second derivative of 8*k**7/21 - 8*k**6/5 - 23*k**5 + 8*k**4/3 + 58*k**3 + 56*k**2 + 3*k + 214. Solve l(m) = 0 for m.
-4, -1/2, 1, 7
Let y(l) be the second derivative of l**6/40 + l**5/4 + l**4/4 - 4*l**3 + 44*l**2 + 3*l. Let o(h) be the first derivative of y(h). Factor o(c).
3*(c - 1)*(c + 2)*(c + 4)
Let t(z) be the first derivative of -z**4/20 + 27*z**3 + 407*z**2/5 + 5333. Let t(n) = 0. What is n?
-2, 0, 407
Let v(c) be the third derivative of -13/24*c**4 + 7/60*c**5 - 5*c**2 - 1/210*c**7 + 1/120*c**6 + c**3 + 0*c + 22. Solve v(i) = 0.
-3, 1, 2
Factor 29*t**3 - 2*t**5 - 196*t + 27*t**3 + 53*t**3 - 43*t**3 + 4*t**5 - 26*t**4 + 154*t**2.
2*t*(t - 7)**2*(t - 1)*(t + 2)
Let s = 579 + -527. Let k(x) = -5*x**2 + 7*x + 6. Let j(q) = -44*q**2 + 62*q + 52. Let z(p) = s*k(p) - 6*j(p). Factor z(o).
4*o*(o - 2)
Let t(q) be the first derivative of 20/63*q**3 + 4/3*q - 1/42*q**4 + 143 - 23/21*q**2. Factor t(l).
-2*(l - 7)*(l - 2)*(l - 1)/21
Let y(o) be the third derivative of o**5/30 - 77*o**4/2 + 920*o**3/3 - 8068*o**2. Factor y(m).
2*(m - 460)*(m - 2)
Let v(t) be the second derivative of 0*t**3 + 0*t**2 + 0 + 0*t**4 - 5/2*t**5 - 23/6*t**6 + 25/42*t**7 - 100*t. Factor v(f).
5*f**3*(f - 5)*(5*f + 2)
Let u be (17/((-374)/33)*16/(-36))/(12/9). Factor -5/2 + 3/2*k**4 - 5*k**2 - 27/4*k + 1/4*k**5 + u*k**3.
(k - 2)*(k + 1)**3*(k + 5)/4
Factor -54675 - 54945*t - 811/3*t**2 - 1/3*t**3.
-(t + 1)*(t + 405)**2/3
Let x = -291 + -13. Let i = -1823/6 - x. Factor 0*g**3 + i*g**4 - 1/6*g**2 + 0 + 0*g.
g**2*(g - 1)*(g + 1)/6
Let u(f) = -f**2 - 2083*f - 4171. Let i(c) = 1040*c + 2085. Let h(n) = 9*i(n) + 5*u(n). Factor h(a).
-5*(a + 2)*(a + 209)
Suppose -7*x = -8 - 27. Factor 9*s**2 + 11 - x + 101*s**3 - 104*s**3 + 15*s - 3*s**4.
-3*(s - 2)*(s + 1)**3
Suppose 1193 = 3490*k - 9277. Determine u so that -16/3*u + 16/3*u**k - 8*u**2 + 20/3 + 4/3*u**4 = 0.
-5, -1, 1
Let z = 7144 + -14287/2. Solve 8/3*r + 2/3 + 13/6*r**2 + z*r**3 = 0.
-2, -1/3
Let k(b) be the third derivative of 4/105*b**5 + 0*b**3 - 1/735*b**7 + 0 + 1/420*b**6 + 0*b - 1/7*b**4 + 155*b**2. Factor k(y).
-2*y*(y - 2)**2*(y + 3)/7
Let z(d) = -d**3 + 16*d**2 + 40*d - 21. Let n be z(18). Let t = n - 49. Determine k so that 1/4 - 1/2*k**t + 1/4*k + 1/4*k**4 - 1/2*k**3 + 1/4*k**5 = 0.
-1, 1
Let t(w) be the first derivative of -w**7/5880 - w**6/360 - w**5/210 + w**4/14 - w**3/3 + 37*w**2/2 + 28. Let q(k) be the third derivative of t(k). Factor q(x).
-(x - 1)*(x + 2)*(x + 6)/7
Let z(p) = 620*p**2 - 620*p + 72. Let l(a) = 2*a**2 - 26. Let c(d) = 6*l(d) + 2*z(d). Find u such that c(u) = 0.
-3/313, 1
Suppose 0 = 13*t + 272 - 350. Let q be 20/2 + -2 + 1. Let 4*g - 4*g - t*g**3 + q*g**4 - 3*g**5 = 0. What is g?
0, 1, 2
Let u(s) be the second derivative of s**5/80 + 5*s**4/16 - 37*s**3/24 - 51*s**2/8 - s + 28. Let u(v) = 0. Calculate v.
-17, -1, 3
Let i(j) = 59*j**2 - 37*j - 138. Let c(h) = 167*h**2 - 112*h - 411. Let m(k) = -6*c(k) + 17*i(k). Determine l, given that m(l) = 0.
-40, -3
Let t(g) be the second derivative of 0*g**2 - 5 + 0*g**4 + 8/15*g**3 - 13*g - 1/100*g**5. Determine o, given that t(o) = 0.
-4, 0, 4
Let i be -113*(-1 - 1) - (101 - 106). Factor 30 - i*x**2 - 28*x + 115*x**2 + 114*x**2.
-2*(x - 1)*(x + 15)
Let r(k) be the third derivative of 0*k**3 + 0 + 3/280*k**8 - k + 1/60*k**4 + 4/175*k**7 - 1/150*k**6 - 2/75*k**5 + 3*k**2. Factor r(p).
2*p*(p + 1)**2*(3*p - 1)**2/5
Let k = 4541/8090 + -261/1618. Solve -k*d**3 - 1/5*d**5 + 3/5*d + 0 - 4/5*d**4 + 4/5*d**2 = 0.
-3, -1, 0, 1
Factor 102/7 + p**2 + 359/7*p.
(p + 51)*(7*p + 2)/7
Factor -504/13 - 216/13*b - 10/13*b**2 + 2/13*b**3.
2*(b - 14)*(b + 3)*(b + 6)/13
Let l = 20 + -18. Suppose -5*v - l*s = -0*v - 2544, -5*s - 2022 = -4*v. Suppose i + i + v - 512 + 2*i**2 = 0. What is i?
-2, 1
Determine w so that 8/17*w**2 - 40/17*w + 6/17*w**3 + 0 = 0.
-10/3, 0, 2
Let r be -18*(-9)/4*24/18. Let q be 2/(-6) + (-3)/(r/(-186)). Factor 145*o - 80*o - 75*o + q*o**3 - 45*o**2 + 45*o**4.
5*o*(o - 1)*(o + 1)*(9*o + 2)
Let k be (-160*(-7)/(-119))/((-1646)/21). Let c = k - 2/823. Suppose 4/17*n + 0 + c*n**2 = 0. Calculate n.
-2, 0
Determine x so that 10*x**2 - 275 - 2195/2*x = 0.
-1/4, 110
Solve -74*j**2 + 2/5*j**3 - 366/5 + 734/5*j = 0 for j.
1, 183
Let v(x) be the first derivative of -23 - 10082/11*x - 2/33*x**3 + 142/11*x**2. Let v(d) = 0. What is d?
71
Let n(g) be the second derivative of 2*g**7/21 + 8*g**6/3 + 67*g**5/5 + 44*g**4/3 - 136*g**3/3 - 128*g**2 + 1215*g. Suppose n(q) = 0. What is q?
-16, -2, -1, 1
Let p = 3669/44 - 3661/44. Factor 2/11*j**2 - p*j**3 + 0 + 0*j.
-2*j**2*(j - 1)/11
Let m(t) be the first derivative of -t**6/21 - 26*t**5/35 - 17*t**4/7 + 32*t**3/7 - 1499. Solve m(k) = 0.
-8, -6, 0, 1
Let d(t) be the third derivative of 13/24*t**6 + 1/42*t**7 + 58 + 4*t**5 + 0*t + 2*t**2 + 80/3*t**3 + 85/6*t**4. Find f such 