, 1
Let i = -27027 - -27027. Let c(j) be the first derivative of 0*j + 2/15*j**3 + i*j**2 - 27 + 2/15*j**4 + 2/75*j**5. Factor c(z).
2*z**2*(z + 1)*(z + 3)/15
Let f(n) = -21*n**2 - 295*n + 56. Let s(w) = w**2 - 1. Let p(i) = -f(i) + 4*s(i). Determine b, given that p(b) = 0.
-12, 1/5
Let k(q) = -q**3 + 5*q**2 - 14. Let f be k(4). Factor 30*o**4 - f*o**3 + 4*o**2 - 16*o**4 - 16*o**4.
-2*o**2*(o - 1)*(o + 2)
Let b = -20180 + 20182. Determine j, given that -2/5*j**3 + 16/5*j + 0 + 68/15*j**b = 0.
-2/3, 0, 12
Factor c**3 + 3*c - 5128*c**2 + 5054*c**2 - 3*c.
c**2*(c - 74)
Factor 4/3*h**4 + 400/3 - 56/3*h**3 - 560/3*h + 92*h**2.
4*(h - 5)**2*(h - 2)**2/3
Let i(t) = 3*t**3 - 116*t**2 - 93*t + 30622. Let v(l) = 3*l**3 - 117*l**2 - 90*l + 30621. Let b(n) = -3*i(n) + 4*v(n). Factor b(s).
3*(s - 27)**2*(s + 14)
Suppose 2*v = -r - 2*r + 35, -2*v - 85 = -5*r. Suppose -11 = 2*q - r. Factor 7*u**3 + q*u + 5*u**2 - 2*u**2 - u**3 - 5*u**3.
u*(u + 1)*(u + 2)
Let a be (((-6)/(-20))/((-3969)/315))/((-305)/(-18) - 17). Solve -18/7*y**2 + 0*y + a*y**4 + 3/7*y**3 + 0 = 0 for y.
-3, 0, 2
Let n(t) = t + 10644. Let r be n(0). Factor 10639*v**3 + 6*v**2 - r*v**3 + 2*v**4 - 4*v**2.
v**2*(v - 2)*(2*v - 1)
Let o be 20/25 - ((-1836)/20 + -2). Let d = -94 + o. Factor d*r**2 + 0 + 0*r - 1/5*r**3.
-r**2*(r - 3)/5
Let a(h) be the second derivative of -h**7/49 + 79*h**6/70 - 1683*h**5/140 + 1079*h**4/28 - 781*h**3/14 + 279*h**2/7 - 2*h + 1. Solve a(g) = 0 for g.
1/2, 1, 6, 31
Let j(f) be the third derivative of 5*f**8/448 - 5*f**7/42 + 19*f**6/48 - f**5/2 - 5*f**4/96 + 5*f**3/6 - 204*f**2. Determine u so that j(u) = 0.
-1/3, 1, 4
Let l(q) be the first derivative of 56 + 3/5*q**5 + 213*q**4 + 30246*q**3 + 76235043*q + 2147466*q**2. Let l(w) = 0. Calculate w.
-71
Let p(q) be the second derivative of -1/7*q**4 - 6/7*q**2 - 1 + 13*q + 11/21*q**3 + 1/70*q**5. Suppose p(z) = 0. Calculate z.
1, 2, 3
Factor -725*y - 9*y**2 + 10*y**2 + 33*y + y**2.
2*y*(y - 346)
Suppose -8*x - 15 - 1 = 0. Let t(i) = 2*i**3 + 4*i**2 + 3. Let j be t(x). Factor -40 + 2*r**2 - 32*r**2 + 7*r - 5*r**j - 31*r - 36*r.
-5*(r + 2)**3
Let n(q) be the first derivative of -5*q**4/2 + 214*q**3/3 - 442*q**2 + 320*q - 6837. Let n(y) = 0. What is y?
2/5, 5, 16
Let j(z) be the third derivative of -z**6/120 + 119*z**5/60 - 61*z**2 - 3*z. Factor j(q).
-q**2*(q - 119)
Suppose 128*m - 125*m + 4*l = -16, 2*m - 12 = 3*l. Let m - 1/2*k**2 - 1/2*k = 0. What is k?
-1, 0
Let c(y) be the first derivative of 4*y**5/5 + 35*y**4/3 - 212*y**3/9 - 22*y**2/3 + 104*y/3 + 141. Suppose c(m) = 0. What is m?
-13, -2/3, 1
Let x(i) = -1664 + 850 + 7*i + 856 - i. Let f be x(-7). Factor f*v - 3/7*v**4 + 0*v**2 + 0 - 3/7*v**3.
-3*v**3*(v + 1)/7
Solve -62*p**2 - 59*p**2 + 17*p - 15 + 3*p + 116*p**2 = 0 for p.
1, 3
Let -1/3*y**3 - 20 + 56/3*y - 11/3*y**2 = 0. What is y?
-15, 2
Let d(u) be the first derivative of 2*u**5/25 + u**4 + 6*u**3/5 - 1579. Determine w so that d(w) = 0.
-9, -1, 0
Let v(n) be the second derivative of 0*n**2 - 7/24*n**4 + 1/2*n**3 + 17 - 4*n + 1/40*n**5. Determine b, given that v(b) = 0.
0, 1, 6
Determine f, given that 41/5*f**2 + 174/5*f - 216/5 + 1/5*f**3 = 0.
-36, -6, 1
Determine n, given that 60*n**4 - 7*n - 3*n**2 - 12*n**4 - 47*n**4 + 6 + 3*n**3 = 0.
-3, -2, 1
Suppose 0 = 9*w - 28 - 8. Let y(f) = -210*f. Let t be y(-1). Let t*u**3 - 16*u**4 + 84*u - 12 - 142*u**2 - 59*u**w - 65*u**2 = 0. What is u?
2/5, 1
Let l = -199 + 217. Solve 138*v - 3*v**2 - 117*v + 0*v**2 - l = 0 for v.
1, 6
Suppose 28*n - 663 = 11*n. Factor n*u + 24 - 21 + 21*u - 2*u**2 - 61.
-2*(u - 29)*(u - 1)
Find g such that g**2 - 449*g - 2614 + 474*g + 2714 = 0.
-20, -5
Suppose -5*b + 36 = 4*y - 9*b, 5*b + 25 = 0. Factor -17*u**4 - 15*u**4 + y*u**5 - 4*u**3 + 3*u**3 - 3*u**3 + 0*u**5 + 32*u**2.
4*u**2*(u - 8)*(u - 1)*(u + 1)
Let d(f) be the first derivative of f**4/20 - 29*f**3/5 - f**2/10 + 87*f/5 + 2775. Factor d(k).
(k - 87)*(k - 1)*(k + 1)/5
Let n(s) be the first derivative of -4*s**5/5 + 17*s**4 + 292*s**3 + 830*s**2 - 2600*s + 233. Factor n(o).
-4*(o - 26)*(o - 1)*(o + 5)**2
Let x(z) = 4*z**2 - 4*z**2 + 2*z**2 - 2 + 4*z**2 - 5*z**2. Let t(g) = -4*g**2 + 18*g + 10. Let l(v) = -3*t(v) - 15*x(v). Factor l(w).
-3*w*(w + 18)
Let v(w) = -7*w**4 - 199*w**3 - 1285*w**2 - 2682*w - 1594. Let j(z) = -4*z**4 - z**3 - z**2 - 1. Let p(s) = -j(s) + v(s). Find q, given that p(q) = 0.
-59, -3, -1
Let j(u) be the first derivative of -u**3/8 + 825*u**2/8 - 226875*u/8 - 127. Find b, given that j(b) = 0.
275
Factor 4*v**3 - 24 + 24 - 76*v - 3687*v**2 + 3384*v**2.
v*(v - 76)*(4*v + 1)
Let o = -337813 - -3715945/11. Let i = -1 - -3. Factor o*l**i - 4/11 + 2/11*l.
2*(l - 1)*(l + 2)/11
Let x(j) = 9*j**2 - 836*j - 214379. Let i(g) = 10*g**2 - 827*g - 214380. Let n(y) = 10*i(y) - 11*x(y). Determine b, given that n(b) = 0.
-463
Let a(i) be the first derivative of 2*i**3/15 - 34*i**2 + 2890*i + 2016. Factor a(f).
2*(f - 85)**2/5
Let m(s) = -s**3 - 16*s**2 - 206*s - 874. Let h be m(-6). Factor 1/2*d - 3*d**h + 5/2.
-(d - 1)*(6*d + 5)/2
Suppose -70*p = -58*p - 36. Suppose 3*r - 15 = -3*z, -p*z + 2 = -5*r + z. Factor 1/2*j**3 + 1/4*j**4 + 0*j**r + 0 + 0*j.
j**3*(j + 2)/4
Let f(v) = v**3 - 31*v**2 - 51*v + 192. Let p be f(32). Let u = p + 2081/5. Solve 1/5*y**2 + 0 + 0*y + u*y**5 + 3/5*y**3 + 3/5*y**4 = 0.
-1, 0
Let o be 6/(-1 + 1 + 12/13002). Suppose 0*k**2 + 8*k**2 + 6505*k - o*k - 4*k**2 = 0. What is k?
-1, 0
Let w(z) be the first derivative of -39*z**5/4 + 387*z**4/16 - 53*z**3/4 - 63*z**2/8 + 15*z/2 - 4324. Find p, given that w(p) = 0.
-2/5, 5/13, 1
Let w(x) be the second derivative of -x**4/96 - 37*x**3/24 + 231*x**2/16 - x - 5854. Determine u, given that w(u) = 0.
-77, 3
What is h in -880/9 - 2/9*h**2 + 76/3*h = 0?
4, 110
Let k(x) = x**4 + 4*x**3 - 16*x**2 - 28*x - 15. Let q(r) = 2*r**3 + r**2 - 1. Let u(b) = -k(b) + 3*q(b). Factor u(d).
-(d - 6)*(d + 1)**2*(d + 2)
Let d be (-1234)/(-266) - (-23 + 26). Let l = 42/19 - d. Factor 1/7*p**5 + 0*p + l*p**2 - 4/7*p**4 + 0 - 1/7*p**3.
p**2*(p - 4)*(p - 1)*(p + 1)/7
Let h(i) be the first derivative of i**4/4 - i**3/3 + 2*i - 11. Let k(u) = 16*u**3 - 84*u**2 + 4*u + 104. Let w(l) = 20*h(l) - k(l). Solve w(g) = 0 for g.
-16, -1, 1
Suppose 10 - 12 = -j + 5*c, -5*j + 160 = 5*c. Factor -176*h**3 + 352*h**3 - 181*h**3 - j*h + 102*h - 10*h**2.
-5*h*(h - 3)*(h + 5)
Let n(k) be the third derivative of k**6/8 - 73*k**5/20 + 95*k**4/4 + 44*k**3 - 5*k**2 + 16*k. Suppose n(b) = 0. What is b?
-2/5, 4, 11
Solve 0 - 66246/17*p**2 + 730/17*p**3 - 66978/17*p - 2/17*p**4 = 0 for p.
-1, 0, 183
Let v = -49 + 52. Suppose -5*s - 5*g + 33 = -2, -g = -v*s + 9. Factor -s*l**2 + 933 - 933.
-4*l**2
Find a such that 720/13 - 170/13*a**2 + 964/13*a + 6/13*a**3 = 0.
-2/3, 9, 20
Suppose -77*t + 75*t + 6 = 0. Find i such that -9*i**4 - 114*i**2 - 10 - 7 - 4 - 81*i - 66*i**t + 3*i**5 = 0.
-1, 7
Let f(g) = 2272*g + 195394. Let p be f(-86). Factor 0 + 4/7*v**3 - 88/7*v + 12*v**p.
4*v*(v - 1)*(v + 22)/7
Let v = -426 + 428. Suppose 50*a - 5*a**v + 29*a**2 - 17 - 6*a**2 + 142 - 13*a**2 = 0. What is a?
-5
Let l(a) be the second derivative of a**5/20 - 7*a**3/2 + 10*a**2 - 65*a + 1. Let l(j) = 0. What is j?
-5, 1, 4
Solve -86/7*w - 8 - 1/7*w**3 - 31/7*w**2 = 0 for w.
-28, -2, -1
Let u(z) be the third derivative of z**7/1470 + z**6/120 - z**5/420 - z**4/24 + 8925*z**2. Let u(s) = 0. Calculate s.
-7, -1, 0, 1
Let q(n) be the second derivative of -n**6/540 + 2*n**5/45 + n**4/4 - 11*n**3/6 + 86*n. Let j(a) be the second derivative of q(a). Determine o so that j(o) = 0.
-1, 9
Let d = 1733/858 - 387/286. Let 1/3 - 1/6*u**5 + 1/3*u**3 - 1/6*u + 1/3*u**4 - d*u**2 = 0. What is u?
-1, 1, 2
Determine y so that -46/7*y**3 + 46/7*y - 2/7*y**4 + 0 + 2/7*y**2 = 0.
-23, -1, 0, 1
Let r be (178009 - 1)/(-7 + (-85)/(-10)). Suppose -115*d**2 - 2*d**3 - r - 825*d + 35*d**2 - 8301*d - 154*d**2 + 34 = 0. Calculate d.
-39
Suppose 3*c = 22 - 13. Factor 3469*r**4 - c*r**3 - 3466*r**4 + 0*r**3.
3*r**3*(r - 1)
Let q(l) be the third derivative of l**7/525 + 61*l**6/600 - 469*l**5/100 + 838*l**4/15 - 1504*l**3/15 - l**2 + 661. Suppose q(w) = 0. What is w?
-47, 1/2, 8
Suppose -4*t - 5*r + 27 = -0*r, 3*r - 6 = t. Let g(j) = j**2 - 7*j + 3. Let u(q) = q**2 - 13*q + 5. Let z(b) = t*u(b) - 5*g(b). Factor z(