**2 - 9*h**2 + 3*h**3 + d*h**4 + 6*h - 9*h**5 - 12*h**4 = 0. Calculate h.
-1, 0, 2/3, 1
Let x = -11 - -631. Solve -x*d + d**3 - 14*d**2 + 620*d = 0 for d.
0, 14
Suppose -8 = 4*z + 2*d - 6, z - 4 = 4*d. Let c = 323 + -321. Factor 3/2*b**c + 0 + z*b.
3*b**2/2
Let p = -4426 + 6429/2. Let t = -1211 - p. Factor -1/2*v**2 + 1/4*v**3 - 1/4*v + t.
(v - 2)*(v - 1)*(v + 1)/4
Let r be (-3 - 8/(-6))*18/(-5). Let g(q) = -q**4 + q**3 + q**2 + 2*q. Let l(w) = -3*w**4 - 9*w**3 + 9*w**2 + 75*w - 54. Let o(s) = r*g(s) - l(s). Factor o(a).
-3*(a - 3)**2*(a - 1)*(a + 2)
Let p(h) be the first derivative of -6*h**4 + 21*h**3 + 12*h**2 - 63*h - 1491. Factor p(k).
-3*(k - 1)*(k + 1)*(8*k - 21)
Let x(n) be the second derivative of -1/20*n**5 - 3/2*n**3 + 3*n + 0*n**2 + 3 - 5/6*n**4. Solve x(r) = 0.
-9, -1, 0
Factor -467/4*d**2 + 0 + 233/2*d + 1/4*d**3.
d*(d - 466)*(d - 1)/4
Let n(o) = 5*o + 28. Let b be n(-5). Suppose -q + 3*v = -12, -14*q + 5*v = -18*q - b. Factor -6*r**2 - 80/3*r + 14/3*r**q + 8.
2*(r - 3)*(r + 2)*(7*r - 2)/3
Let s(t) be the third derivative of t**7/490 + 9*t**6/70 + 81*t**5/35 + t**2 + 64*t. Factor s(y).
3*y**2*(y + 18)**2/7
Suppose 0 = -3*j + 22 + 14. Suppose 0 = 7*o - 10*o + j. Factor -2*p**3 + o*p**3 - 66*p + 58*p.
2*p*(p - 2)*(p + 2)
Let y(z) be the second derivative of -z**7/14 + 6*z**6/5 - 81*z**5/20 - z**4 + 18*z**3 + 467*z. Determine n so that y(n) = 0.
-1, 0, 2, 9
Let c(a) be the second derivative of -25/24*a**4 + 9 + 35/36*a**3 + 3/8*a**5 - 1/36*a**6 + 6*a + 0*a**2. Suppose c(d) = 0. Calculate d.
0, 1, 7
Determine b so that 8/9*b**3 - 50/9*b - 1/9*b**4 + 7/9*b**2 - 16/3 = 0.
-2, -1, 3, 8
Let v(r) be the first derivative of 55/9*r**3 - 5/36*r**6 + 307 - 20*r + 35/8*r**4 - 25/3*r**2 + 1/3*r**5. Let v(p) = 0. Calculate p.
-2, -1, 1, 6
Let u(j) = -j**2 - j - 1. Let s(i) be the first derivative of -i**4/4 - i**3 - 4*i**2 - 6*i + 30. Let f(a) = -5*s(a) + 30*u(a). Find d, given that f(d) = 0.
0, 1, 2
Let v = 36 - 32. Let g(a) = 2*a**2 - 11*a + 15. Let z be g(v). Let 0*f**2 - 1/3 + 1/6*f**z - 1/2*f = 0. Calculate f.
-1, 2
Let t(r) be the third derivative of r - 74*r**2 - r**5 + 0 + 0*r**3 + 75/2*r**4 + 1/120*r**6. Factor t(i).
i*(i - 30)**2
Let v(a) be the second derivative of 0 + 23*a + 0*a**2 - 3/20*a**5 + 0*a**4 - 1/14*a**7 + 0*a**3 + 1/5*a**6. Factor v(r).
-3*r**3*(r - 1)**2
Let d(c) be the second derivative of c**4/54 - 50*c**3/27 - 17*c**2/3 + 384*c. Find x such that d(x) = 0.
-1, 51
Let z = -5549 - -5553. Let k(q) be the second derivative of 1/15*q**z + 0*q**2 - 6*q + 0 - 1/100*q**5 - 1/10*q**3. Factor k(a).
-a*(a - 3)*(a - 1)/5
Let g be (-12)/66 + (19292/(-1386))/(-13). Let f(l) be the second derivative of -1/18*l**4 - 4*l**2 + 0 + 8*l - g*l**3. Find u such that f(u) = 0.
-6, -2
Determine l so that 451061*l**4 + 9095*l**3 + 977192*l**5 - 34635*l**3 - 4521491*l**4 - 40*l**2 + 1064413*l**5 = 0.
-2/639, 0, 2
Let k(u) be the second derivative of -u**5/10 - 79*u**4/3 - 1216*u**3/3 - 2400*u**2 + 18*u - 3. Determine z so that k(z) = 0.
-150, -4
Let n(o) be the third derivative of -o**6/2880 - o**5/96 - 25*o**4/192 + 127*o**3/6 - 3*o**2 - 22. Let z(b) be the first derivative of n(b). Factor z(q).
-(q + 5)**2/8
Factor 567 - 18*a**2 + 20*a**2 - 283 - 284 + 264*a.
2*a*(a + 132)
Let z(j) = -2*j**2 - 6*j. Let q be z(-3). Suppose q = 2*c - n - 10, -c + 3 = 3*n + 5. Factor 11 + 12*l**3 + 20*l**5 - 4*l**3 - 11 + 28*l**c.
4*l**3*(l + 1)*(5*l + 2)
Let l(u) be the first derivative of -4*u**5/15 + 11*u**4/3 - 4*u**3 - 238*u**2/3 - 392*u/3 - 3564. Determine j so that l(j) = 0.
-2, -1, 7
Suppose -2*r - 15 = -7*r. Let q be 3*(-644)/(-102) + -341 + 327. Determine p so that -16/17 - q*p - 50/17*p**2 + 18/17*p**r = 0.
-1, -2/9, 4
Let f = -127 + 128. Let i be 3/(-6)*4 + f - -20. Let 4*x**2 + 0*x**2 - 15*x - 3*x**3 - i*x**2 - 6 + 3*x**2 = 0. Calculate x.
-2, -1
Let o(f) = f**3 + 2*f**2 - 2. Let i(v) = -3*v**3 - 13*v**2 + 49*v - 32. Let q(c) = -4*i(c) + 4*o(c). Factor q(t).
4*(t - 1)*(t + 6)*(4*t - 5)
Let l be (-286)/39 + (-25)/(375/(-270)). Find i such that -l*i**2 + 4/3*i**4 - 2/3*i**5 + 16/3*i**3 - 32/3*i + 64/3 = 0.
-2, 2
Let w = 1289 + -2077. Let i = w - -2366/3. Factor i*d - 1/6*d**4 - d**2 + 4/3 - 5/6*d**3.
-(d - 1)*(d + 2)**3/6
Let u = -1050253 + 5251369/5. Let 14/5*d**5 + 0 + 438/5*d**3 + u*d**2 - 72/5*d + 276/5*d**4 = 0. Calculate d.
-18, -1, 0, 2/7
Let l(d) = -105*d + 350. Let u be l(-16). Let y = u - 2030. Determine r, given that 3/5*r**2 + 6/5*r + y = 0.
-2, 0
Let m = -13 + 13. Suppose 59*z - 54*z - 10 = m. Determine y, given that 6*y**2 - 204*y**3 + 208*y**3 - y**z - y**2 - 4*y - 4*y**4 = 0.
-1, 0, 1
Let i(j) be the third derivative of j**6/24 - j**5/4 - 5*j**4/6 + 162*j**2 + 13*j - 2. Suppose i(p) = 0. What is p?
-1, 0, 4
Let p be (55/(-25) + 0)*550/(-1320). Let m(z) be the third derivative of -1/42*z**7 + 1/4*z**6 + 5/4*z**4 - p*z**5 + 0*z - 23*z**2 + 0*z**3 + 0. Solve m(c) = 0.
0, 1, 2, 3
Suppose -18*s - 112 - 68 = 0. Let x be 35*(-2)/s - (-5)/(-1). Find c, given that x - c**3 - 4/3*c**2 + 17/3*c = 0.
-3, -1/3, 2
Solve -64*f**5 + 112 + 604*f**3 + 2200*f**2 - 273*f**4 - 591*f**4 + 52*f**2 + 960*f = 0.
-14, -1, -1/4, 2
Let f(y) be the second derivative of -y**4/20 + 18*y**3/5 + 351*y**2/10 + y + 1388. Factor f(x).
-3*(x - 39)*(x + 3)/5
Let h(l) be the second derivative of 1/20*l**5 + 147*l + 3/2*l**4 + 1 + 8*l**2 + 11/2*l**3. Factor h(c).
(c + 1)**2*(c + 16)
Suppose 6*m - 2 - 28 = 0. Suppose -2*q = m*q - 14. Factor -10*v**q + 10*v**2 - 8*v**2 - 2 + 10*v.
-2*(v - 1)*(4*v - 1)
Factor -2/17*m**5 - 30/17*m**3 + 0 + 0*m + 18/17*m**4 - 50/17*m**2.
-2*m**2*(m - 5)**2*(m + 1)/17
Let n(k) = -3*k**4 + 39*k**3 - 12*k**2 - 165*k - 105. Let z(f) = -7*f**4 + 78*f**3 - 24*f**2 - 330*f - 211. Let h(x) = 5*n(x) - 3*z(x). Factor h(v).
3*(v - 4)*(v + 1)**2*(2*v - 9)
Determine v so that -2*v**3 - 5934*v - 2*v**2 + 376 + 6302*v + 88*v**2 = 0.
-2, 47
Let i(n) be the first derivative of -n**5/15 - n**4/2 - 2*n**2 - 60. Let s(m) be the second derivative of i(m). Factor s(f).
-4*f*(f + 3)
Let g(s) be the third derivative of s**6/3420 - s**5/570 - 25*s**3/3 - 51*s**2. Let u(k) be the first derivative of g(k). Factor u(j).
2*j*(j - 2)/19
Let f = 33 - 28. Let y be f + 1 + 8/(-2). Factor -180 - 6*t**2 + t**2 + 184 + t**y.
-4*(t - 1)*(t + 1)
Let y(m) be the first derivative of m**5/10 - 11*m**4/8 - 73*m**3/6 - 109*m**2/4 - 24*m + 10229. Factor y(r).
(r - 16)*(r + 1)**2*(r + 3)/2
Suppose 0 = 12*c - 20 - 16. Solve 5*q + 113*q**c - 47*q**3 - 13*q**2 + q**4 - 55*q**3 + 12 - 16*q = 0 for q.
-12, -1, 1
Let 1/3*q**2 + 1728 + 48*q = 0. What is q?
-72
Solve -907*k**2 + 61*k - 16*k + 910*k**2 = 0 for k.
-15, 0
Let o(g) = 2*g**2 + 4*g + 3. Let x be o(-4). Suppose 4*b + 3 - x = 0. Suppose -s - 3*s - s**2 + b*s + s = 0. What is s?
0, 1
Let v be 6/(-1 - -1 - -2). Find w, given that -3*w**4 - 174 - 171*w**2 - 957*w + 61 - 310 + 57*w**v - 303 = 0.
-2, -1, 11
Let u be 4*((-56)/16)/(-7). Factor 10*l + 2*l + l**4 - 7*l**u + 0*l**4 - l**2 - 5*l**3 + 0*l.
l*(l - 6)*(l - 1)*(l + 2)
Factor 3127/3*v**2 - 815365*v + 814323 - 1/3*v**3.
-(v - 1563)**2*(v - 1)/3
Let a(b) be the second derivative of b**5/80 - 119*b**4/8 + 14161*b**3/2 - 1685159*b**2 + 2*b + 214. Factor a(p).
(p - 238)**3/4
Suppose -5*z - 5 = 3*r, -16 = 2*z - 20*r + 24*r. Factor z*h + 10*h + 8*h - 35*h**2 + 12*h**3 + 5*h**4 - 2*h**3.
5*h*(h - 1)**2*(h + 4)
Let f(m) be the third derivative of 1/462*m**8 + 0 + 0*m**4 - 1/165*m**6 - 1/330*m**5 + 0*m - 72*m**2 + 1/1155*m**7 + 0*m**3. Suppose f(g) = 0. What is g?
-1, -1/4, 0, 1
Suppose 2*j + 4*h - 19 = -7, 5*j = -4*h + 18. Let y(r) = 11*r**3 - 7*r**2 - 11*r + 5. Let v(w) = w**3 - 2*w**2 - w + 1. Let d(p) = j*v(p) - y(p). Factor d(b).
-3*(b - 1)*(b + 1)*(3*b - 1)
Let 1/2*b**3 + 31877*b + 1007/4*b**2 + 189003/4 = 0. What is b?
-251, -3/2
Let a(b) be the second derivative of 5*b**3 + 0*b**2 + 2 - 41/4*b**4 + 5*b + 3/5*b**5. Factor a(g).
3*g*(g - 10)*(4*g - 1)
Let k(f) = -12*f**3 - 16*f**2. Let m(u) be the third derivative of -u**6/120 - u**5/60 - 2*u**2 + 25*u. Let y(h) = -k(h) + 10*m(h). Factor y(r).
2*r**2*(r + 3)
Let 2/7 + 14456/7*d + 26121992/7*d**2 = 0. Calculate d.
-1/3614
Let s(m) be the third derivative of -m**5/70 - 663*m**4/14 - 439569*m**3/7 - m**2 + m - 1884. Factor s(q).
-6*(q + 663)*