 = 0.
-2, 0, 3
Let k(j) be the second derivative of j**6/180 - 17*j**5/540 - j**4/54 - j**3/3 + 3*j**2/2 - 2*j - 3. Let h(m) be the second derivative of k(m). Factor h(n).
2*(n - 2)*(9*n + 1)/9
Let y be -27 + (29 - 116/120) - (-6)/20. Let -y*t**3 - 80/3*t - 32/3*t**2 - 64/3 = 0. Calculate t.
-4, -2
Let o = -58 - -44. Let f = 16 + o. Factor z**f - z - 7*z + 11*z.
z*(z + 3)
Solve -12*l**4 + 240 + 3867*l**3 + 3863*l**3 + 555*l**2 - 7721*l**3 + 1098*l = 0 for l.
-5, -2, -1/4, 8
Let n(d) = -5*d**2 - 361*d + 746. Let w(x) = 5*x**2 + 360*x - 745. Let m(f) = -5*n(f) - 4*w(f). Factor m(z).
5*(z - 2)*(z + 75)
Let x = -1703 + 1706. Let j(q) be the third derivative of 2*q**2 + 3/8*q**x - 1/160*q**6 - 3/80*q**5 + 0*q + 1/32*q**4 + 0. Determine b so that j(b) = 0.
-3, -1, 1
Let x(h) = -5757*h - 40297. Let a be x(-7). Let -1/3*b**4 - 48 + 22/3*b**3 - 97/3*b**a - 88*b = 0. Calculate b.
-1, 12
Let n(v) be the second derivative of 231*v + 2/189*v**7 + 0 - 4/45*v**6 + 13/45*v**5 - 4/9*v**4 + 0*v**2 + 8/27*v**3. Factor n(t).
4*t*(t - 2)**2*(t - 1)**2/9
Suppose -d - 51 = -3*y - 5*d, 4*y - 4*d - 68 = 0. Solve 16 + 17*m**2 - y*m - 35*m**2 + 19*m**2 = 0.
1, 16
Let b(m) be the second derivative of -m**4/18 + 10*m**3/9 + 13*m**2 - 2*m + 1146. Let b(i) = 0. Calculate i.
-3, 13
Suppose 199 = 17*k - 617. Factor 4*o**4 - 189 + k*o - 5*o**3 - 7*o**3 + 157 + 4*o**2 - 12*o**2.
4*(o - 2)**2*(o - 1)*(o + 2)
Factor -80*b + 16*b**2 + 16*b**2 + b**2 - 1536 - 51*b**2 + 22*b**2.
4*(b - 32)*(b + 12)
Let b(v) be the second derivative of -v**5/60 + 467*v**4/36 - 54755*v**3/18 + 54289*v**2/6 + 3468*v. Suppose b(d) = 0. What is d?
1, 233
Let i = 8/18817 + 18801/37634. Suppose 0 + 242*b + 45/2*b**3 - 264*b**2 - i*b**4 = 0. What is b?
0, 1, 22
Let q(m) be the third derivative of -m**6/210 - 214*m**5/105 - 1616*m**4/21 - 8448*m**3/7 + 10400*m**2. Factor q(l).
-4*(l + 8)**2*(l + 198)/7
Find t such that 3*t**5 - t**5 + 32*t + 14*t**4 - 3244*t**3 + 12*t**4 + 3210*t**3 - 82*t**2 + 12 + 44 = 0.
-14, -1, 1, 2
Suppose 29*s - 8*s = 5*s - 28*s. Let c(f) be the first derivative of -f**5 - 1 + s*f**2 + 10/3*f**3 + 0*f**4 - 5*f. Factor c(h).
-5*(h - 1)**2*(h + 1)**2
Let -6534/5 - 2/5*i**3 - 138/5*i**2 - 2574/5*i = 0. Calculate i.
-33, -3
Let u(l) = -9*l**3 + 50*l**2 - 51*l + 4. Let z = 5 - -1. Let o(s) = -s**3 - 1 + 234*s - 235*s + 2*s**3. Let b(p) = z*o(p) - u(p). Factor b(n).
5*(n - 2)*(n - 1)*(3*n - 1)
Suppose 3*u - 2*d - 9 = 0, -3 = -u + 2*d - 3*d. Suppose -u*t + 4*t - 4 = 0. Factor 0*i + 11 - 3*i**3 - 8 - 2*i + i**4 + 5*i**3 - t*i**2.
(i - 1)**2*(i + 1)*(i + 3)
Let l(n) = -24*n**4 - 32*n**3 - 4*n - 20. Let i(r) = -r**4 - r**3 - r - 1. Let c be 4/(-10)*2*(-6 + -19). Let y(k) = c*i(k) - l(k). Factor y(o).
4*o*(o - 1)*(o + 2)**2
Let j be ((-125)/(-36))/(-101 - (-10612)/105). Factor 40/3*w + j*w**4 + 50*w**2 + 4/3 + 250/3*w**3.
(5*w + 2)**4/12
Let q(y) = -42*y + 170. Suppose 4*x = 28 - 12. Let r be q(x). Determine c, given that -2/3*c**r + 2/9*c**4 + 0*c**3 - 4/9*c + 0 = 0.
-1, 0, 2
Let c(a) be the third derivative of 1/10*a**5 - a**2 - 20*a - 1/15*a**6 + 0 + 1/12*a**4 + 0*a**3. Factor c(q).
-2*q*(q - 1)*(4*q + 1)
Let z(j) be the first derivative of j**6/30 + 12*j**5/25 + j**4 - 50*j**3/3 - 225*j**2/2 - 250*j - 2808. Let z(g) = 0. Calculate g.
-5, -2, 5
Let r(x) be the first derivative of x**8/5040 + x**7/630 + x**6/270 + 59*x**3/3 + 9. Let d(p) be the third derivative of r(p). Factor d(v).
v**2*(v + 2)**2/3
Let n(k) be the third derivative of 2*k + 1/14*k**4 - 17/140*k**5 + 1/70*k**6 - 18*k**2 + 0*k**3 + 0. Determine i so that n(i) = 0.
0, 1/4, 4
Let a = -97548 + 482809/5. Let y = 987 + a. Solve y*m + 2/5 + 2/5*m**2 = 0 for m.
-1
Let z(l) be the first derivative of -45 + 6*l**3 + 0*l**2 + 0*l + 1/300*l**5 + 0*l**4 + 1/3600*l**6. Let g(b) be the third derivative of z(b). Factor g(h).
h*(h + 4)/10
Let x(m) = m**2 - 3*m - 25. Let a be x(7). Factor -39*k**a + 18*k**3 - 5*k**2 + 26*k**3.
5*k**2*(k - 1)
Solve -224*q**4 + 52912*q**5 + 24*q + 1431*q**3 - 209*q**3 - 53674*q**5 - 568*q**2 + 1276*q**4 = 0 for q.
-1, 0, 6/127, 1/3, 2
Let v = -6 - -20/3. Let c = 52807/158418 - 1/158418. Factor -c*w**3 + 0 - v*w + w**2.
-w*(w - 2)*(w - 1)/3
Let l(m) be the first derivative of -121*m**5/12 + 275*m**4/6 - 250*m**3/3 - 3*m**2/2 + 85*m - 191. Let c(p) be the second derivative of l(p). Factor c(w).
-5*(11*w - 10)**2
Let p(v) be the first derivative of 3*v**4/4 - 28*v**3 + 495*v**2/2 + 1350*v + 1149. Suppose p(w) = 0. What is w?
-2, 15
Let a be 1/(-10) - 2042/(-20). Factor 306*r**2 - 2228*r**2 + 146*r - 8 + a*r.
-2*(31*r - 2)**2
Let h(n) be the second derivative of -n**5/160 - 41*n**4/96 - 5*n**3 + 252*n**2 - n - 392. Factor h(j).
-(j - 7)*(j + 24)**2/8
Let y(h) be the third derivative of 1/600*h**6 + 0 - 1/40*h**5 - 5/2*h**3 - 32*h**2 + 0*h + 0*h**4. Let p(b) be the first derivative of y(b). Factor p(d).
3*d*(d - 5)/5
Let u(v) = 3*v**3 - v**2 - 8*v - 6. Let y(l) = -2*l**3 - 2*l**2 + 1. Let r(z) = u(z) + 2*y(z). Factor r(d).
-(d + 1)*(d + 2)**2
Suppose m = -4*c + 9, 3*c + 14*m = 9*m + 11. Find i, given that 16*i - 23*i**3 - 3*i**c - 10*i**2 - 13*i**3 + i**2 - 8*i = 0.
-2/3, 0, 1/3
Let n = -354186/5 - -70838. Let a be 0 - (-3)/(6/4). Factor -1/5*y**a - n*y - 4/5.
-(y + 2)**2/5
Let y(g) be the third derivative of 2/15*g**5 + 0 + 209*g**2 + 1/12*g**4 + 0*g + 0*g**3. Factor y(h).
2*h*(4*h + 1)
Let o(p) = 3*p**3 - 170*p**2 + 426*p - 280. Let g(c) = -c**3 + 85*c**2 - 212*c + 140. Let z = 399 - 406. Let m(d) = z*g(d) - 4*o(d). Factor m(h).
-5*(h - 14)*(h - 2)*(h - 1)
Let q be 4*(15 - 16) - (114/(-54) - 2). Let -q*f**2 - 2/9 - 1/3*f = 0. What is f?
-2, -1
Suppose -173 - 1096 = -27*z. Let 7 + 2*a**4 + 7*a**3 - 46 + 32*a**2 + 5 - 18*a**3 - 36*a + z*a**3 = 0. Calculate a.
-17, -1, 1
Let h(w) be the third derivative of w**5/330 - 217*w**4/22 - 1303*w**3/33 + 10722*w**2. Factor h(y).
2*(y - 1303)*(y + 1)/11
Let m(p) be the third derivative of 22 + 4*p**2 + 0*p - 1/30*p**5 + 17/12*p**4 + 6*p**3. Suppose m(a) = 0. Calculate a.
-1, 18
Let g(q) = 5*q - 6. Let v be g(2). Let 25*z**v + z + z**5 + 4*z**3 - z - 29*z**4 = 0. What is z?
0, 2
Factor -26/11*i**2 + 0*i - 15/11*i**3 + 0 - 1/11*i**4.
-i**2*(i + 2)*(i + 13)/11
Solve -4*z**3 + 0 - 50/3*z**2 - 12*z + 2/3*z**4 = 0 for z.
-2, -1, 0, 9
Let u = 397 - 282. Solve 4*b + 19 + u*b**2 - 28*b**3 + 76*b - 4 + 78*b**3 = 0.
-1, -3/10
Let t(m) = -186*m**4 - 31*m**3 - 137*m**2 - 180*m - 78. Let o(x) = 335*x**4 + 62*x**3 + 274*x**2 + 361*x + 156. Let v(l) = 5*o(l) + 9*t(l). Factor v(r).
(r + 1)**2*(r + 3)*(r + 26)
Let l = 625/22 - 4155/154. Let 3 + 1/7*k**2 + l*k = 0. Calculate k.
-7, -3
Let q(a) = -a**5 - 27*a**4 + 77*a**3 - 34*a**2 - a. Let r(s) = -9*s**4 + 24*s**3 - 11*s**2. Let x(i) = -2*q(i) + 7*r(i). Determine j so that x(j) = 0.
0, 1/2, 1, 2
Let q(j) be the first derivative of 10*j**4 + 112/3*j**3 - 52/35*j**5 + 0*j**2 + 0*j + 1/21*j**6 - 71. Factor q(c).
2*c**2*(c - 14)**2*(c + 2)/7
Factor 286*l + 2541 + 196 - l**2 - 985.
-(l - 292)*(l + 6)
Let h(b) = 659*b - 7247. Let c be h(11). Solve 2/9*y + 0 + 7/9*y**c = 0.
-2/7, 0
Find v such that -266/3*v**2 + 8/3 - 354*v = 0.
-4, 1/133
Factor -16*o**2 - 10 + 8*o**2 - o**3 - 20*o + 2 - 6 - 2.
-(o + 2)**2*(o + 4)
Let y(f) be the third derivative of -7*f**7/30 + 3997*f**6/20 - 2927509*f**5/60 - 139895*f**4/2 - 120050*f**3/3 - 155*f**2 + f - 12. Factor y(s).
-(s - 245)**2*(7*s + 2)**2
Let -2151*d + 551*d**3 + 2171*d - 2606*d**3 - 8160 + 5*d**4 + 6120*d**2 = 0. Calculate d.
-1, 2, 408
Factor -3076 - 15*l**3 - 10*l**3 + 22*l**3 + 5*l**2 + 112*l**2 + 126*l + 2836.
-3*(l - 40)*(l - 1)*(l + 2)
Factor -103514*n**2 + 780 + 207031*n**2 - 103518*n**2 - 779*n.
-(n - 1)*(n + 780)
Let r(m) be the second derivative of 0 + 133*m + 1/42*m**4 + 10/21*m**3 + 9/7*m**2. Factor r(z).
2*(z + 1)*(z + 9)/7
Factor -149645 - 1254*a - 540*a + 64*a + 10*a**2 - 15*a**2.
-5*(a + 173)**2
Factor -1891335*o + 3459*o + 899*o**2 - o**3 + 1849*o**2.
-o*(o - 1374)**2
Let x(o) = o**3 - 17*o**2 + 16*o + 3. Let z be x(16). Factor -4*s**5 + 2*s**5 + 5*s**4 + 3*s**3 - 3*s - 5*s**2 + 0*s - s + z*s**5.
s*(s - 1)*(s + 1)**2*(s + 4)
Let d(l) be the second derivative of -6 - 1/10*l**4 + 26/5*l**2 - 37/15*l**3 + 5*l. Factor d(t).
-2*(t + 13)*(3*t - 2)/5
Let j be 101925/(-63) - (-3 - 2). Let p = j