0 + g*f**2 + 4/11*f.
2*f*(f + 1)**2*(9*f + 2)/11
Let v(q) be the first derivative of -q**7/210 - q**6/18 - q**5/5 - 3*q**3 - 5. Let u(r) be the third derivative of v(r). Factor u(a).
-4*a*(a + 2)*(a + 3)
Let t(x) be the third derivative of x**9/90720 - x**8/1620 + 31*x**7/2520 - x**6/20 - x**5/30 + 56*x**2. Let r(n) be the third derivative of t(n). Factor r(s).
2*(s - 9)**2*(3*s - 2)/9
Let j(g) be the third derivative of 5*g**8/336 - 4*g**7/21 + g**6 - 17*g**5/6 + 115*g**4/24 - 5*g**3 + 910*g**2. Suppose j(b) = 0. Calculate b.
1, 2, 3
Let r(g) be the first derivative of -71/6*g**3 + 648*g + 306*g**2 + 1/8*g**4 - 13. Factor r(u).
(u - 36)**2*(u + 1)/2
Suppose -4*s**3 + 0 + 34/5*s**2 + 2/5*s**4 + 56/5*s = 0. Calculate s.
-1, 0, 4, 7
Let x be (-2 + 0)/((-4)/22). Suppose -x*t + 48 = -3*t. Factor 2 - 10*n - 5*n**3 + t*n**2 + 3*n**3 + 4*n.
-2*(n - 1)**3
Let f(x) be the second derivative of -3*x**4/28 - 880*x**3/7 + 1761*x**2/14 - x - 1471. Factor f(d).
-3*(d + 587)*(3*d - 1)/7
Let z be ((-161)/((-4830)/12))/(1/8). Suppose -4*a = -15 + 3. What is p in -z - 2/5*p**4 - 16/5*p**a - 42/5*p**2 - 44/5*p = 0?
-4, -2, -1
Let g = -225791/12 - -18816. Let i(m) be the third derivative of 0 + 26*m**2 - 1/120*m**5 - 1/240*m**6 + g*m**3 + 1/48*m**4 + 0*m. Determine r so that i(r) = 0.
-1, 1
Let i(w) = w**2 + 2*w - 4. Let k(x) = -4. Let n(d) = -1. Let v(b) = -k(b) + 2*n(b). Let r(a) = i(a) + 2*v(a). Suppose r(u) = 0. What is u?
-2, 0
Let l be (-4)/27*(-783)/870. Factor l*r + 8/5 - 2/15*r**2.
-2*(r - 4)*(r + 3)/15
Let a be (60/(-75))/((-2)/5). Factor -12*r**2 - 30 - 19*r + 24 + r**2 - 10*r**a - r**4 - 9*r**3.
-(r + 1)**3*(r + 6)
Let c(m) be the second derivative of -m**6/60 - 13*m**5/20 - 35*m**4/8 + 73*m**3/3 - 40*m**2 + 37*m. Suppose c(f) = 0. What is f?
-20, -8, 1
Let l(z) = 20*z**2 - 20180*z - 10180815. Let g(u) = -27*u**2 + 30270*u + 15271222. Let t(f) = -5*g(f) - 7*l(f). Suppose t(w) = 0. Calculate w.
-1009
Let q(v) be the first derivative of -25*v - 10*v**2 + 20 + 5/3*v**3. Determine u so that q(u) = 0.
-1, 5
Let a(h) be the first derivative of h**5/80 - 3*h**4/16 - 7*h**3/8 - h**2/2 + 28*h - 84. Let p(y) be the second derivative of a(y). Factor p(o).
3*(o - 7)*(o + 1)/4
Let y = 121087/469 - 395/67. Let v = y + -252. Factor 2/7*i**2 + 6/7*i + 0 - 6/7*i**3 - v*i**4.
-2*i*(i - 1)*(i + 1)*(i + 3)/7
Let 105*i**3 + 264 + 5129*i**2 + 42*i**3 - 716*i + 5009*i**2 - 9842*i**2 + 17*i**3 - 8*i**4 = 0. What is i?
-3, 1/2, 1, 22
Let p(o) be the third derivative of -o**6/280 + 31*o**5/70 - 255*o**4/14 + 900*o**3/7 - 1182*o**2. Factor p(h).
-3*(h - 30)**2*(h - 2)/7
Let n(s) be the second derivative of -3*s + 0*s**2 - 1/30*s**6 + 1/42*s**7 - 3/20*s**5 - 1/3*s**3 + 1 + 5/12*s**4. Factor n(u).
u*(u - 1)**3*(u + 2)
Let z(r) = -r**2 + 2743*r + 5492. Let j be z(-2). Factor -11/3*d**j + 0 - 10/3*d - 1/3*d**3.
-d*(d + 1)*(d + 10)/3
Let y(k) be the first derivative of 0*k**4 + 0*k**2 + 1/180*k**6 - 7/60*k**5 - 2*k**3 + 0*k - 40. Let v(m) be the third derivative of y(m). Factor v(z).
2*z*(z - 7)
Let w be (-21)/360*(-3 - (-38)/7). Let g = 21/40 - w. Find u, given that g + 2/3*u**3 + 2*u + 2*u**2 = 0.
-1
Let r(c) be the first derivative of -1/12*c**5 + 1/90*c**6 - 9 + 2/9*c**4 - 2/9*c**3 + 0*c**2 - 26*c. Let g(n) be the first derivative of r(n). Factor g(a).
a*(a - 2)**2*(a - 1)/3
Let u(h) be the first derivative of h**6/6 + 62*h**5/15 + 217*h**4/12 - 122*h**3/9 - 80*h**2/3 - 1351. Solve u(p) = 0.
-16, -5, -2/3, 0, 1
Suppose -2 = -3*k + 4*y, -126444*k - y = -126443*k - 3. Solve -64/5*n**5 + 0*n - 1056/5*n**4 - 64/5*n**k + 0 - 516/5*n**3 = 0 for n.
-16, -1/4, 0
Factor 3*r**3 + 168456*r - 84254*r - 84379*r + 252 - 78*r**2.
3*(r - 28)*(r - 1)*(r + 3)
Let u = 1173 + -1171. Suppose u*r = -2, r = m + 4*m - 11. Factor 22/7*z**3 - 8/7*z**m - 3/7*z + 2/7 + 5/7*z**5 - 18/7*z**4.
(z - 1)**4*(5*z + 2)/7
Let v(t) = 3*t**3 - 179*t**2 - 4058*t - 13811. Let a(o) = o**3 - 45*o**2 - 1014*o - 3453. Let s(l) = -13*a(l) + 3*v(l). Factor s(p).
-4*(p - 24)*(p + 6)**2
Let y(t) be the third derivative of 11/27*t**3 - 5/54*t**4 - 1/270*t**5 + 0 + 6*t**2 - 2*t. Find x such that y(x) = 0.
-11, 1
Let y(q) be the first derivative of -5*q**6/6 - 1889*q**5/3 - 330225*q**4/2 - 15361500*q**3 + 7717500*q**2 - 72. Let y(v) = 0. What is v?
-210, 0, 1/3
Let w(t) be the third derivative of 0 + 0*t + 1/5*t**3 + 29*t**2 - 1/100*t**5 - 1/40*t**4. Let w(j) = 0. Calculate j.
-2, 1
Let l(n) = n**2 - 847*n + 1720. Let x(r) = 4*r**2 - 4236*r + 8600. Let p(y) = 24*l(y) - 5*x(y). Solve p(j) = 0 for j.
-215, 2
Let t(x) be the second derivative of 67*x**4/66 - 43*x**3/11 - 10*x**2/11 - 2739*x. Let t(k) = 0. Calculate k.
-5/67, 2
Let y be 5 - ((-27)/135 + (-88)/10). Suppose -2 = 6*m - y. Determine p, given that -9/5 - 1/5*p**m + 6/5*p = 0.
3
Factor r**5 + 25746*r**3 + 94*r**2 + 13*r**2 + 36*r**2 - 25887*r**3 - 3*r**4.
r**2*(r - 13)*(r - 1)*(r + 11)
Let m(d) = -d**2 - 15*d - 59. Let f be m(-8). Let b be (-23)/(-14) - (0 + f)/(-6). Let -b*g**4 - 2*g - 30/7*g**2 - 26/7*g**3 - 2/7 = 0. Calculate g.
-1, -1/4
Let b be (-254)/(-7) + 363/77 + -5. Let q be (10/(-35))/(0 + b/(-28)). Factor -2/9*o**5 - 2/3*o**3 + 0*o - 2/3*o**4 - q*o**2 + 0.
-2*o**2*(o + 1)**3/9
Suppose 16*v + 55 = 87. Determine c so that 48*c + 26 + 3*c**2 + 23 + 5*c**2 - 4*c**v - 5 = 0.
-11, -1
Let c(t) be the second derivative of t**8/6720 - t**7/840 + t**6/360 - 21*t**3/2 + t**2/2 + 23*t. Let q(v) be the second derivative of c(v). Factor q(l).
l**2*(l - 2)**2/4
Let k(y) be the third derivative of y**7/315 - 2*y**6/45 - 22*y**5/45 - 4*y**4/3 + 3221*y**2. Factor k(c).
2*c*(c - 12)*(c + 2)**2/3
Factor 16*c - 1/2*c**4 - c**2 - 4*c**3 - 21/2.
-(c - 1)**2*(c + 3)*(c + 7)/2
Factor 1462/15*t - 734/15*t**2 + 4/5.
-2*(t - 2)*(367*t + 3)/15
Let 2222*l**3 + 1527*l**2 - 975*l**4 + 1292*l + 977*l**4 - 1136*l + 2070*l - 5977*l**2 = 0. Calculate l.
-1113, 0, 1
Let b(v) be the first derivative of -3/5*v**5 + 0*v**2 - 41 - 3/2*v**4 + 1/2*v**6 + 0*v + 0*v**3. Factor b(h).
3*h**3*(h - 2)*(h + 1)
Suppose -2*c = 4*k - 60, 0 = 68*c - 69*c + 4*k - 60. Suppose 0*m**2 - 3/8*m**3 + c*m + 0 = 0. What is m?
0
Let g(c) = -14*c**2 - 7. Let v(z) = 249*z**2 + 2034*z + 126. Let p(l) = 18*g(l) + v(l). Factor p(q).
-3*q*(q - 678)
Let h be 138 + -150 - ((-460)/(-28))/(-5) - -9. Solve 16/7*b**2 - 2/7*b**3 + 24/7*b - h*b**4 + 0 = 0.
-2, 0, 3
Let k(h) be the third derivative of h**7/5880 - h**6/84 - 3*h**5/40 - h**4/8 + 2*h**3/3 - 62*h**2. Let n(y) be the second derivative of k(y). Factor n(l).
3*(l - 21)*(l + 1)/7
Let v(j) be the third derivative of j**5/150 - 63*j**4/10 - 379*j**3/15 + 3*j**2 + 59. Factor v(w).
2*(w - 379)*(w + 1)/5
Let -1032*d + 2*d**2 - 966*d + 2100*d = 0. Calculate d.
-51, 0
Let u(b) = 3*b - 24. Let r be u(10). Let l be ((-12)/r)/((-30)/20). Solve 2/3*d**3 + 0*d - l*d**2 + 0 = 0.
0, 2
Let i(q) = 17*q**2 - 601*q + 1794. Let u(a) = 15*a**2 - 600*a + 1785. Let t(p) = 5*i(p) - 6*u(p). Solve t(x) = 0 for x.
3, 116
Let w(n) be the third derivative of -n**8/280 + 62*n**7/525 + 34*n**6/75 + 10*n**2 - 17. Suppose w(y) = 0. Calculate y.
-2, 0, 68/3
Let c(t) be the second derivative of -t**5/40 + 5*t**4/8 - 4*t**3 - 8*t**2 - t + 10. Let n(q) be the first derivative of c(q). Factor n(v).
-3*(v - 8)*(v - 2)/2
Let z(w) be the first derivative of -w**5/20 + 37*w**4/8 - 6*w**3 - 37*w**2/4 + 73*w/4 + 174. Factor z(l).
-(l - 73)*(l - 1)**2*(l + 1)/4
Let w(z) = -52*z**2 + 1165*z - 295. Let q(d) = -157*d**2 + 3495*d - 860. Let p(c) = -2*q(c) + 7*w(c). Factor p(a).
-5*(a - 23)*(10*a - 3)
Let q(i) be the first derivative of 2/5*i**2 + 14 + 0*i + 1/10*i**4 - 2/3*i**3 + 4/25*i**5. Determine f, given that q(f) = 0.
-2, 0, 1/2, 1
Let h be (-9)/6*8/18*-3. Determine g, given that 1008*g + 82*g**2 - 1008*g - 51*g**3 + 3*g**4 + 44*g**h = 0.
0, 3, 14
Let j(v) be the second derivative of -v**4/78 - 100*v**3/39 + 525*v**2/13 - 2990*v. Factor j(x).
-2*(x - 5)*(x + 105)/13
Let i(j) be the first derivative of 321*j**4/4 - 118*j**3 + 33*j**2/2 + 1764. Factor i(g).
3*g*(g - 1)*(107*g - 11)
Suppose -179*v - 50*v - 293*v = 700*v + 1096*v. Factor 46/5*b**3 + v*b - 16/5*b**2 + 0 + 6/5*b**4.
2*b**2*(b + 8)*(3*b - 1)/5
Solve 30*l**3 + 2040*l - 402*l**2 - 2700 - 3/4*l**4 = 0 for l.
2, 10, 18
Let y = 1864097/15 - 124273. Let l be 2*-1