z. Factor x(j).
-2*(j - 2)**2*(j + 1)
Let v(i) be the second derivative of -29*i**4/54 + i**3/3 + 20*i**2/9 + i - 893. Solve v(d) = 0.
-20/29, 1
Determine d, given that 9169*d**3 - 3060*d**3 + 170*d - 3060*d**3 - 320 - 3054*d**3 + 155*d**2 = 0.
-2, 1, 32
Let v(u) be the second derivative of -u**4/6 - 107*u**3/3 - 210*u**2 + 6*u + 61. Suppose v(f) = 0. Calculate f.
-105, -2
Let l = 15761/4 - 3940. Let s(n) be the second derivative of 1/12*n**3 - 1/40*n**5 - l*n**2 - 15*n + 1/24*n**4 + 0. Factor s(g).
-(g - 1)**2*(g + 1)/2
Let n be (-6 - -1)*27*(-60)/4050. Factor 2/7*l**3 + 48/7 - 4*l - 22/7*l**n.
2*(l - 12)*(l - 1)*(l + 2)/7
Let f(w) be the third derivative of -w**5/12 + 1945*w**4/3 - 6052840*w**3/3 - 31*w**2 + 38. Factor f(y).
-5*(y - 1556)**2
Let t(q) = q**2 - 3*q - 9. Let b be t(-3). Suppose v - b = -2*k, 2*k + 2*k + 12 = 0. Suppose 2*n**2 - 16 - 20 - v + 49 = 0. Calculate n.
-1, 1
Let z(t) be the second derivative of 3*t**5/20 + 7*t**4/4 - 5*t**3/2 - 14*t**2 - 2*t - 13. Let x(k) be the first derivative of z(k). Factor x(g).
3*(g + 5)*(3*g - 1)
Factor -1/8*t**2 - 927/8 + 39*t.
-(t - 309)*(t - 3)/8
Suppose 19 = 6*y - 5*y. Let w be 1*(-2)/(-6) - (-544)/24. Factor -y*p**3 - 4*p**5 + 0*p**5 + w*p**3.
-4*p**3*(p - 1)*(p + 1)
Let n(h) be the second derivative of 180*h + 60*h**5 + 0 + 125/3*h**4 + 32*h**6 + 0*h**2 + 0*h**3 + 128/21*h**7. Factor n(x).
4*x**2*(4*x + 5)**3
Let s(m) = -8*m**3 - 51*m**2 - 54*m + 21. Let b(o) = -3*o**2 - 3. Let z(g) = 6*b(g) - 3*s(g). Solve z(q) = 0 for q.
-3, 3/8
Let g = -291263/3 - -97089. Solve x**3 - 4/3*x**4 + 1/3*x**5 + g*x**2 + 0 - 4/3*x = 0 for x.
-1, 0, 1, 2
Factor -1/3*t**3 - 10137856*t - 3184*t**2 - 32278933504/3.
-(t + 3184)**3/3
Let s(h) be the second derivative of h**7/21 - 13*h**6/15 + 67*h**5/10 - 57*h**4/2 + 72*h**3 - 108*h**2 + 2606*h. Factor s(n).
2*(n - 3)**3*(n - 2)**2
Let g(m) be the second derivative of -1/5*m**6 - 1/40*m**5 + 0*m**3 + 0*m**2 + 1/48*m**4 + 52*m + 0. Factor g(o).
-o**2*(4*o + 1)*(6*o - 1)/4
Let d(b) be the first derivative of -b**5 + 5*b**4/2 + 25*b**3 + 2867. Let d(h) = 0. What is h?
-3, 0, 5
Let h(g) be the second derivative of -1/6*g**3 + 332*g + g**2 + 1/20*g**5 + 0 - 1/6*g**4. What is t in h(t) = 0?
-1, 1, 2
Let k = 1368 - 1366. Let u(b) be the first derivative of -1/20*b**5 - 18 - 1/8*b**4 + 1/12*b**3 + 0*b + 1/4*b**k. Factor u(n).
-n*(n - 1)*(n + 1)*(n + 2)/4
Let s(f) = -15*f**3 + 2102*f**2 + 4381*f + 2187. Let m(d) = -8*d**3 + 1048*d**2 + 2192*d + 1094. Let y(z) = 11*m(z) - 6*s(z). Determine b, given that y(b) = 0.
-1, 544
Let c(d) be the first derivative of 3*d**5/5 - 63*d**4/4 + 116*d**3 - 234*d**2 + 1308. Factor c(f).
3*f*(f - 13)*(f - 6)*(f - 2)
Let q = 29 - 18. Let g be (-5)/q*37/((-555)/18). Solve -2/11*j**3 + 0 - 4/11*j**2 + g*j = 0 for j.
-3, 0, 1
Let i(j) be the first derivative of -j**3/12 - 198*j**2 - 156816*j + 719. Factor i(a).
-(a + 792)**2/4
Let j(c) = 4*c**2 - 120*c + 580. Let a be j(6). Let 24/5*s + 52/5*s**2 - 36/5*s**a - 16/5 - 2*s**5 - 14/5*s**3 = 0. Calculate s.
-2, -1, 2/5, 1
Let g = 152 + -147. Let q(y) = 8*y - 30. Let f be q(g). Solve 8*s + f*s + 16*s**3 - 44*s**2 + 4*s**4 + 6*s = 0 for s.
-6, 0, 1
Let j(c) be the first derivative of c**4/22 + 10*c**3/33 + 6*c**2/11 + 573. Factor j(i).
2*i*(i + 2)*(i + 3)/11
Let t = 358 - 313. Suppose 59 = 7*z + t. Suppose 24/5*d - 36/5 - 4/5*d**z = 0. What is d?
3
Let r = 49123/21 - 2339. Let x(o) be the first derivative of -9 + 10/7*o**2 + r*o**3 - 1/7*o**4 + 12/7*o. What is i in x(i) = 0?
-1, 3
Suppose -16*o - 3*j = -17*o + 11, 4*o - j - 11 = 0. Factor 3346*k**o - 3342*k**2 + 3*k**3 - 4*k**4 - 23*k**3 + 20*k.
-4*k*(k - 1)*(k + 1)*(k + 5)
Suppose 2*q - 4*j + 660 = 636, 0 = -2*j + 12. Let o be ((-2)/(-9))/(12/108). Factor -1/2*s**5 + s**o + 1/2*s - s**4 + 0*s**3 + q.
-s*(s - 1)*(s + 1)**3/2
Let d = 6814 - 81763/12. Let a(s) be the third derivative of -d*s**4 + 0*s + 0 - 15*s**2 - 25/6*s**3 - 1/60*s**5. Factor a(n).
-(n + 5)**2
Suppose -f - 10 = 3*h, 0 = 4*f - f - 5*h - 40. Let n be 16/40 + (-2)/f. Determine l, given that 753*l**3 - 753*l**3 + 15*l**2 - 12 - 3*l**4 + n*l**4 = 0.
-2, -1, 1, 2
Let x(y) be the second derivative of -y**6/60 + 74*y**5/5 - 11099*y**4/3 + 29008*y**3 - 86436*y**2 + 49*y - 2. Solve x(t) = 0 for t.
2, 294
Factor -5433*z**3 - 4513 + 34933 + 10821*z**3 + 3*z**4 - 5520*z**3 + 13884*z + 825*z**2.
3*(z - 26)**2*(z + 3)*(z + 5)
Let y(i) = -20*i - 130. Let l(o) = 8*o + 52. Let f(u) = -12*l(u) - 5*y(u). Let a be f(-6). Factor -52*d**4 + 2*d - 1 + 2*d**2 + 51*d**4 - a*d.
-(d - 1)**2*(d + 1)**2
Let l be 10/(-45) - (-2)/((-18)/(-335)). Let m = 40 - l. Factor -7*t**2 - 5*t**4 - 4*t**4 + t**4 + 14*t**m + t.
-t*(t - 1)*(2*t - 1)*(4*t - 1)
Let q(x) = -12*x - 8*x + 13 - 88 - 22. Let k be q(-5). Suppose 0*t + 0 - 3/2*t**2 - 1/2*t**k = 0. Calculate t.
-3, 0
Let n(b) be the first derivative of -b**6/6 + 1012*b**5/5 - 127511*b**4/2 - 171028*b**3 - 257049*b**2/2 - 552. Factor n(l).
-l*(l - 507)**2*(l + 1)**2
Let c(i) be the first derivative of 2*i**3/51 - 45*i**2/17 + 172*i/17 + 6928. Determine w so that c(w) = 0.
2, 43
Factor -9/7*q + 1/7*q**2 - 22/7.
(q - 11)*(q + 2)/7
Let j(x) be the second derivative of x**7/126 + x**6/9 + x**5/4 - 5*x**4/18 - 8*x**3/9 + 24*x - 26. Find n such that j(n) = 0.
-8, -2, -1, 0, 1
Let n(h) be the third derivative of -h**2 + 0*h + 34 + 0*h**3 + 1/90*h**5 + 4/3*h**4. Solve n(y) = 0.
-48, 0
Let m(g) = 43*g**2 + 893*g + 971. Let r(k) = -16*k**2 - 296*k - 324. Let n(a) = 4*m(a) + 11*r(a). Determine t, given that n(t) = 0.
-1, 80
Let o be (-15)/(-4) + (18/8)/9. Suppose 3*n + o*q - 24 = 70, -4 = -q. Let -25*b**4 + 20 - b**2 - 5*b**5 - n*b**3 - 9*b**3 + 40*b + 5*b**2 + b**2 = 0. What is b?
-2, -1, 1
Let r(y) be the third derivative of -y**2 + 3/5*y**3 - 1/6*y**4 + 0 + 1/150*y**5 + 0*y. Factor r(i).
2*(i - 9)*(i - 1)/5
Suppose -5*s + 5*g = -5, 2*s = 30*g - 27*g - 2. Let h(z) be the second derivative of 1/10*z**s - 2/3*z**4 + 0*z**2 + 28*z + z**3 + 0. Factor h(r).
2*r*(r - 3)*(r - 1)
Let j(k) = -17*k**2 + 368*k + 717. Let q(h) = 7*h**2 + 1. Let c(a) = j(a) + 3*q(a). Factor c(b).
4*(b + 2)*(b + 90)
Let t(h) = h**3 - h**2 - 1. Let j be (8 - 25) + 0 + 2. Let p(w) = -4*w**3 + 19*w**2 + 25*w + 17. Let i(y) = j*t(y) - 3*p(y). Find b, given that i(b) = 0.
-12, -1
Let d be 26 + 1 + (-59466)/2226. Let w be ((-96)/21 + 1)*-4. Factor 16/7*f**2 - w - d*f**3 - 10/7*f.
-2*(f - 5)**2*(f + 2)/7
Factor 4/9*h**2 + 0 - 520/9*h.
4*h*(h - 130)/9
Let j = -154 - -158. Factor -18*f - j*f**2 + 3*f - 17*f - 23 - 25.
-4*(f + 2)*(f + 6)
Let k be (-1)/((-13)/39 - 0). Let j(y) be the second derivative of -21/20*y**5 + 0 + 3*y**2 - 3/2*y**4 + 8*y + 2/5*y**6 + 7/2*y**k. Find b, given that j(b) = 0.
-1, -1/4, 1, 2
Let a(n) be the third derivative of 0 + 85/24*n**4 - 1/12*n**5 + 0*n - 103*n**2 + 0*n**3. Factor a(q).
-5*q*(q - 17)
Let r(x) be the first derivative of x**7/21 + 6*x**6/25 + 7*x**5/50 - x**4/5 + 29*x + 22. Let m(i) be the first derivative of r(i). What is l in m(l) = 0?
-3, -1, 0, 2/5
Let f be (-2232)/(-4836) + (-9)/((-117)/202). Suppose -295/3*y**3 - 76/3*y**2 + 196/3*y - f + 25/3*y**4 = 0. Calculate y.
-1, 2/5, 12
Let u(o) be the second derivative of -33*o + 8*o**2 + 0 - 16/9*o**3 + 1/15*o**5 - 5/9*o**4. Factor u(j).
4*(j - 6)*(j - 1)*(j + 2)/3
Let -322*c**2 + 162/5*c**3 - 700 + 990*c - 2/5*c**4 = 0. Calculate c.
1, 5, 70
Let i(r) be the first derivative of r**6/80 + 9*r**5/160 + r**4/16 - 195*r - 49. Let b(n) be the first derivative of i(n). Determine g so that b(g) = 0.
-2, -1, 0
Let n(d) be the second derivative of d**6/50 + 3*d**5/20 - 3*d**4/20 - 9*d**3/2 - 81*d**2/5 - 17*d + 54. Factor n(a).
3*(a - 3)*(a + 2)*(a + 3)**2/5
Let n(d) be the second derivative of d**4/60 + 79*d**3/30 - 396*d**2/5 + 1593*d. What is o in n(o) = 0?
-88, 9
Let x(p) = -p**3 - 19*p**2 + p + 23. Let q be x(-19). Suppose 0 = -q*j + 63 - 55. Suppose -15*l**4 + 2 - 5*l - 3 + 25*l**j - 6 - 3 + 5*l**3 = 0. What is l?
-1, -2/3, 1
Solve 551*d - 13*d**4 + 196114*d**3 - 1762*d**2 + 0*d**5 - 30*d**4 - d**5 - 196664*d**3 + 1805 = 0 for d.
-19, -5, -1, 1
Factor -14 + 1/8*t**2 - 27/4*t.
(t - 56)*(t + 2)/8
Let i be ((-2)/(-4))/((-1)/6). Let g be (-5)/i + 1/3. Let -2*y + g*y - 2*y**3 + 2*y**2 = 0. What is y?
0, 1
Let t(q) = 49*q - 2. Let o be t(