e of u(x). Factor y(v).
2*v*(v + 2)/5
Suppose -132*j + 217 + 28 = -19. Let q(g) be the second derivative of 1/70*g**7 + 9/100*g**5 + 0*g**2 + 1/20*g**4 + 0 + 0*g**3 + 3/50*g**6 - j*g. Factor q(t).
3*t**2*(t + 1)**3/5
Let t be 8/78*(-156 + 144 - (-54)/4). Factor -2/13*k**2 + 0 - t*k.
-2*k*(k + 1)/13
Let i(z) = -24*z**2 + 1640*z + 18630. Let s(x) = x**2 - 71*x - 810. Let h(l) = 6*i(l) + 141*s(l). Determine o, given that h(o) = 0.
-30, -27
Let c = 62 - 60. Determine o, given that 749*o**3 + 32*o**c - 744*o**3 + 13*o**2 = 0.
-9, 0
Let d = 75238/3771 + -166/419. Determine b, given that -d*b**4 + 70/3*b + 104/9*b**2 - 178/9*b**3 + 8 - 32/9*b**5 = 0.
-4, -1, -3/4, 1
Let g(w) be the first derivative of 328 + 7/3*w**2 + 12*w + 1/6*w**4 - 20/9*w**3. Factor g(k).
2*(k - 9)*(k - 2)*(k + 1)/3
Let f be ((-85)/(-102))/(45/27). Let t(m) be the second derivative of f*m**4 + 20*m + 0*m**5 + 1/2*m**3 - 1/14*m**7 - 1/5*m**6 + 0*m**2 + 0. Factor t(s).
-3*s*(s - 1)*(s + 1)**3
Let f(y) be the second derivative of 5*y**4/12 + 65*y**3/3 - 140*y**2 - 24*y - 99. Factor f(t).
5*(t - 2)*(t + 28)
Let f(u) be the second derivative of u**5/20 + u**4/12 + u**2/2 - 2*u + 62. Let o(q) = -3*q**3 - 9*q**2 + 2*q - 5. Let b(v) = -5*f(v) - o(v). Factor b(k).
-2*k*(k - 1)**2
Let o(p) be the second derivative of -p**5/12 - 310*p**4/9 - 1235*p**3/18 + 64*p - 58. Factor o(j).
-5*j*(j + 1)*(j + 247)/3
Let k(p) = p**3 + 381*p**2 - 762*p + 1536. Let g be k(-383). Factor -20/3*c - 10/3*c**3 + 35/3*c**2 - 5/3*c**g + 0.
-5*c*(c - 1)**2*(c + 4)/3
Let n be (-1)/(-3)*(-3 + -2)*-21. Let g = -34 + n. Suppose 4*l**3 - 12*l**2 - 2 - 16 + 35 - g = 0. What is l?
-1, 2
Let d be 765/(-23256)*19 - 45/8*-1. Factor 1/7*s**4 - d*s - 100/7 + 51/7*s**2 - 13/7*s**3.
(s - 5)**2*(s - 4)*(s + 1)/7
Suppose 0 = -40*g + 32*g + 24. Let -7*c**g + 3*c**3 + 25267*c - 25269*c - 1 + 7*c**2 = 0. What is c?
-1/4, 1
Let d = 307 + -305. Suppose 2*t**4 + 10*t**3 - 10*t**d + 20*t**2 + 2*t**2 = 0. Calculate t.
-3, -2, 0
Let i(s) be the first derivative of -21/2*s**2 - 56 + 4*s**3 + 9*s. Factor i(b).
3*(b - 1)*(4*b - 3)
Let d(l) be the third derivative of -l**8/80640 - l**7/3360 + l**5/30 - 17*l**4/4 + 101*l**2. Let g(j) be the third derivative of d(j). Factor g(n).
-n*(n + 6)/4
Let a(y) be the second derivative of y**6/50 + 21*y**5/10 - 111*y**4/5 + 452*y**3/5 - 912*y**2/5 - 1418*y. Let a(t) = 0. Calculate t.
-76, 2
Let v(y) be the first derivative of -y**3/3 + 5*y**2 + 11*y - 1301. Let v(j) = 0. Calculate j.
-1, 11
Let i(r) be the first derivative of -1/21*r**6 - 4/21*r**3 + 3/7*r**2 - 7 - 1/7*r**4 - 2/7*r + 6/35*r**5. Find c, given that i(c) = 0.
-1, 1
Let l(t) be the second derivative of t**5/40 - t**4/2 + 29*t**3/12 - 9*t**2/2 - 699*t. Solve l(s) = 0.
1, 2, 9
Let p be 746*(-7)/84 - (-2)/12. Let h be 9/(-6) - p*(-5)/(-180). Suppose 4/3 - h*t - 2/9*t**3 - 8/9*t**2 = 0. Calculate t.
-3, -2, 1
Let y = -9 + 11. Suppose 4*v - 4*n - 16 = 0, -5*n = -0*v - 2*v + 20. Solve 6*b**2 - 2*b**2 + 4*b**3 + v*b**y = 0.
-1, 0
Suppose -98/9*d**3 - 32/9*d**5 + 130/9*d + 62/9*d**2 - 112/9*d**4 + 50/9 = 0. Calculate d.
-5/4, -1, 1
Let l(w) = w**3 - 17*w**2 - 46*w + 2. Let n be l(20). Let i = n - 282. Factor 8/7*k + 4/7*k**2 + i.
4*k*(k + 2)/7
Determine p, given that -45916*p**2 + 366*p + 10*p**3 - 45690*p**2 + 92222*p**2 = 0.
-61, -3/5, 0
Let d be (-12)/26 + (35875/(-910))/25*-19. Factor -185/2*r - 31 - 183/2*r**2 + 1/2*r**4 - d*r**3.
(r - 62)*(r + 1)**3/2
Let t(h) be the second derivative of h**6/600 + h**5/300 - h**4/12 + 4*h**3/15 - 105*h**2 + 52*h. Let g(n) be the first derivative of t(n). Factor g(a).
(a - 2)*(a - 1)*(a + 4)/5
Let h(o) be the first derivative of 5/12*o**3 - 6 + 0*o - 3/16*o**4 + o**2. Factor h(w).
-w*(w + 1)*(3*w - 8)/4
Let l be (0/2)/(-11*10/(-55)). Suppose 5*s - 3*d + 8*d = -10, 2*d + 4 = l. Factor 0 + s*m**3 + 0*m**2 + 0*m - 2/7*m**4.
-2*m**4/7
Let r = 10580/29 - 71537/203. Factor -810/7*q**2 + r*q**3 + 3000/7 + 300*q - 3/7*q**4.
-3*(q - 10)**3*(q + 1)/7
Let 63*q + 21*q**3 + 336 - 3*q**4 + 36*q**2 - 472*q + 181*q - 72*q = 0. What is q?
-4, 2, 7
Let m(c) be the first derivative of 0*c**2 + 1/8*c**3 - 1 + 3/40*c**5 + 5/32*c**4 + 1/80*c**6 - 14*c. Let r(j) be the first derivative of m(j). Factor r(q).
3*q*(q + 1)**2*(q + 2)/8
Factor -119*f**2 - 2*f**3 + 4*f**3 - 5*f**3 + 53*f**2 - 655 + 2683 - 195*f.
-3*(f - 4)*(f + 13)**2
Suppose 0*m = 2*m - 4*b - 520, -3*m - 4*b + 820 = 0. Suppose -259*j = -m*j + 18. Factor 0*s + 0 - 2/7*s**4 - 2/7*s**5 + 0*s**j + 0*s**3.
-2*s**4*(s + 1)/7
Let p(j) be the first derivative of 2*j**5/55 - 7*j**4/22 - 26*j**3/11 - 53*j**2/11 - 4*j + 8109. Suppose p(v) = 0. Calculate v.
-2, -1, 11
Suppose -49 = -3*h - 4*d, -h + 4*d = -0*h - 27. Suppose -h*m + 15 = -14*m. Find z such that -9*z**2 + 33*z**m - 77*z**3 + 41*z**3 + 12*z = 0.
-4, 0, 1
Let y(a) = -32*a + 23. Let i(t) = 11*t - 8. Let h(w) = 17*i(w) + 6*y(w). Let z be h(0). Factor -4*g + 2*g**2 - 6*g**z + 4*g**4 + 66*g**3 - 62*g**3.
4*g*(g - 1)*(g + 1)**2
Factor 2/11*h**3 + 108/11*h**2 - 222/11*h + 112/11.
2*(h - 1)**2*(h + 56)/11
Factor 13/8*n + 11/8*n**3 + 1/8 + 23/8*n**2.
(n + 1)**2*(11*n + 1)/8
Suppose -51 = -284*n + 312 + 205. Find j such that 9/8*j**3 - 9/8*j**n - 33/8*j - 9/4 + 3/8*j**4 = 0.
-3, -1, 2
Let f(o) = o**5 + 13*o**4 - 13*o**3 + 3*o**2 - 8. Let k(a) = a**5 + a**4 - a**3 - 2. Suppose 0 = -3*d - 33 + 21. Let n(h) = d*k(h) + f(h). Factor n(p).
-3*p**2*(p - 1)**3
Factor -70*v + 2583*v**2 - 17736 - 24584 - 850*v - 2588*v**2.
-5*(v + 92)**2
Let w(j) be the third derivative of j**5/20 - j**3/2 + 4*j**2 + 57*j. Let w(v) = 0. What is v?
-1, 1
Let p(a) be the third derivative of 0 + 1/4*a**5 - 19*a**2 + 0*a + 4*a**3 + 1/72*a**6 + 0*a**4. Let x(m) be the first derivative of p(m). Factor x(f).
5*f*(f + 6)
Let s(t) be the third derivative of -t**7/210 - 31*t**6/40 + 383*t**5/60 - 161*t**4/8 + 97*t**3/3 + t**2 + 10*t - 8. Factor s(p).
-(p - 2)*(p - 1)**2*(p + 97)
Let n(s) be the first derivative of s**4/4 + 23*s**3/3 + 31*s**2 + 40*s - 3730. What is j in n(j) = 0?
-20, -2, -1
Let g(w) be the second derivative of -w**5/10 - 101*w**4/36 + 7*w**3 - 2*w - 135. Factor g(l).
-l*(l + 18)*(6*l - 7)/3
Suppose 616 - 577 = 13*d. Let c(f) be the second derivative of 1/90*f**5 + 35/27*f**d - 25/9*f**2 + 0 - 14*f - 11/54*f**4. Factor c(h).
2*(h - 5)**2*(h - 1)/9
Let c(j) be the second derivative of -j**4/8 + 5*j**3/4 - 75*j. Let c(a) = 0. Calculate a.
0, 5
Let g(q) be the third derivative of 0*q + 138*q**2 - 1/15*q**5 + 1/60*q**6 + 0 + 2*q**3 - 5/12*q**4. Factor g(f).
2*(f - 3)*(f - 1)*(f + 2)
Let g(a) be the first derivative of -a**3 + 33*a**2/2 + 180*a - 1350. Factor g(n).
-3*(n - 15)*(n + 4)
Solve -61 - 183*i + 42 + 189*i + 439 + 416*i + 2*i**2 = 0 for i.
-210, -1
Let n(g) be the first derivative of -47*g**4 - 368*g**3/3 - 86*g**2 + 8*g + 992. Let n(p) = 0. Calculate p.
-1, 2/47
Let h(t) = 2*t**2 + 3*t + 13. Let o(f) be the second derivative of f**4/6 + f**3 + 7*f**2 - 32*f. Let i(s) = -2*h(s) + 3*o(s). Suppose i(j) = 0. Calculate j.
-4, -2
Determine n so that -252/13 + 2/13*n + 252/13*n**2 - 2/13*n**3 = 0.
-1, 1, 126
Suppose 341*c - 1314 + 760 = 810. Solve 0 - 2/5*u**5 + 4/5*u - 6/5*u**c + 6/5*u**2 - 2/5*u**3 = 0.
-2, -1, 0, 1
Let i(a) be the second derivative of 0*a**2 + 1/3*a**3 - 1/30*a**5 + 81*a + 0 + 1/9*a**4. Factor i(y).
-2*y*(y - 3)*(y + 1)/3
Let w(z) = z**3 + 16*z**2 + 19*z - 7. Let p = 93 + -55. Let s(o) = 39 - o**2 + 0*o**2 - o - p. Let g(t) = -22*s(t) - 2*w(t). Factor g(f).
-2*(f + 1)*(f + 2)**2
Let s(d) be the second derivative of -d**5/50 + 208*d**4/15 + 139*d**3/5 - 4735*d - 2. Factor s(t).
-2*t*(t - 417)*(t + 1)/5
Suppose -70 = -3*f + 4*z, f - z = -f + 40. Let v(d) be the first derivative of -f - 2/15*d**3 - 12/5*d - 7/5*d**2. Suppose v(j) = 0. Calculate j.
-6, -1
Determine r, given that -2051*r**3 - 864*r - 432 - 2045*r**3 - 252*r**2 + 4076*r**3 = 0.
-6, -3/5
Find o, given that -3/5*o**5 + 0 - 24/5*o**2 + 24/5*o**4 - 9*o**3 + 48/5*o = 0.
-1, 0, 1, 4
Suppose 0 = 13*a - 31*a - 6570. Let g = 368 + a. Factor 0*p**2 + 0*p**4 + 4/7*p**g + 0 - 4/7*p**5 + 0*p.
-4*p**3*(p - 1)*(p + 1)/7
Solve 1266992 - 4*k**5 + 23959967 + 2000*k**3 + 17973041 - 180000*k**2 + 200*k**4 = 0.
-20, 30
Let z be 8/(-14)*(-1 + 2 - -1)/((-110)/1430). Factor -96/7*w - 80/7*