0 - 2/5*d**2 + 20*d.
-2*d*(d - 50)/5
Suppose 43 = -19*n + 347. Suppose n*z - 52*z = -21*z. Factor -10/19*t**3 + 4/19*t**2 + 6/19*t + z.
-2*t*(t - 1)*(5*t + 3)/19
Let k = 558 + -537. Let o be 80/30*9/k. Factor -o + 12/7*n - 8/7*n**3 + 12/7*n**2.
-4*(n - 2)*(n + 1)*(2*n - 1)/7
Let x(n) be the second derivative of 5*n**4/12 + 355*n**3/6 - 555*n**2 - 16*n - 140. Factor x(s).
5*(s - 3)*(s + 74)
Let c(j) be the second derivative of 17*j - 4/15*j**6 - 3/5*j**5 + 2 - 8/3*j**3 + 2/21*j**7 + 0*j**2 + 8/3*j**4. Factor c(z).
4*z*(z - 2)*(z - 1)**2*(z + 2)
Let p(b) be the third derivative of -b**6/1200 + 457*b**5/600 - 51983*b**4/240 - 52441*b**3/60 + 296*b**2 - 2. Find l such that p(l) = 0.
-1, 229
Let h(r) be the second derivative of 215*r**4/42 + 4*r**3/21 - 1206*r. Suppose h(f) = 0. What is f?
-4/215, 0
Let w be ((-5)/(-2))/(3/6). Factor 3 - 5*r**2 - 4 + 1 - w + 10*r.
-5*(r - 1)**2
Factor -268*t**3 + 4*t**4 + 59*t**3 - 2289*t**2 - 79*t**3 + 288*t + 3389*t**2 - 5184 + 4080*t**2.
4*(t - 36)**2*(t - 1)*(t + 1)
Let i = 534674 + -534672. Determine u so that -2/3*u**3 + 82/3*u + 14 + 38/3*u**i = 0.
-1, 21
Factor -31/10*n + 1/10*n**2 + 3.
(n - 30)*(n - 1)/10
Solve 204 - 96*w**2 - 3*w**4 - 12*w - 58*w**2 + 60*w**3 + w**2 = 0.
-1, 2, 17
Factor -163*p - 4*p**2 - 102*p + 213*p - 48*p + 360 - 72*p.
-4*(p - 2)*(p + 45)
Let m = -8 + 7. Let r be ((-12)/8)/(m/(-2)). Let t(u) = u**3 + 7*u**2 + 3*u. Let v(j) = -6*j**3 - 34*j**2 - 14*j. Let o(b) = r*v(b) - 14*t(b). Factor o(n).
4*n**2*(n + 1)
Let s(f) be the second derivative of f**6/75 - f**5/50 - f**4/3 - 8*f**3/15 + 4*f + 175. Factor s(m).
2*m*(m - 4)*(m + 1)*(m + 2)/5
Let c(n) be the first derivative of -27 + 0*n - 13/3*n**4 - 16/3*n**3 - 2/9*n**6 - 8/5*n**5 - 8/3*n**2. Find i such that c(i) = 0.
-2, -1, 0
Suppose 2*i - 7 - 1 = 0. Factor -2*h - 3*h**2 + h**4 + 3*h**2 - 4*h**3 + h**2 + i*h**2.
h*(h - 2)*(h - 1)**2
Factor 0 + 142/3*d - 1/6*d**2.
-d*(d - 284)/6
Find i such that -24/7*i - 2/7*i**2 + 128 = 0.
-28, 16
Let a(s) = s**3 + 22*s**2 + 17*s - 68. Let v be a(-21). Factor -1338*w**3 + 1339*w**3 + 17*w**2 + 0*w + v*w.
w*(w + 1)*(w + 16)
Let 49/4*y**2 - 244*y + 1/4*y**3 + 1040 = 0. Calculate y.
-65, 8
Let k(a) be the third derivative of 3/35*a**7 + 0 - 1/30*a**6 + 0*a**3 + 0*a + 27*a**2 + 1/42*a**8 - 3/10*a**5 - 1/6*a**4. Let k(l) = 0. What is l?
-2, -1, -1/4, 0, 1
Let n(w) be the third derivative of 121*w**8/504 + 649*w**7/315 - 1219*w**6/90 + 494*w**5/45 + 154*w**4/9 + 64*w**3/9 - 68*w**2 - 2*w. Solve n(r) = 0.
-8, -2/11, 1, 2
Let q(k) be the first derivative of k**4/6 + 106*k**3/3 + 2809*k**2 + 129*k - 309. Let w(b) be the first derivative of q(b). Factor w(v).
2*(v + 53)**2
Let l(w) be the third derivative of 5*w**8/336 - 13*w**7/42 + 35*w**6/24 + 49*w**5/12 - 116*w**2 + w + 6. Let l(r) = 0. What is r?
-1, 0, 7
Let d(g) = 2*g**3 + g**2 - 3. Let h be d(2). Suppose -u + h = 15. Factor 0*w**u - 2*w + 6 - 2*w**2 - 6.
-2*w*(w + 1)
Find d, given that -8*d + 3/4*d**3 + 0 + 95/4*d**2 = 0.
-32, 0, 1/3
Let u(k) be the second derivative of k**7/42 - 2*k**6/15 + 3*k**5/20 + 1569*k. Determine z so that u(z) = 0.
0, 1, 3
Let f(b) = -28*b - 41. Let i be f(-3). Factor -44*d**2 + 43 + 80*d + 5*d**3 + 4*d**2 - i.
5*d*(d - 4)**2
Let k = 1418 + -1413. Suppose -2*u - 5*t = -90 + 62, -2*u = -k*t + 12. Suppose -3/2*j**2 + 3*j - 15/2*j**3 + 0 - 3*j**u = 0. What is j?
-2, -1, 0, 1/2
Let l be (298/(-745))/((-11)/5 - 35/(-175)). Let j be (0 - 4/(-10))/1. Determine n so that 0 - l*n**2 + j*n = 0.
0, 2
Let b(p) be the first derivative of 5*p**4/4 - 460*p**3/3 + 905*p**2/2 - 450*p - 255. Factor b(l).
5*(l - 90)*(l - 1)**2
Let -1234/15*u + 1094/15*u**2 - 14/15*u**3 + 154/15 = 0. What is u?
1/7, 1, 77
Determine q so that -12*q**4 + 6*q**2 + q**5 - 12*q**3 - 4*q**5 - 73 + 15*q + 0*q**5 + 40 + 39 = 0.
-2, -1, 1
Let s(a) = -2*a**2 - a + 3. Let x(j) = -2*j**2 - 2*j + 4. Let u(k) = -k**2 + 13*k - 6. Let l be u(13). Let b(p) = l*x(p) + 4*s(p). Solve b(t) = 0.
-3, 1
Let z(g) = -3*g**3 + 6*g**2 - 7*g + 84. Let m(i) = -8*i**3 + 17*i**2 - 20*i + 231. Let p(t) = 4*m(t) - 11*z(t). Factor p(a).
a*(a - 1)*(a + 3)
Let w(y) = -7*y**2 + 3435*y - 22. Let f(l) = -3*l**2 + 1145*l - 8. Let c(t) = -11*f(t) + 4*w(t). Determine x so that c(x) = 0.
-229, 0
Let h(n) = 2*n**2 + 13*n + 14. Let q be h(-5). Let l be 1/((-12)/(-10) - (q + 2)). Factor -1 - 3*x - 4*x - l*x**2 - 4 + 17*x.
-5*(x - 1)**2
Let v(t) be the first derivative of 25*t**4/42 + 10*t**3/7 + 9*t**2/7 - 52*t + 79. Let a(p) be the first derivative of v(p). Determine b so that a(b) = 0.
-3/5
Let g be (-6 + 55/10)*-6 - -2. Suppose 0 = b + 5*l - 24, -2*b + 4*b + l = 12. Let 2/11*s - 4/11*s**3 + 4/11 + 4/11*s**b + 2/11*s**g - 8/11*s**2 = 0. What is s?
-2, -1, 1
Factor 106*s**3 + 219*s + 397 - 103*s**3 - 60*s**2 + 63 + 242.
3*(s - 13)*(s - 9)*(s + 2)
Factor 100*n + 1305*n**3 + 60*n**2 - 1300*n**3 - 5 + 5.
5*n*(n + 2)*(n + 10)
Let x(a) be the third derivative of a**8/26880 + a**7/1680 + a**6/240 + a**5/20 + 50*a**2 - 2*a. Let s(k) be the third derivative of x(k). Factor s(n).
3*(n + 2)**2/4
Suppose -5*a + 8*a = 36. Suppose 12 = -9*f + a*f. Factor -6*s**2 + 27*s - 21*s - f*s**2 + 2*s**3 + 2*s**4.
2*s*(s - 1)**2*(s + 3)
Let -652/5*s**3 + 0 - 8/5*s**5 - 1256/5*s**2 - 124/5*s**4 - 96*s = 0. Calculate s.
-6, -5, -4, -1/2, 0
Let d(m) = -3*m**2 - 968*m + 1913. Let w(b) = -b**2 - 322*b + 638. Let g(u) = 2*d(u) - 7*w(u). Solve g(l) = 0 for l.
-320, 2
Let n(b) be the second derivative of b**7/105 + 2*b**6/75 - 32*b**5/25 - 29*b**4/3 - 15*b**3 - 1781*b + 2. Solve n(g) = 0 for g.
-5, -1, 0, 9
Let k(o) be the third derivative of 5/3*o**5 + 5*o**3 + 111*o**2 + 0*o - 11/24*o**6 + 185/24*o**4 + 0. Let k(u) = 0. Calculate u.
-1, -2/11, 3
Let y = -163942/5 + 32617. Let s = -170 - y. What is b in -7/5*b - 2/5*b**4 - 1/5*b**2 + 3/5 + s*b**3 = 0?
-1, 1/2, 1, 3
Factor 700/17*d - 61250/17 - 2/17*d**2.
-2*(d - 175)**2/17
Find g, given that 326*g**2 + 262*g + 398*g - 1312 + 321*g**2 + 320*g**2 - 969*g**2 = 0.
2, 328
Let f(d) be the first derivative of d**6/420 - d**5/70 + d**4/42 - 2*d**2 - 2*d + 42. Let u(y) be the second derivative of f(y). Factor u(r).
2*r*(r - 2)*(r - 1)/7
Let z be (-113)/(-1469) + 46/78. Find t such that 4/3 + z*t - 2/3*t**2 = 0.
-1, 2
Let n(c) be the first derivative of -3/4*c**4 - 12*c + 6*c**2 + 4*c**3 + 3 - 9/20*c**5. Determine b, given that n(b) = 0.
-2, 2/3, 2
Let r(x) = 15*x**2 - 155*x + 440. Let w(u) be the first derivative of -8*u**3/3 + 39*u**2 - 220*u - 141. Let g(s) = 3*r(s) + 5*w(s). Factor g(a).
5*(a - 11)*(a - 4)
Let h = -36407 + 36409. What is a in -2*a + 1/2 + h*a**3 - 2*a**4 + 3/2*a**2 = 0?
-1, 1/2, 1
Let j(l) = -42*l**2 - 99*l - 24. Let s(a) = -37*a**2 - 99*a - 24. Let k(m) = 5*j(m) - 6*s(m). Determine w, given that k(w) = 0.
-8, -1/4
Let k be (2/4)/(41/4 - 10). Factor 4*t**3 - 6*t**3 + 53*t**2 - 2*t**4 - k*t**3 - 45*t**2 + 16*t.
-2*t*(t - 2)*(t + 2)**2
Suppose 0 + 0*h + 33/4*h**4 + 9*h**3 + 3/4*h**2 = 0. What is h?
-1, -1/11, 0
Let h(d) = 12*d**2 + 37*d + 6. Let m be h(-3). Factor -2*l**3 - 13*l**3 + 12*l**m - 140*l**2 - 45*l**3 - 5*l**4 - 80 + 3*l**3 - 180*l.
-5*(l + 1)*(l + 2)**2*(l + 4)
Let w(q) = 11*q**3 + q**2. Let v(f) = 6*f**3 + 346*f**2 + 1850*f. Let r(j) = -v(j) + w(j). Factor r(a).
5*a*(a - 74)*(a + 5)
Let a(i) be the third derivative of -i**8/112 + 23*i**7/350 + 93*i**6/200 - 583*i**5/100 + 89*i**4/5 - 24*i**3 + 150*i**2. What is o in a(o) = 0?
-5, 3/5, 1, 4
Let r(b) = -2*b**3 + 19*b**2 - 10*b + 13. Let h be r(9). Factor 5*l**3 - 6*l**3 - h*l**4 + 3*l**4.
-l**3*(l + 1)
Let i(y) = y**3 + y**2 - y. Let o = -276 + 275. Let z(f) = -12*f + 9. Let l = -9 - -6. Let r(d) = l*i(d) + o*z(d). Factor r(u).
-3*(u - 1)**2*(u + 3)
Let x = -4305 - -4307. Let j(l) be the second derivative of 0 + l**4 + 1/20*l**5 - 12*l + 0*l**x + 6*l**3. Factor j(w).
w*(w + 6)**2
Let g(a) be the second derivative of -9*a**5/50 - 773*a**4/5 - 6172*a**3/15 - 2056*a**2/5 - 7117*a. Solve g(j) = 0.
-514, -2/3
Let n(d) be the first derivative of -d**8/6720 + d**7/210 - 2*d**6/45 - 9*d**3 - d**2 + 53. Let b(i) be the third derivative of n(i). Factor b(w).
-w**2*(w - 8)**2/4
Let i be (-1456)/721 + (0 - 0) - -2. Let b = i + 834/515. Find v, given that 4*v - 38/5*v**2 - 29/5*v**3 + b + 21/5*v**4 = 0.
-1, -2/7, 2/3, 2
Factor 4