 2/3
Let t(s) be the third derivative of -s**5/150 - 159*s**4/5 - 303372*s**3/5 - 2415*s**2. Factor t(b).
-2*(b + 954)**2/5
Factor 72 + 28*r - 5*r + 88*r**4 + 3*r**5 + r**5 + 448*r**2 + 312*r**3 + 269*r.
4*(r + 1)**4*(r + 18)
Factor 0*q + 0*q**2 + 0 + 2/13*q**5 - 80/13*q**3 - 6*q**4.
2*q**3*(q - 40)*(q + 1)/13
Factor -2540*f**3 + 3007*f**3 - 70 + 3*f**5 + 8083*f**3 + 1435 + 2145*f**4 + 8535*f + 768 + 12810*f**2.
3*(f + 1)**4*(f + 711)
Let j(u) be the first derivative of 40*u**2 + 715 + u**4 - 12*u**3 - 34*u - 897 - 14*u. Solve j(b) = 0 for b.
1, 2, 6
Let l(s) be the third derivative of s**8/9240 + s**7/1540 - s**3/6 + 31*s**2. Let x(t) be the first derivative of l(t). Let x(g) = 0. What is g?
-3, 0
Let z(r) be the first derivative of r**5 + 25*r**4/2 - 65*r**3/3 - 55*r**2 - 3526. Find j such that z(j) = 0.
-11, -1, 0, 2
Let g(k) be the second derivative of -2*k**7/21 + 316*k**6/15 - 771*k**5/5 + 914*k**4/3 + 1240*k**3/3 - 2448*k**2 + 2775*k. Determine d so that g(d) = 0.
-1, 2, 153
Let g(x) = -x**2 - 30*x + 64. Suppose 0 = -214*u + 206*u - 256. Let j be g(u). Factor j + 2/5*r**2 + 14/5*r.
2*r*(r + 7)/5
Find x such that 288*x**2 - 304*x - 54*x**3 + 38*x**4 - 42*x**4 + 36*x**3 - 42*x**3 = 0.
-19, 0, 2
Let l(m) be the first derivative of 40 + 0*m + 216/7*m**3 + 0*m**2 + 54/35*m**5 - 81/7*m**4 - 1/14*m**6. Factor l(f).
-3*f**2*(f - 6)**3/7
Suppose -7*r = -5*r - 6. Factor 150*l**r - 4*l - 16*l**2 + 148*l**3 + 16*l - 294*l**3.
4*l*(l - 3)*(l - 1)
Let r be (-1 - 5)/((-18)/(-3) - (52 + -42)). Let 1/2*k**2 - 2 + r*k = 0. Calculate k.
-4, 1
Factor 25*o**3 - 16*o**3 + 190*o + 59*o + 195 - 10*o**3 + 57*o**2 + 4*o**3.
3*(o + 1)*(o + 5)*(o + 13)
Let q be -8*(-3)/120*15. Factor 9*r**3 + 2*r**q - 12*r**3 - 6*r**2 + 6 + r.
-(r - 1)*(r + 1)*(r + 6)
Let z(d) be the third derivative of -d**5/30 + 13*d**4/4 + 82*d**3/3 - 40*d**2 - 5. Determine a so that z(a) = 0.
-2, 41
Suppose 21*o - 1935 = 6*o. Factor -8*b - 934 - 11*b - 53*b + o*b**2 + 934 - 15*b**3.
-3*b*(b - 8)*(5*b - 3)
Let 547*b**2 + 314*b**2 - 5*b**3 - 8195*b - 26245*b - 36*b**2 + 33620 = 0. Calculate b.
1, 82
Let l(v) be the first derivative of v**6/2520 + v**5/84 + 16*v**3/3 - 132. Let t(b) be the third derivative of l(b). Determine s so that t(s) = 0.
-10, 0
Let o be ((-36 - 2 - -35) + 1*-19)/(-7). Factor -o + 9/7*l + 1/7*l**2.
(l - 2)*(l + 11)/7
Let b = -34 + 239/7. Suppose 120*h - 236 = -42 + 286. Let -b*u**3 + 0 + 2/7*u**2 + 0*u - 1/7*u**h = 0. What is u?
-2, 0, 1
Suppose 0 = 27*o - o - 52. Factor 3*f**2 + f**2 - 5 - 35 - 9*f**o + 50*f - 5*f**3.
-5*(f - 2)*(f - 1)*(f + 4)
Let n(y) be the first derivative of 0*y - 4/3*y**3 - 4*y**2 + 4/5*y**5 - 34 + 2*y**4. Factor n(r).
4*r*(r - 1)*(r + 1)*(r + 2)
Suppose 10*k + 58 = -19*k. Let t be (-24)/4 + (k - -10). Factor -7/3 + 1/6*i**t - 5/6*i.
(i - 7)*(i + 2)/6
Let s(c) be the second derivative of c**4/16 + 47*c**3/4 + 69*c**2 - 2*c - 2482. Solve s(m) = 0 for m.
-92, -2
Factor -4967*y**2 + 402*y - 4972*y**2 + 329*y + 9938*y**2.
-y*(y - 731)
Let l be (35/((-385)/66))/(3/(-2)). Solve -386 - 185*g**3 - 525*g**2 - 311 - 515*g + 527 - 5*g**l = 0 for g.
-34, -1
Let z = 823 + -835. Let i be ((-910)/(-80) + z)*(-6)/5. Factor 11/4*o - i + o**2.
(o + 3)*(4*o - 1)/4
Let n = 97 - 95. Let d be (n/(-8))/(44/(-66)). Factor 3/4*u**2 + 0 + 3/8*u**3 + d*u.
3*u*(u + 1)**2/8
Factor -8*n**3 + 480*n + 56*n**2 - 31*n**3 - 45*n**3 + 4*n**4.
4*n*(n - 20)*(n - 3)*(n + 2)
Let l(g) be the second derivative of g**6/90 + g**5/15 - g**4/2 + 8*g**3 - 2*g - 41. Let w(n) be the second derivative of l(n). Factor w(d).
4*(d - 1)*(d + 3)
Let g(h) = 2*h**2 + 43*h + 23. Let s be g(-21). Let m(f) = f**3 - f + 1. Let d(o) = -2*o**3 + 404*o**2 - 10402*o + 10002. Let y(q) = s*m(q) - d(q). Factor y(j).
4*(j - 50)**2*(j - 1)
Let p = 26825 - 26815. Let y(d) be the second derivative of -p*d + 1/66*d**4 - 10/11*d**2 + 1/11*d**3 - 2. Let y(a) = 0. What is a?
-5, 2
Let z = 265 + 218. Suppose 700*o**4 - 472*o**3 - z*o**3 - 1915*o**2 - 20 + 2110*o**2 + 80*o = 0. Calculate o.
-2/7, 1/4, 2/5, 1
Let t(k) be the first derivative of -k**4/102 - 7*k**3/51 + 8*k**2/17 - 52*k + 57. Let r(b) be the first derivative of t(b). Factor r(w).
-2*(w - 1)*(w + 8)/17
Let c = -255125 - -255127. Factor -v**c + 0 - 3/2*v + 1/2*v**3.
v*(v - 3)*(v + 1)/2
Let y = 1997 - 530. Let i = -16129/11 + y. Suppose 6/11*o**5 + 4/11*o**4 + 2/11*o + 0 - i*o**3 - 4/11*o**2 = 0. Calculate o.
-1, 0, 1/3, 1
Suppose -2*u + 2*q = -3167 + 3179, 66 = 4*u + 5*q. Suppose 1/6*c**5 + 19/3*c**u + 964/3*c**2 + 1024/3 + 1664/3*c + 230/3*c**3 = 0. What is c?
-16, -2
Factor 83 - 1/4*i**3 + 163/4*i**2 + 124*i.
-(i - 166)*(i + 1)*(i + 2)/4
Let m(q) be the second derivative of -2*q**6/45 + 159*q**5/5 - 6399*q**4 + 37446*q**3 - 4819*q. Factor m(b).
-4*b*(b - 237)**2*(b - 3)/3
Let g be (-1*6/(-7))/(675/1050). Factor -20 + 64/3*h - g*h**2.
-4*(h - 15)*(h - 1)/3
Let m(z) = -z**3 + 337*z**2 + 1349*z - 57. Let t be m(-4). Suppose -297/4*d**2 - 735/4*d**3 + t + 0*d - 225/2*d**4 = 0. What is d?
-1, -2/5, 1/6
Let c(r) be the third derivative of r**5/120 - 3*r**4/4 - 19*r**3/3 - 656*r**2. Let c(j) = 0. What is j?
-2, 38
Let m(o) = 4*o**3 - 37*o + 42. Let w(b) = 5*b**3 + b**2 - 34*b + 40. Let r(c) = -4*m(c) + 3*w(c). Factor r(p).
-(p - 8)*(p - 1)*(p + 6)
Factor -1028/3 + 3596/3*c + 7/3*c**2.
(c + 514)*(7*c - 2)/3
Factor 4/3*z**2 - 13/3*z**4 + 0*z - 7/6*z**5 + 0 - 10/3*z**3.
-z**2*(z + 2)**2*(7*z - 2)/6
Let w(y) be the second derivative of y**4/48 + 135*y**3/8 - 203*y**2/4 + 1620*y. Let w(z) = 0. Calculate z.
-406, 1
Let 4/5*m**5 - 48/5*m**4 + 152/5*m**3 - 32/5 + 132/5*m - 208/5*m**2 = 0. Calculate m.
1, 8
Let m = -14 - -18. Let a be -3 + 6*(-3 + m). Factor 0 + 0*o - 4/3*o**4 - 4/3*o**a + 4/3*o**2 + 4/3*o**5.
4*o**2*(o - 1)**2*(o + 1)/3
Let c = 4 + -2. Factor 108*u + 61 - 593 - 440 - 5*u**2 + c*u**2.
-3*(u - 18)**2
Suppose -23/2 - 1/2*d + 23/2*d**2 + 1/2*d**3 = 0. What is d?
-23, -1, 1
Factor -42*l + 7/3*l**3 + 13/6*l**2 + 54 + 1/6*l**4.
(l - 2)**2*(l + 9)**2/6
Let w(p) be the third derivative of -p**5/60 + 181*p**4/24 - 30*p**3 - 1869*p**2. Suppose w(z) = 0. Calculate z.
1, 180
Let c(v) = -2*v**2 + 6*v - 8. Let a(z) = z**2 + 37*z - 10*z + 4 - 5 - 26*z. Let w(m) = -4*a(m) - c(m). Find i such that w(i) = 0.
-6, 1
Let x be -8*1/(12/(-15)). Suppose 0*z - x*z = -4*z. Factor 2/5*d**2 + z + 2*d.
2*d*(d + 5)/5
Let l(p) = p + 2. Suppose -2*u - 4*f = -20, 4*f - 32 + 8 = -4*u. Let g be l(u). Factor 6*v - 6*v**3 + 0*v**2 + 3*v**g - 7*v**2 + 3*v**2 + v**2.
3*v*(v - 2)*(v - 1)*(v + 1)
Let l(b) be the second derivative of -5*b**4/48 - 35*b**3/4 - 585*b**2/8 + 2123*b. Determine a so that l(a) = 0.
-39, -3
Let n(k) = 2*k**3 - 3*k + 1. Let p = 31 - 29. Let o(t) = p*t**3 + 2*t**3 - 45*t**2 - 4*t + 46*t**2 - t**3. Let v(q) = 4*n(q) - 3*o(q). Factor v(u).
-(u - 1)*(u + 2)**2
Let l be ((-16)/(-36) + 0)/(5/((-845)/(-2))). What is h in l + 52/9*h + 2/9*h**2 = 0?
-13
Let d(f) be the third derivative of f**6/720 + f**5/12 - 7*f**4/16 + 20*f**3/3 - 68*f**2. Let s(y) be the first derivative of d(y). Factor s(k).
(k - 1)*(k + 21)/2
Suppose 3*z + 137*y + 24 = 134*y, 17*y + 196 = -2*z. Let 3/2 - 9/4*w**z + 37/4*w + 47/4*w**2 + 7/4*w**3 = 0. What is w?
-1, -2/9, 3
Let x(k) = -5*k**2 - 40*k - 56. Let o(c) = 5. Let b(j) = 29. Let h(n) = -b(n) + 6*o(n). Let p(d) = 4*h(d) - x(d). Factor p(m).
5*(m + 2)*(m + 6)
Let x(t) be the third derivative of t**7/140 - 23*t**6/40 + 53*t**5/10 - 145*t**4/8 + 123*t**3/4 - 43*t**2 - 34*t. Let x(j) = 0. What is j?
1, 3, 41
Suppose c + 63 = 67. Suppose 3*x = y - c*y + 12, y - 3 = -2*x. Let 14/13*r**3 - 2/13*r**2 - 30/13*r**4 + 0 + 0*r + 18/13*r**y = 0. Calculate r.
0, 1/3, 1
Let w = 627 - 622. Determine u, given that 163*u + w*u**2 + 4500 + 202*u - 665*u = 0.
30
Let u(g) be the first derivative of -30*g - 12*g**3 - 20 + 63/2*g**2 + 3/4*g**4. Solve u(f) = 0 for f.
1, 10
Factor 2904*m**3 + 2909*m**3 + 2903*m**3 - 8718*m**3 + 14 - 30*m + 18*m**2.
-2*(m - 7)*(m - 1)**2
Let p = -251 - -253. Suppose 0 = 3*g + 13 - 25. Let -p*l**2 + g + 33*l + 30*l - 65*l = 0. What is l?
-2, 1
Let n = 2080215/14 + -297165/2. Let -2/7*d**2 - 4 - n*d = 0. What is d?
-14, -1
Let l(o) be the third derivative of 5*o**2 + 65/4*o**4 - 19*o + 1/60*o**6 + 0 - 169/3*o**3 - 9/10*o**5. Factor l(p).
2*(p - 13)*