 21
Let a(i) = 36*i**4 + 870*i**3 + 5353*i**2 + 859*i - 10. Let r(k) = 54*k**4 + 1305*k**3 + 8032*k**2 + 1288*k - 16. Let g(q) = -8*a(q) + 5*r(q). Factor g(n).
-3*n*(n + 12)**2*(6*n + 1)
Factor 360*g**2 - 189*g**3 - 54 - 285*g - 1 + 224*g**3 - 55.
5*(g - 1)*(g + 11)*(7*g + 2)
Let k be 3429/9 + (1 - 2). Let c be 2/(-10) - k/(-25). Solve 30*n**2 - 1 + 2*n**5 + 15*n**4 + 4 - c*n - 5*n**5 - 30*n**3 = 0.
1
Let g(o) be the second derivative of -1/21*o**7 + 9*o**3 + 19/3*o**4 + 60*o + 1/5*o**6 + 0 + 11/5*o**5 + 7*o**2. What is y in g(y) = 0?
-1, 7
Solve 104/17*t - 20/17*t**3 + 64/17 + 18/17*t**2 + 2/17*t**4 = 0 for t.
-1, 4, 8
Suppose -95 = -36*v + 49. Suppose -8*g + v*g = 2*g. Factor g - 2/5*t**2 - 4/5*t.
-2*t*(t + 2)/5
Let n(m) be the second derivative of 155/2*m**3 + 5/12*m**4 + 8*m - 235*m**2 + 0. Determine x, given that n(x) = 0.
-94, 1
What is m in -717602/5 - 2/5*m**2 - 2396/5*m = 0?
-599
Let r = 12178 + -12176. Let g(q) be the first derivative of 0*q + 15/4*q**r - 26 + 1/2*q**3. Factor g(v).
3*v*(v + 5)/2
Let g(q) = -18*q + 99. Let n(u) = 17*u - 98. Let s(z) = -4*g(z) - 5*n(z). Let o be s(7). Solve d - 5/2*d**o + 3/2*d**2 + 0 = 0.
-2/5, 0, 1
Find j, given that -8*j**3 - 2*j**3 - 10*j**3 - 11*j**2 - 14*j + 24 + 11*j**3 + 10*j**3 = 0.
-2, 1, 12
Let y(l) be the second derivative of 4/5*l**2 + 0 + 31*l - 4/3*l**3 + 17/30*l**4 - 2/25*l**5. Factor y(u).
-2*(u - 2)**2*(4*u - 1)/5
Let d = 9908/1735 + 378/347. Factor 8/3*t - d - 2/15*t**2.
-2*(t - 17)*(t - 3)/15
Let a(s) be the third derivative of 0 + 21*s**2 + 1/3*s**4 - 1/12*s**5 - 1/3*s**3 + 0*s + 1/180*s**6. Let n(k) be the first derivative of a(k). Factor n(d).
2*(d - 4)*(d - 1)
Let y = 22 + 4. Let n be (y + -4 + -4)*1. Factor 143*p**2 + 3*p**3 + 0*p**3 - 128*p**2 - n*p.
3*p*(p - 1)*(p + 6)
Let l(t) be the third derivative of -17*t**6/180 - 67*t**5/360 + t**4/144 + 65*t**2 - 4*t. Factor l(p).
-p*(p + 1)*(68*p - 1)/6
Let r = -525 - -528. Factor -u**3 - 3*u**5 + 6*u**r + 22*u**3 + 9*u**4 + 5*u**4 + 15*u**2 - 5*u**4.
-3*u**2*(u - 5)*(u + 1)**2
Let 0 + 0*z**2 + 0*z - 1683/2*z**4 + 840*z**3 + 3/2*z**5 = 0. What is z?
0, 1, 560
Suppose -6*t = -1264 + 166. Find k, given that 48*k**2 + 57*k**3 + 16*k - t*k**3 + 90*k**3 - 28*k**4 = 0.
-2, -2/7, 0, 1
Let a = -67536 + 67539. Factor -10/11*j + 6/11 + 2/11*j**2 + 2/11*j**a.
2*(j - 1)**2*(j + 3)/11
Let z = 854 - 836. Suppose -z = q - 20. Solve 0*b + 3/8*b**4 - 3/4*b**3 + 0*b**q + 0 = 0 for b.
0, 2
Let x be (4/48)/(9/24). Let f(m) be the third derivative of 1/90*m**5 + 0 + 0*m + x*m**3 + 1/8*m**4 - m**2. Solve f(u) = 0 for u.
-4, -1/2
Suppose -138*d + 5*q + 47 = -135*d, -269 = d + 39*q. Find p, given that -6/7*p**d - 8/7*p + 0 + 30/7*p**2 - 16/7*p**3 = 0.
-4, 0, 1/3, 1
Let d(k) be the second derivative of 5*k - 121/12*k**4 - 2*k**2 + 3 + 22/3*k**3. Factor d(p).
-(11*p - 2)**2
Factor -182*p**3 + 515/2*p**2 + 30 + 194*p + 49/2*p**4.
(p - 5)*(p - 3)*(7*p + 2)**2/2
Let 4203 - 8445 + 28*x**2 + 4210 + 4*x**4 + 36*x - 36*x**3 = 0. Calculate x.
-1, 1, 8
Factor -52*t**5 + 749 - 749 + 144*t**4 - 17*t**3 - 256*t**2 + t**3 + 64*t**3.
-4*t**2*(t - 2)**2*(13*t + 16)
Suppose -2*i = 2*r - 126, -3*i = -2*r + r + 63. Let x be ((-36)/r)/(2/(-14)). Determine q so that x*q**2 - 8 + 5*q**2 - q**2 - 8*q - 2*q**2 = 0.
-2/3, 2
Let v(m) be the third derivative of -5*m**8/336 - 13*m**7/7 - 60*m**6 + 800*m**5/3 + 10719*m**2. Factor v(f).
-5*f**2*(f - 2)*(f + 40)**2
Let g(j) be the second derivative of -j**5/40 + 5*j**4/12 - 11*j**3/12 - 35*j**2/2 - 2461*j. Determine l so that g(l) = 0.
-2, 5, 7
Let w(l) = 17*l**3 - 53*l**2 - 122*l - 62. Let m = -326 - -321. Let r(u) = -3*u**3 - u**2. Let g(j) = m*r(j) - w(j). Determine z so that g(z) = 0.
-1, 31
Let q(f) be the second derivative of -f**5/50 + 129*f**4/10 - 12416*f**3/5 - 37636*f**2/5 + 1127*f. Factor q(x).
-2*(x - 194)**2*(x + 1)/5
Let b(u) = -75*u**2 - 2332*u - 168. Let c(f) = 220*f**2 + 7000*f + 500. Let x(i) = -8*b(i) - 3*c(i). Factor x(m).
-4*(m + 39)*(15*m + 1)
Let n(t) be the second derivative of 2 + 36*t**2 + 1/40*t**5 + 11/12*t**4 - 51*t + 35/4*t**3. Factor n(q).
(q + 3)**2*(q + 16)/2
Let j(n) be the first derivative of 16/3*n + 2/9*n**3 + 87 + 3*n**2. Factor j(c).
2*(c + 1)*(c + 8)/3
Let u(t) be the second derivative of t**5/10 - 290*t**4/3 - 1163*t**3/3 - 582*t**2 + 101*t - 4. Find m such that u(m) = 0.
-1, 582
Let f(b) = -b**3 - b**2 - b + 3. Suppose 0 = -0*k - 6*k. Let z be f(k). Suppose -a**2 + 2*a - a**z - 744 + 744 = 0. Calculate a.
-2, 0, 1
Let t(f) be the third derivative of 0 - 3/14*f**4 - 1/140*f**5 + 4*f**2 - 11/14*f**3 + 0*f. Factor t(j).
-3*(j + 1)*(j + 11)/7
Let u(n) be the first derivative of 17/8*n + 125 + 1/24*n**3 + 9/8*n**2. Factor u(v).
(v + 1)*(v + 17)/8
Let n be ((-7455)/(-426))/((-7)/(-3)). Let 48*t + 128 + 1/4*t**3 - n*t**2 = 0. Calculate t.
-2, 16
Let g(t) be the second derivative of t**6/75 - 63*t**5/25 - 43*t**4/10 + 254*t**3/15 + 852*t. Let g(a) = 0. Calculate a.
-2, 0, 1, 127
Suppose 668/3*z + 223112/3 + 1/6*z**2 = 0. What is z?
-668
Let u(r) = r - 1. Let h be u(4). Let f(s) = -s**3 + 9*s**2 - 8*s + 3. Let g be f(8). Solve 12*w**2 - 11*w**g + 8*w + 21*w**h - 6*w**3 = 0 for w.
-2, -1, 0
Let z(b) be the second derivative of -19/18*b**4 - 4/15*b**5 + 0 - 64*b - 10/9*b**3 + 1/45*b**6 + 0*b**2. Factor z(n).
2*n*(n - 10)*(n + 1)**2/3
Let d(y) be the second derivative of -y**5/90 + 995*y**4/54 - 248003*y**3/27 + 247009*y**2/9 - 21*y + 2. Solve d(h) = 0 for h.
1, 497
Let g(c) = -463*c - 41. Let q be g(-3). Determine v so that -1336 + 18*v**3 - 3*v**3 + q - 3*v**4 - 15*v - 9*v**2 = 0.
-1, 1, 4
Let v(n) be the first derivative of -n**3/12 - 269*n**2/8 + 135*n/2 + 9558. Suppose v(r) = 0. Calculate r.
-270, 1
Let d(y) be the third derivative of y**6/60 + 8*y**5/15 + 13*y**4/12 - 10*y**3 - 15*y**2 - 4*y + 2. Factor d(t).
2*(t - 1)*(t + 2)*(t + 15)
Let s = -13 - -23. Let u be (-10)/(-4)*(-6 + (-144)/(-20)). Factor 16 + 5*v**u + 7*v**3 - s + 15*v - 33*v**2.
3*(v - 2)*(v - 1)*(4*v + 1)
Let q(a) be the second derivative of 0*a**2 - 13*a - 273/5*a**5 - 3 + 2744/3*a**3 - 1078/3*a**4 - 41/15*a**6 - 1/21*a**7. Factor q(z).
-2*z*(z - 1)*(z + 14)**3
Let g be (((-4)/(-2))/(-2) - 207/(-3588)*26)*0. Find i, given that g - 28/3*i - 26/3*i**2 + 2/3*i**3 = 0.
-1, 0, 14
Let m(l) be the first derivative of -35*l**4/24 - 37*l**3/12 - l**2/2 + 98*l - 6. Let r(s) be the first derivative of m(s). What is z in r(z) = 0?
-1, -2/35
Suppose 0 = -2*p + 5*w - 4, -8*w = p - 12*w + 8. Suppose -7*d + 11*d - 4*x = p, 3*d - 4 = 2*x. Factor 1/2*i**4 - 1/4*i + 0 - 1/2*i**2 + 1/4*i**5 + d*i**3.
i*(i - 1)*(i + 1)**3/4
Let y(h) = -h**3 + 5*h**2 + 6*h + 7. Let x be y(6). Suppose 0 = 5*m - 32 + x. Factor 2 - 13*q + 7*q + 2*q**m + 2*q**5 + 4*q**3 - 10*q**4 - 2*q + 8*q**2.
2*(q - 1)**3*(q + 1)*(2*q - 1)
Suppose -3*o + s + 41 = 0, 0 = 4*o - 14*s + 13*s - 55. Let x be 2 - (26/o)/(14 + -13). Let -x*n**3 + 0*n + 0 - 1/7*n**2 = 0. What is n?
-1, 0
Let i be (20/(-7))/((-13)/364*-8). Let o be -1 + -4 + 6 - i/8. Solve -9/4*l**3 - o - 39/4*l**2 - 39/4*l = 0 for l.
-3, -1, -1/3
Let y(p) be the second derivative of p**7/4200 + p**6/600 + p**5/300 - 14*p**3 - 42*p. Let o(z) be the second derivative of y(z). Factor o(t).
t*(t + 1)*(t + 2)/5
Suppose -66*w - 20 = -71*w. Suppose w*z - 20 = -m - 1, -5*z = -m - 17. Solve 5*y**4 + 3*y**2 + 23*y**3 - y**5 - 7*y**m - 10*y**3 - 13*y**3 = 0 for y.
0, 1, 3
Let c(d) = -256*d**4 + 532*d**3 + 8*d**2 - 1544*d - 1044. Let p(x) = 13*x**4 - x**3 - x**2 + 1. Let z(v) = c(v) + 20*p(v). Determine g, given that z(g) = 0.
-128, -1, 2
Let v(k) = -74*k**2 + 382*k + 120. Let z(o) = -15*o**2 + 77*o + 24. Let l be 32 + -27 + -2*1. Let w(c) = l*v(c) - 14*z(c). Factor w(h).
-4*(h - 6)*(3*h + 1)
Let m(n) = n**3 - n + 4. Let o be m(0). Suppose 15261*k**2 + 15912*k - 98*k**o - 41687*k**2 - 10252*k**3 + 6976*k**3 - 2312 = 0. Calculate k.
-17, 2/7
Factor -337*r**3 - 2723*r**2 - 515*r**2 - 338*r**3 + 1016*r**3 - 339*r**3.
2*r**2*(r - 1619)
Let p(w) be the first derivative of -1/10*w**2 - 1/15*w**3 + 58 + 0*w + 1/10*w**4. Solve p(m) = 0.
-1/2, 0, 1
Let b(m) be the second derivative of 0*m**3 + 26 - 29/60*m**4 + m + 2/5*m**2 + 7/150*m**6 + 1/35*m**7 - 6/25*m**5. Find h such that b(h) = 0.
-2, -1, -1/2, 1/3, 2
Let p = -5 - -31. Let l(k) = k**3 - 3*k**