Let u(h) = -6*h**3 - 26*h**2 - 20*h + 71. Let p = -457 - -453. Let d(k) = k**3 + 5*k**2 + 4*k - 14. Let g(a) = p*u(a) - 22*d(a). Factor g(n).
2*(n - 3)*(n - 2)*(n + 2)
Suppose 0 - 22 = -2*r. Suppose r*o - 6*o = 20. Factor -22 + 32 - o*k - 5*k**2 - k.
-5*(k - 1)*(k + 2)
Let x(b) = 4*b + 20. Let y be x(-4). Let u(o) be the first derivative of -15 + 2/3*o**3 - 2*o + 3*o**2 - 3/2*o**y. Factor u(i).
-2*(i - 1)*(i + 1)*(3*i - 1)
Let f = 519 + -526. Let b be (-42)/(-49)*f/(-9). Solve -k**4 - 2/3 + b*k**5 + k + 5/3*k**2 - 5/3*k**3 = 0.
-1, 1/2, 1, 2
Let q(p) be the first derivative of 58/35*p**5 - 15/14*p**4 - 3/7*p**6 - 13 - 50/21*p**3 + 24/7*p**2 - 8/7*p. Let q(d) = 0. What is d?
-1, 2/9, 1, 2
Let q(f) be the first derivative of -f**3/21 - 136*f**2/7 + 39*f - 1674. Let q(v) = 0. Calculate v.
-273, 1
Suppose 45*r - 59*r + 70 = 0. Let b = 1633/5 + -324. Let 9/5*h + 2/5 + 1/5*h**2 - 3/5*h**4 - b*h**3 + 4/5*h**r = 0. Calculate h.
-1, -1/4, 1, 2
Let n(i) be the third derivative of i**6/60 - 7*i**5/3 + 22*i**4 - 2*i**2 - 209*i. Suppose n(x) = 0. Calculate x.
0, 4, 66
Let b(i) = -5*i**3 + 260*i - 180. Let k(g) = -g**2 - 6*g + 1. Let u(o) = b(o) + 20*k(o). Find x such that u(x) = 0.
-8, 2
Let h(o) be the third derivative of 1/135*o**5 + 0*o**3 + 11*o**2 + o - 1/27*o**4 + 1/3024*o**8 + 1/180*o**6 - 1/378*o**7 + 0. Factor h(d).
d*(d - 2)**3*(d + 1)/9
Suppose -228*l - 2536*l + 103287 = -62553. Factor -5/2*j**4 + 55/2*j**3 - 90*j - l*j**2 + 0.
-5*j*(j - 6)**2*(j + 1)/2
Suppose -4*o - 4*s = -5120, 6*s = 8*s - s. Factor 163840*r - 20480*r**2 + 1/2*r**5 + o*r**3 - 524288 - 40*r**4.
(r - 16)**5/2
Suppose 0 = -27*r + 60 + 48. Suppose -3*o + 14 = -25. Solve -o + 9 - 6*p**3 - 12*p**r - 34*p**3 - 24*p - 48*p**2 = 0.
-1, -1/3
Let g be (-1 - -1 - -1) + 1. Suppose g*d - 6 = -d. Suppose 5 - 2*p**d + 1 - 2*p + 2 - 4*p = 0. Calculate p.
-4, 1
Let m(j) be the first derivative of -1/16*j**4 + 93 - 1/20*j**5 + 0*j + 1/8*j**2 + 1/12*j**3. Factor m(g).
-g*(g - 1)*(g + 1)**2/4
Let p(g) be the first derivative of g**3/6 + 87*g**2/4 - 135*g + 4450. Solve p(k) = 0.
-90, 3
Let -3*p**2 + 224 - 18257*p + 16 + 18127*p + 8*p**2 = 0. What is p?
2, 24
Find w such that -28/3*w**3 - 32/3*w**2 + 28/3*w + 10 + 2/3*w**4 = 0.
-1, 1, 15
Let w(j) = j**4 - 3*j**3 - 79*j**2 + 148*j - 82. Let s(d) = 2*d**4 - 6*d**3 - 156*d**2 + 295*d - 162. Let z(m) = 5*s(m) - 9*w(m). Factor z(x).
(x - 9)*(x - 1)**2*(x + 8)
Suppose -82*r = -106 - 58. Let y(l) be the first derivative of -5/8*l**4 - 24 + 0*l - 10/3*l**3 - 15/4*l**r. Factor y(s).
-5*s*(s + 1)*(s + 3)/2
Let v(h) be the third derivative of h**5/60 - 25*h**4/12 + 24*h**3 - 231*h**2. Let l be v(47). What is i in -11/10*i**4 - 1/5*i**l + 11/10*i**2 + 1/5*i + 0 = 0?
-1, -2/11, 0, 1
Solve 180/7*u**2 - 6/7*u**3 - 216*u + 3888/7 = 0 for u.
6, 18
Let z(m) be the third derivative of m**5/120 + 25*m**4/48 + 12*m**3 + 5*m**2 + 189*m. Factor z(a).
(a + 9)*(a + 16)/2
Let p(k) be the first derivative of 2*k**3/3 + 35*k**2/2 - 18*k + 55. Let m be p(-18). Factor 3/7*b**3 + m + 0*b**2 + 0*b + 3/7*b**4.
3*b**3*(b + 1)/7
Let h(c) be the first derivative of 23/22*c**4 + 1/33*c**6 + 0*c - 56/33*c**3 + 12/11*c**2 - 16/55*c**5 - 107. Suppose h(z) = 0. Calculate z.
0, 1, 2, 3
Let b(s) = -18981*s + 113890. Let r be b(6). Factor -39*z**3 - 49/8*z**5 - 16*z**2 - 28*z**r + 0 - 2*z.
-z*(z + 2)**2*(7*z + 2)**2/8
Let i = 73263/2 + -36630. Factor i*r**3 + 0 + 2*r + 15/4*r**2 - 1/4*r**4.
-r*(r - 8)*(r + 1)**2/4
Let x(i) be the third derivative of -i**9/20160 + 9*i**8/8960 - i**7/240 - i**4/12 - i**2 + 4. Let m(l) be the second derivative of x(l). Factor m(t).
-3*t**2*(t - 7)*(t - 2)/4
Let 2305*p**3 - 4611*p**3 + 4*p**2 - 2*p**2 + 2304*p**3 = 0. What is p?
0, 1
Factor -50 - 36*n**2 + 184*n - 57 - 47 - 3*n**3 - n + 10.
-3*(n - 3)*(n - 1)*(n + 16)
Let a be ((-60)/(-21))/(-10) + 128/154. Suppose 245*d = 201*d + 88. Suppose -4/11*i**d - a*i + 4/11 = 0. Calculate i.
-2, 1/2
Let h(x) be the third derivative of -x**8/1680 - x**7/56 - 7*x**6/180 - 71*x**3/2 - x**2 - 82. Let i(m) be the first derivative of h(m). Factor i(n).
-n**2*(n + 1)*(n + 14)
Find m such that 100/7*m**4 + 0 + 268/7*m**2 - 4/7*m**5 - 276/7*m**3 - 88/7*m = 0.
0, 1, 22
Let r(h) be the third derivative of -h**6/210 + 16*h**5/7 + h**4/42 - 160*h**3/7 - 3673*h**2. Find q, given that r(q) = 0.
-1, 1, 240
Let x(r) = -r**2 - 5*r. Let q(l) = 215*l + 195. Let y(o) = -q(o) - 5*x(o). Find j, given that y(j) = 0.
-1, 39
Let k = -1 - -3. Let d be (-4)/(-90) + ((-5300)/(-250))/53. Factor d*p + 0 - 4/9*p**k.
-4*p*(p - 1)/9
Let p(b) = 2*b**4 + 20*b**3 - 27*b**2 - 6*b - 3. Let f(q) = -6*q**4 - 39*q**3 + 53*q**2 + 11*q + 7. Let l(v) = -9*f(v) - 21*p(v). Factor l(r).
3*r*(r - 3)**2*(4*r + 1)
Let v(s) be the third derivative of 0*s**4 + 0 + 3/40*s**6 - 1/70*s**7 + 0*s**3 - 1/10*s**5 - 283*s**2 + 0*s. Factor v(u).
-3*u**2*(u - 2)*(u - 1)
Suppose 0 = 4*o + 3*f + 27, -o + 144*f = 146*f + 23. Suppose -35/4*t**2 + 5/4*t**4 + 75/4*t - 15/4*t**o + 45/2 = 0. What is t?
-2, -1, 3
Suppose y + 3*i = 4*i + 15, -76 = -4*y - 4*i. Factor -v**2 + 679*v**3 - 12*v**2 - 72*v - y*v**2 - 676*v**3.
3*v*(v - 12)*(v + 2)
Let m(r) be the first derivative of -18*r + 0*r**2 - 43 + 0*r**3 - 5/36*r**4. Let t(u) be the first derivative of m(u). Factor t(w).
-5*w**2/3
Let y(a) be the third derivative of a**7/490 - 51*a**6/140 + 3141*a**5/140 - 6885*a**4/14 + 36450*a**3/7 - 621*a**2 + 2. Let y(p) = 0. What is p?
6, 45
Let o(m) = -16*m + 1106. Let p be o(69). Let x(g) be the second derivative of 0 - 3*g + 3/140*g**5 + 5/42*g**3 + 1/12*g**4 + 1/14*g**p. Factor x(s).
(s + 1)**2*(3*s + 1)/7
Find l, given that -12*l - 10 - 1/2*l**3 - 9/2*l**2 = 0.
-5, -2
Let c be 15 + (-1309)/85 - (48/(-360) + (-28)/15). Factor c*w**2 - 3/5*w**4 + 0*w - 6/5*w**3 + 1/5*w**5 + 0.
w**2*(w - 4)*(w - 1)*(w + 2)/5
Let n(f) be the first derivative of 0*f - 2*f**4 + 2/9*f**6 + 62 - 32/9*f**3 + 0*f**2 + 4/5*f**5. Solve n(k) = 0 for k.
-4, -1, 0, 2
Let v(m) = -7*m - 96. Let p be v(-14). Suppose -6 + 101*u**p + u + 3*u - 99*u**2 = 0. What is u?
-3, 1
Let l = -132145 - -132149. Let v = -22/7 + 139/42. Solve 1/2*q - v*q**5 + 1/6 + 1/3*q**2 - 1/3*q**3 - 1/2*q**l = 0.
-1, 1
Let g(l) = l**3 + 11*l**2 - 26*l + 3. Let m be g(-13). Let q(i) be the first derivative of -1/8*i**4 + 3/4*i**2 - 7 + 0*i - 1/3*i**m. Factor q(w).
-w*(w - 1)*(w + 3)/2
Let b(l) be the first derivative of 1/7*l**2 + 4/21*l**3 + 0*l + 1/14*l**4 + 60. Determine q so that b(q) = 0.
-1, 0
Let k = -2236937/21 + 106521. Find q, given that 2/7 - k*q - 2/21*q**2 = 0.
-3, 1
Let l(k) be the second derivative of -2*k**6/15 - 118*k**5/5 - 4021*k**4/3 - 21240*k**3 - 145800*k**2 - 8791*k. Factor l(s).
-4*(s + 5)**2*(s + 54)**2
Let r(o) = -o**3 + 6*o**2 - 5*o. Let v be r(4). Let t = -2/6347 + 19045/12694. What is c in -v - t*c**2 + 9*c = 0?
2, 4
Let r(t) be the second derivative of -3*t**5/4 + 577*t**4/4 - 400*t**3 + 342*t**2 + 16*t + 9. Determine f, given that r(f) = 0.
2/5, 1, 114
Let s(n) be the first derivative of -n**3/3 + 21*n**2 - 245*n - 2039. Factor s(p).
-(p - 35)*(p - 7)
Let a(d) be the second derivative of d + 5 + 9/100*d**5 - 23/60*d**4 - 1/150*d**6 + 18/5*d**2 + 1/10*d**3. Find k, given that a(k) = 0.
-1, 3, 4
Let a(j) be the first derivative of -7*j**6/6 + 4*j**5 - 55*j**4/12 + 5*j**3/3 - 48*j - 25. Let o(n) be the first derivative of a(n). Let o(s) = 0. Calculate s.
0, 2/7, 1
Let h(d) be the third derivative of -d**7/420 - 13*d**6/120 - 407*d**2. Factor h(q).
-q**3*(q + 26)/2
Factor 407*n - 1061*n + 542*n - n**2.
-n*(n + 112)
Let r(v) be the third derivative of v**8/672 + v**7/84 - v**6/30 - 2*v**5/5 - 661*v**2. Find s, given that r(s) = 0.
-4, 0, 3
Let r = -9/353 - -1077/706. Find n, given that -3/2*n - r*n**2 + 3 = 0.
-2, 1
Let z(y) = 10*y**3 + 60*y**2 - 5. Suppose 5*b - 10 = -2*q + 2*b, -2*q - 4*b = -10. Let r(c) = -c**4 - c**3 + 1. Let p(o) = q*r(o) + z(o). Factor p(a).
-5*a**2*(a - 4)*(a + 3)
Factor 93*o**2 - 160 - 46*o**3 + 0*o + 4*o + 42*o**3 - 67*o**2 + 134*o**2.
-4*(o - 40)*(o - 1)*(o + 1)
Suppose 4*c = -2*x + 18, 0 = -c - 21 + 18. Let q be 6/x - -4*(-2)/(-40). Factor -q*s**4 + 0 + 3/5*s - 3/5*s**3 + 3/5*s**2.
-3*s*(s - 1)*(s + 1)**2/5
Let o(i) = 3*i**2 + 48*i + 57. Let h(x) = -x**2 - 12*x - 14. Suppose 2*l - 10*l = -24. Suppose 7 +