 4
Let u(n) be the third derivative of 4/27*n**3 - 5/108*n**4 + 0*n + 0 + 1/540*n**5 + 1/1080*n**6 + 22*n**2. Factor u(r).
(r - 2)*(r - 1)*(r + 4)/9
Let p = 42 + -38. Factor -8*i**5 + 0*i**3 + 2*i**p - 11*i**5 + 20*i**5 + i**3.
i**3*(i + 1)**2
Let f = -161/6081 - -6403/12162. Suppose 3/5 + 1/10*m**2 + f*m = 0. Calculate m.
-3, -2
Let d(l) be the third derivative of -l**8/210 - 3*l**7/175 + l**6/30 + l**5/50 - 245*l**2 - 2. Find z, given that d(z) = 0.
-3, -1/4, 0, 1
Let d(p) be the third derivative of -p**6/660 - 53*p**5/165 + 107*p**4/132 + 8070*p**2. Factor d(h).
-2*h*(h - 1)*(h + 107)/11
Let t(j) be the second derivative of -7*j**6/10 - 57*j**5/10 + 3*j**4/4 + 41*j**3 - 60*j**2 - 1620*j. Solve t(a) = 0.
-5, -2, 4/7, 1
Let q(y) = y**2 - y. Suppose -f = -11*f + 7*f. Let u be q(f). Factor u + 2/3*k + 1/3*k**2.
k*(k + 2)/3
Let z = 550709/157342 + -6/78671. Let 19*c**2 - 5/2*c**4 + 12 + z*c**3 - 38*c = 0. Calculate c.
-3, 2/5, 2
Factor 32/3*f**3 + 8*f**4 + 0 + 4/3*f**5 + 0*f + 0*f**2.
4*f**3*(f + 2)*(f + 4)/3
Let q(g) = -20*g**3 - 97*g**2 - 45*g + 20. Let x(k) = 16*k**3 + 95*k**2 + 45*k - 21. Let f(h) = 3*q(h) + 2*x(h). Suppose f(j) = 0. What is j?
-3, -6/7, 1/4
Suppose 9*q**5 + q**4 + 17*q**3 + 46*q - 20 + 63*q - 20*q**2 - 77*q**4 + 177*q**3 - 196*q**2 = 0. What is q?
4/9, 1, 5
Let s(o) be the first derivative of o**3/3 - 11*o**2/2 + 1637. Factor s(v).
v*(v - 11)
Factor 34*l + 80 - 5*l**2 + 11*l - 61*l + l**2 - l**2 + l**3.
(l - 5)*(l - 4)*(l + 4)
Let w(i) = i**3 - 16*i**2 + 14*i + 14. Let a be w(15). Let u(p) = -6*p**2 + 116*p + 122. Let g(z) = 2*z**2 + 2*z. Let h(j) = a*u(j) - 4*g(j). Solve h(y) = 0.
-61, -1
Suppose -189504*m - 5*m**3 + 63729 + 34545 + 1945*m**2 - 616*m - 12627 + 102533 = 0. Calculate m.
1, 194
Let p(q) be the first derivative of 91 + 26/3*q**4 + 0*q + 6/5*q**5 + 46/3*q**3 - 6*q**2. Find b, given that p(b) = 0.
-3, 0, 2/9
Suppose 0*l + 219/5*l**3 + 3/5*l**5 + 0*l**2 + 0 + 222/5*l**4 = 0. What is l?
-73, -1, 0
Let 109*b - b**3 - 4*b**2 + 54*b**2 - 10*b**2 + 84 - 16*b**2 = 0. Calculate b.
-3, -1, 28
Suppose -f + 1 = 0, 3*y = 2*f + 8 - 4. Let x = -19273 - -77167/4. Factor -3/4*d**y - x + 15/2*d.
-3*(d - 5)**2/4
Factor 15*i**3 - 112*i**2 + 225/2 - 1/2*i**4 - 15*i.
-(i - 15)**2*(i - 1)*(i + 1)/2
Let v(n) = 29*n**3 + n**2 + 2*n - 3. Let y be v(1). Let s = -9 + y. Solve -35*w**2 + 9 - 5*w**3 + 15*w**4 - 34*w**5 + 19*w**5 + 11 + s*w**5 = 0 for w.
-2, -1, 1
Suppose 0 = x + a - 10, 6*x - 3*a - 47 = 2*x. Suppose x = 4*z + 3. Factor -44*j**2 + 45*j**z + j + 1 + j.
(j + 1)**2
Let k(z) be the second derivative of -z**4/4 - 17*z**3 - 803*z + 2. Factor k(c).
-3*c*(c + 34)
Let r(a) = a**3 + 13*a**2 - a - 10. Let t be r(-13). Let y be ((-5)/(-15))/((-1)/(-6)). Factor -4*p**y + p**2 - 3 + 9*p**2 - t*p.
3*(p - 1)*(2*p + 1)
Factor -598*y - 60575 + 57503 - 3*y**2 - 518*y - 426*y.
-3*(y + 2)*(y + 512)
Let y = -706242 - -6356192/9. Let x(h) = h**2 - 2*h - 3. Let t be x(3). Factor 4/3*o + y*o**3 + t - 46/9*o**2.
2*o*(o - 3)*(7*o - 2)/9
Let n(w) be the second derivative of -35*w - 5/12*w**4 + 0*w**2 + 10/3*w**3 + 0. Factor n(z).
-5*z*(z - 4)
Let k(p) be the third derivative of -5/48*p**8 - 1/21*p**7 + 37/3*p**5 - 3*p + 77/24*p**6 + 24*p**2 + 40/3*p**3 + 115/6*p**4 + 0. Find o, given that k(o) = 0.
-2, -1, -2/7, 4
Factor -4 + 2*u**4 + 33*u - 1300*u**3 + 1296*u**3 - 29*u + 3*u**2 - u**4.
(u - 2)**2*(u - 1)*(u + 1)
Let p(m) = -5*m**3 - 6*m**2 - 4. Suppose -71 = -5*b - 56. Let f(x) = -x**3 + x**2 - 1. Let c(g) = b*p(g) - 12*f(g). Factor c(v).
-3*v**2*(v + 10)
Let w(k) = -9*k - 177. Let z be w(-20). Factor 189*a**4 + 3*a**3 - 3*a - 190*a**4 + z*a**2 - 2*a**2.
-a*(a - 3)*(a - 1)*(a + 1)
Suppose 0 = -45*o + 49*o - 156. Let r be -3*1 + o/52*8. Factor 0 - 8/5*h + 6/5*h**2 + 2/5*h**r.
2*h*(h - 1)*(h + 4)/5
Let m be (40*(-44)/7480)/(2/(-17)). Suppose 648/5*f**m + 3888/5 - 2592/5*f - 72/5*f**3 + 3/5*f**4 = 0. Calculate f.
6
Let i(n) = 110*n**4 + 3235*n**3 + 30010*n**2 + 91610*n + 90. Let k(d) = 5*d**4 + 147*d**3 + 1364*d**2 + 4164*d + 4. Let t(o) = -2*i(o) + 45*k(o). Factor t(s).
5*s*(s + 8)**2*(s + 13)
Let j(k) be the second derivative of -k**7/1260 + 5*k**6/36 - 125*k**5/12 - 11*k**4/4 - k - 78. Let q(f) be the third derivative of j(f). Factor q(n).
-2*(n - 25)**2
Let z be (-3 - 5/(-15))*6/(-4). Suppose 8 + 10 = z*p - 2*q, 0 = 3*p + 5*q - 7. Determine w, given that 5 - 1 - 2*w**2 + 2*w**4 - p = 0.
-1, 0, 1
Let x(t) be the third derivative of -t**6/120 - t**5/60 - 5*t**4/24 + 7*t**3/6 + t**2 - 16. Let v be x(1). Factor 2/19*o**2 + v + 0*o.
2*o**2/19
What is c in -304 - 10644*c - 953 - 871 - 20*c**2 = 0?
-532, -1/5
Let h = -67 + 69. Find g such that -45*g**3 + 2*g**4 + 37*g**h + 6 + 3*g**4 + 45*g - 76 + 28*g**2 = 0.
-1, 1, 2, 7
Let s(k) = -60*k**3 + 54*k**2 + 84*k - 30. Let m(q) = 12*q**3 - 1908*q + 1891*q + 3 + 3 - 11*q**2. Let z(d) = -21*m(d) - 4*s(d). Factor z(p).
-3*(p - 2)*(p + 1)*(4*p - 1)
Factor -462 + 17*a**4 - 18*a**3 - 824 - 15*a**4 + 102*a**3 + 404 - 84*a + 880*a**2.
2*(a - 1)*(a + 1)*(a + 21)**2
Let o(j) = -10*j**2 - 8*j - 8. Let k(z) = -5*z**2 + 8 - 19*z**2 + 8*z + 36*z**2. Let p(w) = 4*k(w) + 5*o(w). Factor p(q).
-2*(q + 2)**2
Let b(f) be the third derivative of -19/30*f**3 - 1/300*f**5 + 2*f + 0 + 1/6*f**4 - 62*f**2. Find u such that b(u) = 0.
1, 19
Factor 4/5*t**2 + 51380224/5 - 28672/5*t.
4*(t - 3584)**2/5
Let t be (-100)/((-1300)/39) - (-2)/2. Suppose -3*a**3 - 1/2*a**t + 0 + 16*a + 0*a**2 = 0. What is a?
-4, 0, 2
Let z(k) be the first derivative of -12*k**2 - 35 + 28/3*k**3 + 19*k + 7/6*k**4 - 1/2*k**5. Let g(h) be the first derivative of z(h). Factor g(t).
-2*(t - 3)*(t + 2)*(5*t - 2)
Let x(v) = 3*v**2 + 129*v - 1979. Let g be x(12). Let q(s) be the first derivative of g + 96/7*s - 24/7*s**2 + 2/7*s**3. Factor q(a).
6*(a - 4)**2/7
Let g be (12 - 16 - 120)/(2/(-110)). Let b(h) = h**2 + 4*h + 4. Let q be b(-6). Factor 6820*a**2 + q*a - g*a**2 - 4*a**3.
-4*a*(a - 2)*(a + 2)
Let d(v) be the second derivative of v**8/13440 + v**7/1120 + v**6/320 + 49*v**3/6 + 3*v - 9. Let k(q) be the second derivative of d(q). Factor k(z).
z**2*(z + 3)**2/8
Factor -2/19*g**2 - 16119842/19 - 11356/19*g.
-2*(g + 2839)**2/19
Let x be 24/14 + 27/21 + -1. Factor -16*o + 3 + 2*o**3 + 29*o**x + 4*o**4 - 12*o**3 - 11*o**3 + o**3.
(o - 3)*(o - 1)*(2*o - 1)**2
Let h be (11685/(-1640))/((-9)/(-4)) - -4. Suppose h*g**2 - 25/2*g + 35/3 = 0. Calculate g.
1, 14
Let i be ((0 - 2)/(-6))/(7 + -6). Suppose -86*s + 94*s = 24. Find z such that -i*z**2 - s + 2*z = 0.
3
Let k(g) be the first derivative of -g**4 - 196*g**3/3 + 104*g**2 + 400*g - 55. Factor k(r).
-4*(r - 2)*(r + 1)*(r + 50)
Let t(o) be the first derivative of 800*o - 320*o**2 + 2/5*o**5 + 8*o**4 + 16*o**3 - 68. Factor t(m).
2*(m - 2)**2*(m + 10)**2
Factor 862/3*s + 1/6*s**2 + 371522/3.
(s + 862)**2/6
Determine a, given that -5/3*a**2 - 26096415 + 13190*a = 0.
3957
Let o(d) = -880*d**3 - 325*d**2 + 920*d + 685. Let m(l) = -8*l**4 + l**2 - l - 2. Let j(c) = -40*m(c) - o(c). What is h in j(h) = 0?
-11/8, -1, 1
Let g(b) be the first derivative of -b**5/15 - 31*b**4/4 - 617*b**3/9 - 433*b**2/2 - 258*b - 4518. Factor g(p).
-(p + 1)*(p + 3)**2*(p + 86)/3
Let w(h) = 53*h + 389. Let v be w(-5). Let k be (-2*(-2)/(-42))/(v/(-868)). Factor -2/3*n**2 - 7/3*n**4 - 8/3*n**3 + 1/3 + k*n - 2/3*n**5.
-(n + 1)**4*(2*n - 1)/3
Let b(t) be the second derivative of t**7/21 - 4*t**6/15 + 3*t**5/10 + 2*t**4/3 - 4*t**3/3 - 348*t. Suppose b(y) = 0. What is y?
-1, 0, 1, 2
Determine z, given that 22/7*z - 15 - 1/7*z**2 = 0.
7, 15
Let c(x) be the first derivative of -1/15*x**3 + 106 + 18/5*x + 3/10*x**2. What is t in c(t) = 0?
-3, 6
Let l be -3 + 10 + 1/(5/(-15)). Factor -l*m + 10 - 5*m**2 + 11*m - 2*m.
-5*(m - 2)*(m + 1)
Let -1365*a**2 + 1551*a**2 - 3191*a + 3146*a + 34*a**3 + 5*a**3 = 0. What is a?
-5, 0, 3/13
Let n(z) be the first derivative of 1/6*z**6 - 1/2*z**5 + 0*z**4 - 5/2*z**2 - 35*z - 20 + 5/3*z**3. Let w(a) be the first derivative of n(a). Factor w(r).
5*(r - 1)**3*(r + 1)
Let a(w) be the second derivative of -4/3*w**3 - 5/6*w**4 - 43/2*w**2 - 40*w + 7/15*w**5 + 0. Let s(r) be the first derivative of a(r). Factor s(z).
4*(z - 1)*(7*z + 2)
Suppose 127 + 240*d + 193 - 188769*d**5 + 188774*d**5 - 80*d**3 - 80*d**2 = 0. What is d?
-2, 2, 