*u**3 - 8*u - 41/2*u**2 - 1/180*u**5 + 0 - 5/72*u**4. Let t(j) be the first derivative of p(j). Factor t(i).
-i*(i + 5)/3
Let g be 1*(186 + -2)/4. Let h = g - 38. Determine c so that -15*c**3 - 14*c**3 + h*c**2 + 25*c**3 = 0.
0, 2
Let s = 7563 - 7543. Let n(l) be the second derivative of -14*l + s*l**2 - 4/3*l**3 + 1/30*l**4 + 0. What is o in n(o) = 0?
10
Let k(y) be the third derivative of -y**5/120 - 217*y**4/48 - 18*y**3 + 2*y**2 - 1454*y. Factor k(n).
-(n + 1)*(n + 216)/2
Let q(h) be the first derivative of -h**5 + 215*h**4/4 - 1300*h**3/3 + 680*h**2 + 2880*h - 4224. Factor q(o).
-5*(o - 36)*(o - 4)**2*(o + 1)
Let t(g) be the third derivative of -2*g**2 + 2 - 1/6*g**3 + 0*g + 1/240*g**5 + 0*g**4. Determine r so that t(r) = 0.
-2, 2
Solve -22/7*i**3 - 60/7 + 22/7*i + 60/7*i**2 = 0.
-1, 1, 30/11
Let t(g) = -g**2 - 140*g + 1187. Let a be t(8). Determine w so that -2/9*w**a - 2/9*w**2 + 2/9*w**4 + 2/9*w + 0 = 0.
-1, 0, 1
Let z(w) be the third derivative of -2*w**2 - 1/45*w**5 + 2/315*w**7 + 0 - 1/24*w**4 + 1/1008*w**8 - 5*w + 1/180*w**6 + 0*w**3. Factor z(k).
k*(k - 1)*(k + 1)**2*(k + 3)/3
Let x = 1/11293 - -56461/45172. Factor -x*b**2 + 5/2*b - 5/4.
-5*(b - 1)**2/4
Let m(r) be the third derivative of -1/12*r**5 - 91*r**2 - 5/4*r**4 + 1/4*r**6 + 0*r**3 + 0*r + 1/42*r**7 + 0. Factor m(d).
5*d*(d - 1)*(d + 1)*(d + 6)
Let g be ((-595)/(-51) - 14)*(-6)/455. Let z(f) be the first derivative of 8 + 0*f**4 + 0*f**2 + g*f**5 + 0*f - 2/39*f**3. Suppose z(j) = 0. What is j?
-1, 0, 1
Let u(a) be the first derivative of 8*a**2 - 9/4*a**4 + 1/6*a**6 - 41 + 5/3*a**3 - 12*a - 1/5*a**5. Solve u(p) = 0.
-2, 1, 3
Let u(k) be the first derivative of k**6/1440 + k**5/240 - k**4/12 - 13*k**3/3 - k**2 - 16. Let h(g) be the third derivative of u(g). Factor h(b).
(b - 2)*(b + 4)/4
Let w(j) be the first derivative of -j**5/5 + 13*j**4/2 + 85*j**3/3 + 29*j**2 - 37. Factor w(c).
-c*(c - 29)*(c + 1)*(c + 2)
Let s be (3345/(-6))/(6/(-12)). Let k = s + -5561/5. Factor -4/5*x**2 + 0*x + 8/5*x**4 + 0 - k*x**3.
2*x**2*(x - 2)*(4*x + 1)/5
Factor -222 + 5*o**2 - 1254*o + 421 + 394*o + 1501.
5*(o - 170)*(o - 2)
Factor 0*w - 1146/11*w**3 + 0 - 576/11*w**2 + 12/11*w**4.
6*w**2*(w - 96)*(2*w + 1)/11
Let y be 4*(-141)/120 + (-6)/(-5) + 6. Find f such that -1/4*f**3 + 0 - y*f**2 - 9/4*f = 0.
-9, -1, 0
Let k(y) be the second derivative of -y**5/20 - 355*y**4/84 - 529*y**3/7 + 468*y**2/7 - 88*y - 32. Solve k(t) = 0.
-39, -12, 2/7
Let k(m) be the third derivative of m**7/42 - 4*m**6/3 - 43*m**5/2 - 120*m**4 - 585*m**3/2 + m**2 + 31*m - 1. Factor k(z).
5*(z - 39)*(z + 1)*(z + 3)**2
Let w(d) be the third derivative of -19*d**8/1120 + 367*d**7/2100 - 361*d**6/1200 - 109*d**5/200 + 209*d**4/120 - 2*d**3/3 + 650*d**2 - 4*d. Solve w(n) = 0.
-1, 2/19, 1, 4/3, 5
Let c be (0/(-15))/((-362)/181). Determine x, given that 5*x - 125/4*x**4 + 20*x**2 + c - 35/4*x**3 + 15*x**5 = 0.
-2/3, -1/4, 0, 1, 2
Suppose -c = 61867 - 61867. Let b(a) be the second derivative of -1/4*a**3 - 18*a + 0 + 3/16*a**4 + c*a**5 + 0*a**2 - 1/40*a**6. Factor b(g).
-3*g*(g - 1)**2*(g + 2)/4
Let h(t) be the second derivative of 0*t**3 + 1 - 4/105*t**6 - 1/21*t**4 + 0*t**2 - 9/70*t**5 + 14*t. Suppose h(y) = 0. What is y?
-2, -1/4, 0
Let m(z) be the first derivative of -2*z**5/5 + 63*z**4/2 - 82*z**3 + 61*z**2 - 688. Factor m(s).
-2*s*(s - 61)*(s - 1)**2
Let q(m) be the third derivative of m**5/60 + 3887*m**4/24 + 1943*m**3/3 - 24*m**2 - 2*m + 3. Factor q(y).
(y + 1)*(y + 3886)
Suppose 10 = 4*w + a, -w = a - 2 - 2. Factor 0*z**2 + 2*z**w + 8 - 10*z + 2 - 2.
2*(z - 4)*(z - 1)
Let y = -15905 - -15908. Let v(x) be the third derivative of 1/10*x**y + 1/20*x**4 + 1/100*x**5 + 0*x + 0 + 32*x**2. Solve v(u) = 0.
-1
Factor 9/4*i**3 + 0*i**2 + 0*i - 1/4*i**4 + 0.
-i**3*(i - 9)/4
Let c(u) be the second derivative of -4*u + 0*u**2 + 2*u**3 + 3/80*u**5 + 0 + 0*u**4 - 1/240*u**6. Let n(s) be the second derivative of c(s). Factor n(j).
-3*j*(j - 3)/2
Solve 0 - 4*d**2 + 0*d - 2/13*d**4 + 54/13*d**3 = 0.
0, 1, 26
Let b be 12*(2/1 + -3). Let k be (0 - 3)/(b/8). Determine a so that 8*a + 2*a - 2*a**k - 11*a - a**3 = 0.
-1, 0
Let u(p) be the third derivative of -p**6/30 + 13*p**5/5 - 130*p**4/3 - 200*p**3 - 3281*p**2 - 2. Factor u(i).
-4*(i - 30)*(i - 10)*(i + 1)
Let f(d) be the first derivative of -1/4*d**3 - 9/2*d + 89 - 15/8*d**2. Let f(y) = 0. Calculate y.
-3, -2
Let s = 5639/20 + 571/20. Let x = -309 + s. Factor -3/2*n**5 + 3*n**3 - x*n + 0 + 0*n**2 + 0*n**4.
-3*n*(n - 1)**2*(n + 1)**2/2
Let n(o) be the first derivative of -o**6/900 - o**5/18 - 2*o**4/15 - 78*o**2 - 203. Let f(x) be the second derivative of n(x). Find y, given that f(y) = 0.
-24, -1, 0
Let -529/7*y**3 + 0*y - 265/7*y**2 + 1/7*y**5 + 0 - 263/7*y**4 = 0. What is y?
-1, 0, 265
Determine r, given that 18*r**2 + 144*r - 2*r**4 + 3*r**3 - 30 - 72*r - 89*r = 0.
-5/2, -1, 2, 3
Let j(l) be the second derivative of 13/44*l**4 - 1/20*l**5 - 33*l + 1/330*l**6 - 15/22*l**3 + 0 + 0*l**2. What is b in j(b) = 0?
0, 3, 5
Let r(d) be the second derivative of 2/5*d**2 + 58*d + 2/3*d**3 + 0 + 7/15*d**4 + 3/25*d**5. Factor r(p).
4*(p + 1)**2*(3*p + 1)/5
Let t(l) = 3*l**2 + 1276*l + 1276. Let r be t(-1). What is o in 0 + 30*o**4 - 57*o**2 - 27/4*o**r - 21/4*o**5 - 15*o = 0?
-1, -2/7, 0, 2, 5
Let a(y) be the first derivative of y**6/72 - 9*y**5/8 + y**3 - 4*y + 67. Let k(i) be the third derivative of a(i). Factor k(g).
5*g*(g - 27)
Let j(k) be the third derivative of 2 + 1/8*k**4 + 0*k**3 + 1/120*k**6 + 1/210*k**7 + 5*k**2 - 1/12*k**5 + 0*k. Factor j(f).
f*(f - 1)**2*(f + 3)
Let z(g) be the third derivative of g**6/360 + 23*g**5/36 + 406*g**4/9 - 1682*g**3/9 + 79*g**2 + 17*g. Factor z(l).
(l - 1)*(l + 58)**2/3
Suppose 5*h + 4*c - 134 = 0, -3*c = -1 + 13. Factor l**5 + 55*l - 10*l**3 + 80*l + 2*l**5 - h*l**4 - 5*l**5 - 3*l**5 + 50 + 100*l**2.
-5*(l - 2)*(l + 1)**3*(l + 5)
Let q(c) be the first derivative of c**3/3 + 95*c**2 + 376*c - 2680. What is p in q(p) = 0?
-188, -2
Suppose 23*n = 24*n + 52. Let t be (76 + n)*(-1)/(-10). Factor 3/5*y**3 - t - 3*y**2 + 24/5*y.
3*(y - 2)**2*(y - 1)/5
Factor 2/5*c**3 + 112/5*c - 114/5*c**2 + 0.
2*c*(c - 56)*(c - 1)/5
Let d be 22/5 - -1 - (-139 + 65 - -73). Factor -17/5*n**3 - 13/5*n - 2/5 + d*n**2.
-(n - 1)**2*(17*n + 2)/5
Factor 146/3 - 148/3*k + 2/3*k**2.
2*(k - 73)*(k - 1)/3
Solve -1808*j**2 - 26972*j**5 + 13*j**4 + 31*j**4 + 77*j**3 - 429*j**3 + 26976*j**5 - 1920*j = 0.
-15, -2, 0, 8
Let j(s) be the third derivative of s**6/240 + 133*s**5/60 + 18209*s**4/48 + 17161*s**3/3 - 2647*s**2. Determine l, given that j(l) = 0.
-131, -4
Let f be (-825)/110 + -33 + 41. Let f*q**2 - 31*q + 61/2 = 0. Calculate q.
1, 61
Find w, given that -181/2*w**3 - 57/2*w**2 - 3/2*w**4 + 30 + 181/2*w = 0.
-60, -1, -1/3, 1
Find c such that -1096*c**3 + 118 + 275*c + 172*c - 550 + 1116*c**3 + 241*c - 276*c**2 = 0.
1, 2, 54/5
Factor 2/3*i**4 + 96*i + 46*i**2 + 72 + 28/3*i**3.
2*(i + 2)*(i + 3)**2*(i + 6)/3
Suppose -104*t = -111*t + 147. Suppose 4*n - 2 - t = -5*v, -3*n + 5*v - 9 = 0. Let 11/6*l**n - 7/6*l**3 - 1/3*l + 3/2*l**5 - 11/6*l**4 + 0 = 0. What is l?
-1, 0, 2/9, 1
Let h(u) be the second derivative of -u**4/3 - 28*u**3/3 - 26*u**2 + 3632*u. Factor h(v).
-4*(v + 1)*(v + 13)
Let a be -2*(3 + -1) - -4. Let b(i) = -i + 4. Let s be b(a). Factor 563*u**4 - 563*u**s - 4*u**3 - 2*u**2 + 2 + u**5 + 3*u.
(u - 2)*(u - 1)*(u + 1)**3
Let y be ((-18)/(-90)*-3)/(-6). Factor y*f**2 - 1/10*f + 0.
f*(f - 1)/10
Let r(q) be the first derivative of -q**4/4 - 127*q**3/3 - 735*q**2/2 - 1089*q - 5164. Factor r(o).
-(o + 3)**2*(o + 121)
Let v(m) be the first derivative of 1/160*m**6 + 1/16*m**5 - 24 - 9/8*m**3 - 3/2*m**2 + 3/32*m**4 + 0*m. Let j(c) be the second derivative of v(c). Factor j(w).
3*(w - 1)*(w + 3)**2/4
Let s = -42271/54 - -4697/6. Let p(n) be the second derivative of 10*n + s*n**4 + 0*n**2 + 1/9*n**3 + 0 - 1/90*n**5. Suppose p(l) = 0. Calculate l.
-1, 0, 3
Let k be 8 + (2222/101 - 142/5). Find a such that -1/10*a**2 - k + a = 0.
2, 8
Let t(u) = -6*u**3 + 42*u**2 - 141*u + 144. Let n(o) = o**3 - o**2 + o. Let r(g) = -3*n(g) - t(g). Let r(q) = 0. What is q?
2, 3, 8
Suppose -j - 3*j = -3*w - 54, -2*w = 4*j - 64. Let h be 6*(j/3 - 4). Let 10 + h*g - g - 59*g**2 + 26*g**2 - 72*g**2 = 0. Calcu