(t) = t**2 + t. Let q(o) = u*b(o) + z*x(o). Factor q(c).
2*(c - 4)*(c - 1)
Let p(u) = -2*u**2 - 167*u - 767. Let j be p(-5). Let o(g) be the first derivative of g**3 - 3/2*g**2 - 34 - j*g. Factor o(h).
3*(h - 3)*(h + 2)
Let x(c) = 11*c**2 + 125*c + 590. Let z(y) = -17*y**2 - 188*y - 884. Let v = -894 + 886. Let r(p) = v*x(p) - 5*z(p). Let r(w) = 0. What is w?
-10
Factor -385641/5*b - 3/5*b**3 - 26609229/5 - 1863/5*b**2.
-3*(b + 207)**3/5
Let q be (-3)/((-15)/(-75)*-1). Let n(l) be the first derivative of q - l + 3/5*l**2 - 1/15*l**3. What is c in n(c) = 0?
1, 5
Let o(n) = -n**4 + 11*n**2 + n + 1. Let u(j) = -4*j**4 + 15*j**3 + 78*j**2 - 34*j + 5. Let k(f) = 15*o(f) - 3*u(f). Find v, given that k(v) = 0.
-13, -3, 0, 1
Suppose 12*z - 171 - 45 = 0. Factor -41 + 4*c**3 + 39 - 2*c + z*c**2 - 7*c**4 + 3*c - 9*c**5 + 4*c - 9*c**4.
-(c - 1)*(c + 1)**3*(9*c - 2)
Let t be 108*(-1)/(-176) - (-9)/(-36). Factor 0*j**3 + 0 + 2/11*j**5 + 4/11*j**2 - 2/11*j - t*j**4.
2*j*(j - 1)**3*(j + 1)/11
Suppose 10*k - 5*k + 2*b = -918, b = 5*k + 921. Let t = k - -928/5. Find f, given that t*f**2 - 2/5*f**3 + 2/5*f - 8/5 = 0.
-1, 1, 4
Let a = 1083 - 1080. Suppose -a*p = -15*v + 17*v + 2, 0 = 3*v + 4*p + 2. Find n, given that 21/2*n**3 + 0 - n - 1/2*n**v = 0.
-2/7, 0, 1/3
Let f = -1/1223 + 1225/2446. Let d = 645 - 5157/8. Factor -f*h + 1/8*h**4 - 1/2 + 1/2*h**3 + d*h**2.
(h - 1)*(h + 1)*(h + 2)**2/8
Let m be 672/147 + 12/(-21). Let v(g) be the first derivative of -4*g**m - 20/3*g**3 - 19 + 0*g - 4*g**2 - 4/5*g**5. Suppose v(p) = 0. Calculate p.
-2, -1, 0
Let f(c) be the second derivative of 0*c**2 + 1/18*c**4 + 5/9*c**3 + c + 0. What is l in f(l) = 0?
-5, 0
Let n(m) = -m + 16. Let k be n(-10). Let v = -101/4 + k. Factor -v*l + 1/4*l**2 + 0.
l*(l - 3)/4
Let v(q) = q**3 - q**2 - 28*q. Let p(r) = -6*r**3 + 1485*r**2 - 181452*r - 369024. Let j(x) = p(x) + 3*v(x). Factor j(i).
-3*(i - 248)**2*(i + 2)
Let n(u) be the first derivative of u**6/210 + 31*u**5/105 + 30*u**2 + 45. Let f(i) be the second derivative of n(i). Solve f(b) = 0.
-31, 0
Let z(u) = u**2 - 111*u - 699. Let y be z(117). Let r(m) be the second derivative of 3/20*m**5 + 0 - 1/2*m**y + 9*m**2 - 3/2*m**4 + 29*m. Factor r(a).
3*(a - 6)*(a - 1)*(a + 1)
Suppose -d - 2*c - 3 = 3, -5*d - 42 = 4*c. Let y be 25/d + 54/12. Factor -2/3*j - j**4 + 1/3*j**3 + 1/3*j**5 + j**y + 0.
j*(j - 2)*(j - 1)**2*(j + 1)/3
Let z(q) be the first derivative of q**7/2520 - q**6/216 + q**5/180 + q**4/9 - q**3/3 - 19*q - 3. Let u(l) be the third derivative of z(l). Factor u(c).
(c - 4)*(c - 2)*(c + 1)/3
Let f(v) be the first derivative of 41067*v**5/40 + 40365*v**4/16 + 12757*v**3/8 - 345*v**2/4 + 3*v/2 + 48. Solve f(g) = 0.
-1, 2/117
Let f(i) = -3*i**3 - 15*i**2 + 79. Let c be f(-10). Let o be (-4)/10 - (-7897)/5. Factor -c + 10*b**2 + 15*b**3 + o - 25*b**4.
-5*b**2*(b - 1)*(5*b + 2)
Let x(j) be the second derivative of j**3 - 1/10*j**5 + 0*j**2 - 1/30*j**6 + 5/12*j**4 + 2*j + 0. Find b, given that x(b) = 0.
-3, -1, 0, 2
Let n be (-3)/(60/16) + (-1572)/10. Let s be (-157 - n)/(6/490). Factor s*q**2 + 70/3*q + 5/3.
5*(7*q + 1)**2/3
Solve -4595*a**4 - 3151040*a - 5*a**5 - 1264962*a**2 - 862451 - 540358 - 1062575*a**3 + 353989 - 1895243*a**2 = 0.
-458, -1
Suppose 2*s = l + 1 + 9, 3*s = l + 15. Let g(v) be the first derivative of 0*v**4 + 1 + v**3 - 1/5*v**5 + l*v - v**2. Let g(p) = 0. What is p?
-2, 0, 1
Let q = -268570 - -268570. Factor 1/2*l**3 + 0*l**2 + 0 + q*l - 11/2*l**4.
-l**3*(11*l - 1)/2
Let g = 61288 - 183862/3. Suppose -8/3*q**2 + g*q**5 + 0 + 16/9*q + 14/9*q**4 - 4/3*q**3 = 0. What is q?
-2, 0, 2/3, 1
Let d(f) be the first derivative of f**3 - 225*f**2 + 2175*f - 5465. Determine l, given that d(l) = 0.
5, 145
Let r(w) be the second derivative of 2*w + 7/48*w**4 + 5/8*w**3 + 1/80*w**5 + 9/8*w**2 - 5. Determine g, given that r(g) = 0.
-3, -1
Let a(m) be the second derivative of -23*m**4/3 + 1706*m**3/3 - 148*m**2 + 1613*m. Let a(d) = 0. What is d?
2/23, 37
Let a be 13/3 - 10/(-15). Suppose j + 4*w = 23, a*j + 1 = 5*w - 9. Factor 21 - 8*k**2 - k**3 - 3*k**j + 11 + 16*k.
-4*(k - 2)*(k + 2)**2
Suppose 52*f**4 - 256/5 - 184/5*f**3 - 976/5*f**2 + 1184/5*f - 28/5*f**5 = 0. What is f?
-2, 2/7, 1, 2, 8
Let q(g) be the first derivative of -16*g - 12*g**2 - 53 - 4*g**3 - 1/2*g**4. Factor q(h).
-2*(h + 2)**3
Let r be (-1872)/(-266) + -21*23/69. Let i = r - -650/399. Factor -10/3 - i*g + 5/3*g**2.
5*(g - 2)*(g + 1)/3
Let b(g) = -52*g - 117. Let j be b(-5). Let y be 7*j/154 - (-2)/(-1). What is z in 3/4*z**3 + 9/2*z**2 - y*z**4 - 3/4*z + 0 = 0?
-1, 0, 1/6, 1
Let s(o) be the third derivative of -o**7/140 + 21*o**6/10 - 83*o**5/20 - 21*o**4/2 + 167*o**3/4 + 2719*o**2. Suppose s(a) = 0. What is a?
-1, 1, 167
Factor 133*i**3 - 2382*i - 30423*i - 810*i**2 - 138*i**3.
-5*i*(i + 81)**2
Let m = -153 - -155. Suppose 234*l**m - 18*l**2 - 485*l**3 - 140*l + 225*l**2 - 66*l**2 + 305*l**4 - 75*l**5 + 20 = 0. Calculate l.
2/5, 2/3, 1
Suppose -6*f**2 - 27*f + 73*f**2 - 28*f**2 - 351 + 3*f**3 = 0. What is f?
-13, -3, 3
Factor 1/4*k**2 + 159/4 + 14*k.
(k + 3)*(k + 53)/4
Let f(g) be the second derivative of -236 + 47/9*g**2 + g + 1/54*g**4 - 16/9*g**3. Factor f(i).
2*(i - 47)*(i - 1)/9
Let j(n) be the third derivative of -27*n**7/1120 + 3*n**6/80 - n**5/40 + 91*n**4/24 - 2*n**2 + 16. Let x(o) be the second derivative of j(o). Factor x(h).
-3*(9*h - 2)**2/4
Determine d, given that 54 - 28944*d**2 - 805/3*d**5 - 14482*d**3 - 9658/3*d**4 - 21663*d = 0.
-3, 2/805
Factor -3/7*n**3 + 0 + 114/7*n**2 + 117/7*n.
-3*n*(n - 39)*(n + 1)/7
Let n(t) = 15*t**3 + 4535*t**2 + 52295*t + 47600. Let r(x) = x**3 + 267*x**2 + 3076*x + 2800. Let d(h) = -2*n(h) + 35*r(h). Suppose d(q) = 0. Calculate q.
-40, -14, -1
Let r be (-14)/7*(-4)/(8/3). Let -2 - 7 - 3*b + 3*b**2 + 3 + 3*b**2 + r*b**3 = 0. Calculate b.
-2, -1, 1
Let v(a) be the first derivative of 0*a + 2/9*a**3 + 0*a**2 - 108 + 1/8*a**4 - 1/30*a**5. Factor v(f).
-f**2*(f - 4)*(f + 1)/6
Let m(u) be the second derivative of u**6/120 - u**5/20 - 3*u**4/8 - 2*u**3/3 - 2*u**2 - 2*u + 146. Let t(h) be the second derivative of m(h). Factor t(z).
3*(z - 3)*(z + 1)
Let w = 767/60 - 249/20. Let q = -736 + 738. Factor 2/3 - z**q + w*z**4 + 1/3*z**3 - 1/3*z.
(z - 1)**2*(z + 1)*(z + 2)/3
Let l(d) be the first derivative of 148 + 184/3*d - 94/3*d**2 + 4/9*d**3. Factor l(j).
4*(j - 46)*(j - 1)/3
Let h(j) be the third derivative of -10*j**3 - 6*j**2 - 5/336*j**8 + 0 + 1/12*j**6 + 2*j**5 - 5/24*j**4 - 21*j - 2/7*j**7. Let h(k) = 0. Calculate k.
-12, -1, 1
Let n(z) = z**2 - 10*z + 19. Let p be n(6). Let m = p + 21. Factor f**2 + 19 - 34 + m + 2*f.
(f + 1)**2
Let w(i) = 23*i - 227. Let v be w(10). Solve -3*f**4 + 317*f**3 - 158*f**v - f**5 - 5*f**4 + 4*f**4 - 162*f**3 = 0.
-3, -1, 0
Let b(w) = 10 + 2*w**2 - w**3 - 10*w**2 + 2*w**3 - 36*w + 35*w. Let o be b(8). Factor 15*g**o - 854 + 854 - 8*g + 5*g**2.
4*g*(5*g - 2)
Determine w, given that 115/6*w**2 - 35/6*w**3 + 13/3*w + 3/2*w**5 + 0 - 115/6*w**4 = 0.
-1, -2/9, 0, 1, 13
Let z(g) be the second derivative of 9*g**5/80 + 11*g**4/4 + 135*g**3/8 - 75*g**2/4 + 3489*g. Determine i so that z(i) = 0.
-10, -5, 1/3
Solve 1/6*x**5 + 0 + 2/3*x**3 + 0*x**2 + 0*x + 5/6*x**4 = 0 for x.
-4, -1, 0
Let t(a) = -45*a**3 - 54*a**2 + 9*a - 12. Let z(g) = -g**3 - g**2 + g - 5. Let v(c) = -1. Let y(o) = 4*v(o) - z(o). Let j(b) = -t(b) - 15*y(b). Solve j(d) = 0.
-1, -1/2, 1/5
Let m(q) be the third derivative of 0*q - 7/20*q**4 + 79*q**2 + 0 + 2/15*q**5 + 0*q**3 + 1/300*q**6. Factor m(n).
2*n*(n - 1)*(n + 21)/5
Let a(t) be the first derivative of -3*t**3 - 21*t + 19 + 1/8*t**4 + 27*t**2. Let w(g) be the first derivative of a(g). Solve w(k) = 0.
6
Suppose 0 = 2*w - p - 149, 91 = 4*w + 3*p - 232. Determine u, given that w*u**2 - 54*u**2 - 19*u**2 - 8*u - u**4 + 2*u**3 = 0.
-2, 0, 2
Factor -9*i**2 - i - 36*i - 63*i - 135 + 27*i**2 + 17*i**2.
5*(i + 1)*(7*i - 27)
Factor -380*k**2 - 320 - 5/4*k**5 - 560*k - 125*k**3 - 20*k**4.
-5*(k + 2)**2*(k + 4)**3/4
Let t(f) be the first derivative of -56/5*f - 27/5*f**2 - 145 + 2/15*f**3. Factor t(g).
2*(g - 28)*(g + 1)/5
Let i = -1004999/120 - -8375. Let u(b) be the third derivative of -i*b**6 + 0*b + 1/24*b**4 - 29*b**2 + 0 + 1/9*b**3 - 1/90*b**5. Factor u(x).
-(x - 1)*(x + 1)*(3*x + 2