-x**9/1680 + x**8/448 + x**7/420 - x**4/6 - x**3/3 + 106*x. Let a(n) be the third derivative of b(n). Factor a(z).
-3*z**2*(z - 2)*(3*z + 1)
Let y(o) be the third derivative of 0*o + 28/9*o**4 - 4/3*o**3 + 2*o**2 - 31/10*o**5 + 9/20*o**6 - 7. Solve y(f) = 0 for f.
2/9, 3
Let m(g) be the first derivative of g**6/30 + 4*g**5/5 + 32*g**4/5 + 226*g**3/15 - 93*g**2/2 - 270*g + 677. Solve m(f) = 0.
-9, -5, -3, 2
Let n(y) = 8*y**5 + 24*y**4 - 7*y**3 - 203*y**2 + 7. Let k(l) = l**5 + 2*l**4 - l**2 + 1. Let b(f) = 7*k(f) - n(f). Suppose b(r) = 0. Calculate r.
-7, 0, 4
Let z(t) = 14*t**3 + 234*t**2 - 3068*t + 9460. Let n(q) = 3*q**3 - q**2 + q + 7. Let l(a) = -4*n(a) + z(a). Factor l(k).
2*(k - 6)**2*(k + 131)
Find c, given that -1/3*c**4 + 212/3*c**2 - 7*c**3 - 188*c + 464/3 = 0.
-29, 2, 4
Let z(l) be the second derivative of 2 + 1690*l**2 + 5/12*l**4 + 47*l + 130/3*l**3. Factor z(p).
5*(p + 26)**2
Let a(x) be the second derivative of -23*x - 3 - 7/33*x**3 - 1/66*x**4 + 18/11*x**2. Factor a(g).
-2*(g - 2)*(g + 9)/11
Determine o, given that 6*o**5 + 0 + 15/2*o**4 + 0*o - 69/2*o**3 - 9*o**2 = 0.
-3, -1/4, 0, 2
Let c(g) = 2*g**3 + 13*g**2 + 4*g - 10. Let a be c(-5). Let s be -2*(a/12 - 4)*94. Factor -2*d**2 - 5 + 9*d + 32*d**3 + 7*d**2 + 6*d - s*d**3.
-5*(d - 1)*(d + 1)*(3*d - 1)
Suppose -53*w + 51*w = -2022. Let y = -1008 + w. Factor 8/5*t - 8/5*t**2 + 2/5*t**y + 0.
2*t*(t - 2)**2/5
Let z be 2/8*112/(-21)*66/(54 + -76). Solve 0 - 31/2*t**z + 1/2*t**5 + 0*t + 112*t**3 + 128*t**2 = 0.
-1, 0, 16
Let x(i) be the first derivative of -16393*i**2 - 275/2*i**4 - 2418*i**3 - 14/5*i**5 - 8788*i - 85. Factor x(n).
-2*(n + 13)**3*(7*n + 2)
Suppose 3*n**3 - 17/4*n**2 + 0 - 1/4*n**4 - 15/2*n = 0. What is n?
-1, 0, 3, 10
Let k(q) = -58224*q - 232893. Let d be k(-4). Let 1/5*v**d - 2/5*v**2 + 0*v + 0 = 0. What is v?
0, 2
Let p(q) be the third derivative of q**6/40 - 307*q**5/60 + 25*q**4/6 + 34*q**3 + 784*q**2. Factor p(f).
(f - 102)*(f - 1)*(3*f + 2)
Let g = 295 - 2371. Let w = g - -14534/7. Factor 4/7*p**3 + 2/7*p**2 - w*p**4 + 0 - 4/7*p.
-2*p*(p - 2)*(p - 1)*(p + 1)/7
Let s(c) be the second derivative of -1/54*c**4 + 1 + 22/9*c**2 - 7/9*c**3 + 14*c. Factor s(n).
-2*(n - 1)*(n + 22)/9
Let o be (-2 + -4)*(-6)/((-240)/(-20)). Let m(v) be the third derivative of 0*v**o + 0*v**4 - 1/360*v**6 - 1/180*v**5 + 0 - 20*v**2 + 0*v. Factor m(j).
-j**2*(j + 1)/3
Suppose -l + 3 = -2*u, 8*l = 4*l - 3*u + 23. Let p(a) = 11*a**2 + 212*a. Let q(i) = 16*i**2 + 316*i. Let g(v) = l*q(v) - 7*p(v). Factor g(o).
3*o*(o + 32)
Let m(f) = 2*f**3 + f**2 - 16*f - 3. Let p be m(-3). Suppose p = 5*g - 10, 4*n + g + 72 = 86. Factor -1/5*l**n - 2/5*l**2 - 1/5*l + 0.
-l*(l + 1)**2/5
Suppose 11 = -5*a + 1. Let y be (150/100)/(0 - a/4). Determine f, given that 2*f - 6*f**y - 2*f + 12*f**4 - 18*f**4 - 2*f**2 - 2*f**5 = 0.
-1, 0
Let p be (0 - -2) + 42/7. Suppose -2*u - 8*v = -10*v - p, 3*v = u - 12. Let 0*a + 7/3*a**4 + u + 3*a**3 + 2/3*a**2 = 0. Calculate a.
-1, -2/7, 0
Let g(p) be the second derivative of p**6/165 - p**5/5 - 101*p**4/66 - 26*p**3/11 + 225*p + 3. Suppose g(r) = 0. What is r?
-3, -1, 0, 26
Let h(n) = -n**2 + 182*n - 4915. Let f be h(33). Determine i, given that 3/2*i**3 + 0*i + 3*i**f + 0 = 0.
-2, 0
Let u(n) be the second derivative of -n**4/8 + 75*n**2/4 - 36*n + 1. What is z in u(z) = 0?
-5, 5
Let j be (-1483)/(12/20 - 16/(-40)). Let i = j - -1485. Suppose -10/11 - 2/11*k + 2/11*k**3 + 10/11*k**i = 0. What is k?
-5, -1, 1
Let g(v) = -v - 3. Let k be g(-16). Determine m so that -18*m**4 - 12*m + 4*m**3 - 2*m**2 + 3*m**4 + 3*m**4 + k*m**4 + 9 = 0.
-3, 1
Let b(s) = -13 + 5 - 8 + 5*s - s. Let w be b(6). Let h(c) = -11*c**3 + 13*c - 12. Let l(p) = 17*p**3 - 19*p + 18. Let a(g) = w*h(g) + 5*l(g). Factor a(z).
-3*(z - 1)**2*(z + 2)
Let r(f) be the third derivative of -f**5/60 - 2789*f**4/12 - 7778521*f**3/6 - 276*f**2 + 5*f. Factor r(j).
-(j + 2789)**2
Let p(z) be the second derivative of 5/2*z**3 + 4*z + 8*z**2 + 14 - 1/12*z**4. Determine w, given that p(w) = 0.
-1, 16
Let g(r) = -r**2 + 29*r - 69. Let j be g(26). Solve 743*n**2 + 8*n - 784*n**2 - j*n = 0.
-1/41, 0
Let m be ((-39)/12 - (-2)/8) + 6. Let k be (-3 - 1) + m - (0 + -17). Find z such that 11*z**3 + 9*z**3 + z**4 - k*z**3 - 4*z - 4 + 3*z**2 = 0.
-2, -1, 1
Suppose -2*r + 9 = 5*a, 6*a - 3*r - 3 = 8*a. Suppose -a*j - 2*h = -7*h - 20, j = 2*h + 8. Solve 9/4*o**2 - 1/2*o + j = 0.
0, 2/9
Let i(b) = 15*b**2 + 447*b - 471. Let r(f) = 2*f**2 - 2*f - 1. Let k(d) = -i(d) + 9*r(d). Factor k(m).
3*(m - 154)*(m - 1)
Let s = -89430 - -89432. Solve -22/3*l**3 + 0 - 2/3*l**4 - 32*l - 80/3*l**s = 0.
-4, -3, 0
Let u = 654503/2 - 327249. Factor 10/3*q**2 - u*q - 5/6*q**3 + 0.
-5*q*(q - 3)*(q - 1)/6
Let y be 1/(-6) - (-323)/102 - -9. Suppose 2*k = 3*f + 8, 0 = 3*k - 0*k - y. Solve f*q + 21/8*q**3 + 0 - 3/2*q**4 + 3/4*q**2 = 0.
-1/4, 0, 2
Let j(t) = -171*t**3 - 14*t**2 + 27*t. Let m be j(2). Let s = -12328/9 - m. Find h, given that 4/9 - s*h - 2/3*h**2 = 0.
-1, 2/3
Let b = 425 - 423. Let k be b/13 - ((-8080)/195)/8. Solve 8*x + 2/3*x**3 - k - 4*x**2 = 0.
2
Find v such that -19*v**3 + 9*v**4 - 2*v**3 + 25*v - 23*v**2 - 30*v**2 + 63*v**2 - 15*v**2 = 0.
-1, 0, 5/3
Let c be (-6)/(-12) + (-6)/(-4). Let y(h) = 2*h**3 + 2*h**2 + h + 2. Let n be y(0). Let 6*b**c - n*b**2 - 3*b - 86*b**3 + 93*b**3 = 0. Calculate b.
-1, 0, 3/7
Suppose 6*m + 1 = 7*m. Let v be -3 + (-1)/(m/(-5)). Factor r**2 + r**v + 18 + 5*r**2 - 15*r - 4*r**2.
3*(r - 3)*(r - 2)
Let t be (1860/140)/(3/(-106)). Let o = 470 + t. Factor o + 2/7*f**2 + 6/7*f.
2*(f + 1)*(f + 2)/7
Let z(y) be the second derivative of -y**6/24 + y**5/4 + 5*y**4/6 + 5*y**2/2 + 65*y. Let a(m) be the first derivative of z(m). Factor a(s).
-5*s*(s - 4)*(s + 1)
Let h(m) = -m**3 - 24*m**2 - 27*m - 21. Let q be h(-23). Let z = q - 71. Solve 5/6*j - 5/6*j**2 + z = 0 for j.
0, 1
Let b(m) = -40571*m - 162280. Let r be b(-4). Find o, given that -392/9 - 2/9*o**r - 218/9*o**2 - 4*o**3 - 56*o = 0.
-7, -2
Let a be (48/120)/(4/530). Find w, given that 647*w**3 + a*w**2 - 648*w**3 + 800*w - 3201*w + 45*w**2 = 0.
0, 49
Let w(p) be the second derivative of -p**4/36 - 485*p**3/9 - 235225*p**2/6 + 110*p + 3. Factor w(z).
-(z + 485)**2/3
Let j(n) be the second derivative of -n**7/210 - n**6/30 + 2*n**4/3 - 35*n**3/3 - 99*n. Let i(y) be the second derivative of j(y). Find k, given that i(k) = 0.
-2, 1
Let d be (-9 - 9 - -18)*(-4)/(-5 + 1). Factor d - 1/5*n**2 + 6/5*n.
-n*(n - 6)/5
Let d be 60/(-36) + (-61)/(-75)*5. Factor 0 + 12/5*x - d*x**3 + 2/5*x**2 - 2/5*x**4.
-2*x*(x - 1)*(x + 1)*(x + 6)/5
Factor 41408*u**3 - 2161*u + 41230*u**3 + 104661*u - 7050*u**2 + 375000 - 82491*u**3 - u**4.
-(u - 50)**3*(u + 3)
Let v(b) be the second derivative of b**6/40 - 3*b**5/4 + 51*b**4/16 + 63*b**3 + 162*b**2 + 3*b + 236. Suppose v(d) = 0. Calculate d.
-3, -1, 12
Let l = 7162/12775 + -241/1825. Solve l*v**4 + 81/7*v**2 + 81/7*v + 0 + 27/7*v**3 = 0 for v.
-3, 0
Let b(y) be the first derivative of -4/5*y + 6/5*y**2 + 4 - 7/25*y**5 + 11/15*y**3 - 3/5*y**4. Suppose b(i) = 0. What is i?
-2, -1, 2/7, 1
Let a be ((-2)/(-4)*2)/6. Let d(c) be the second derivative of 16/7*c**2 - 8*c + 0 + 8/21*c**3 + 1/70*c**5 - a*c**4. Factor d(f).
2*(f - 4)**2*(f + 1)/7
Let v be -4*(-1)/14 + (-32)/112. Let -n**4 + 13*n**3 - 9*n**3 + v*n**3 + 3*n**3 - 14*n**2 + 8*n = 0. Calculate n.
0, 1, 2, 4
Let n(s) be the first derivative of 2*s**5/45 - 119*s**4/9 + 9598*s**3/9 - 28084*s**2/9 + 27848*s/9 + 148. Determine k, given that n(k) = 0.
1, 118
Factor -878*h - 143*h - 539*h + 4*h**2 + h**2 + 121680.
5*(h - 156)**2
Suppose -4*f + 5*b + 17 = 0, f - 3 = 2*b - 1. Let i be 9/f + (-8)/(128/(-6)). Factor 2*k**2 + 0 + 0*k + i*k**3 - 1/2*k**4.
-k**2*(k - 4)*(k + 1)/2
Let o be 16/6 + (-1)/(-3). Let u = 11 + 5. Factor 8*n**2 + u*n - 2*n**3 - 32 - o*n**3 + n**3.
-4*(n - 2)**2*(n + 2)
Let y(k) = -k**3 - k**2 + 2. Let i(x) = -4*x**3 - 2*x**2 - x + 7. Suppose 15*t - 13*t - 14 = 0. Let f = -1 + -1. Let l(p) = f*i(p) + t*y(p). Factor l(m).
m*(m - 2)*(m - 1)
Let j be 31/(-806)*(-52)/10*(-160)/(-64). Factor -1/6*y**3 + 1/6*y + j - 1/2*y**2.
-(y - 1)*(y + 1)*(y + 3)/6
Let v(i) be the first derivative of 12*i**2 + 0*i**3 - 1/180*i**6 + 0*i - 1/45*i**5 + 17 + 1/12*i**4. Let o(s) be the second derivative o