+ 5)/5
Let u(i) be the third derivative of -109/570*i**5 - 3/380*i**6 - 4/57*i**3 + 54/665*i**7 - 2*i**2 + 0 - 9*i - 10/57*i**4. Suppose u(z) = 0. Calculate z.
-1/2, -2/9, 1
Let r(y) = 16*y**2 - 194*y + 570. Let w(m) = 30*m**2 - 373*m + 1141. Let x(q) = 11*r(q) - 6*w(q). Factor x(j).
-4*(j - 18)*(j - 8)
Let i(t) be the third derivative of t**6/420 + t**5/30 + 5*t**4/42 - 22*t**2 + 21. Suppose i(r) = 0. What is r?
-5, -2, 0
Suppose -3*v + 4699 = -5*a + 146, -4*v - 5*a = -6024. Let r = v + -10574/7. Let -48/7*p**4 + 6/7*p - 45/7*p**2 - 96/7*p**3 + r = 0. What is p?
-1, -1/4, 1/4
Let 3*x**3 + 0*x**3 - 1120*x**2 + 3*x**3 - 4*x**3 + 72035*x + 84765*x = 0. What is x?
0, 280
Suppose 5*f + 0*f + 5*d = 730, 0 = -2*d - 2. Let t be 7*3/f + 2. Solve -t*w**2 - 12/7*w**3 - 6/7*w - 3/7*w**4 + 0 = 0.
-2, -1, 0
Let h be (-89)/(-11) + 3012/(-2761). Suppose 5*p - 3*p - 6 = 0. Factor -12*m + 15*m**p + 10*m**4 - 14*m**2 + 7*m**3 + m**4 - h*m**4.
2*m*(m - 1)*(m + 6)*(2*m + 1)
Let c(u) be the second derivative of u**7/21 - u**6/5 - u**5/2 + 5*u**4/2 + 4*u**3/3 - 12*u**2 + 32*u - 41. What is h in c(h) = 0?
-2, -1, 1, 2, 3
Let t(i) = i**3 - 14*i**2 - 12*i + 10. Let l(q) = 2*q**2 + q. Suppose 1 = -28*g + 27*g. Let z(j) = g*t(j) - 5*l(j). Factor z(h).
-(h - 5)*(h - 1)*(h + 2)
Let y(s) = 0*s**3 - 9*s - 5*s**3 - 42*s**2 + 33*s**2 - 8 + 6*s**3. Let c be y(10). Find n, given that -59*n**c + 21*n + 3*n**3 + 2 + 68*n**2 + 9 - 4*n**3 = 0.
-1, 11
Let t(p) = p**3 - 5097*p**2 + 5091*p + 5. Let d(y) = -3*y**3 + 17838*y**2 - 17817*y - 18. Let a(b) = 5*d(b) + 18*t(b). Suppose a(o) = 0. Calculate o.
0, 1, 851
Let l(c) be the second derivative of c**6/210 + 6*c**5/35 + 11*c**4/42 - 4*c**3/7 - 23*c**2/14 - 578*c + 1. Factor l(w).
(w - 1)*(w + 1)**2*(w + 23)/7
Let j(u) = -u**2 - 5*u - 2. Let o be j(-4). Factor -8*x - 9*x - 10*x - 2*x**o + 11*x - 32.
-2*(x + 4)**2
Let j = 789 - 776. Let b be (-64)/(-126) - (364/98)/j. Factor -4/9*c**4 + 0 + 2/9*c**2 + 0*c + b*c**3.
-2*c**2*(c - 1)*(2*c + 1)/9
Let k be 4 + ((-2200)/60)/11. Let w(h) be the second derivative of 1/12*h**4 + 27*h + k*h**3 + 2*h**2 + 0. Solve w(o) = 0 for o.
-2
Let z(m) be the first derivative of -2*m**3/21 + 614*m**2/7 - 188498*m/7 - 1691. What is r in z(r) = 0?
307
Factor -2/9*v**3 - 494/9*v - 70 + 134/9*v**2.
-2*(v - 63)*(v - 5)*(v + 1)/9
Factor -128*p - 127 - 1/4*p**3 - 131/4*p**2.
-(p + 2)**2*(p + 127)/4
Let x(v) be the third derivative of 3*v**7/14 + 4*v**6/3 + 11*v**5/4 + 25*v**4/12 + 1136*v**2. Factor x(c).
5*c*(c + 1)*(c + 2)*(9*c + 5)
Let b(r) be the third derivative of -r**8/1680 - 11*r**7/525 - 59*r**6/300 + 17*r**5/75 + 407*r**4/120 + 121*r**3/15 - 4303*r**2. Solve b(t) = 0 for t.
-11, -1, 2
Let q(w) be the second derivative of w**6/12 + 196*w**5 + 384160*w**4/3 + 726*w. Solve q(a) = 0 for a.
-784, 0
Let v be (1/4 - (-99)/36)/(311/311). Factor 18/5*n - 42/5*n**2 + 4 + 4/5*n**v.
2*(n - 10)*(n - 1)*(2*n + 1)/5
Let w(k) be the first derivative of -k**8/504 - 11*k**7/315 + k**2/2 - 65*k - 105. Let m(z) be the second derivative of w(z). Determine v so that m(v) = 0.
-11, 0
Suppose 9 = 5*b - 1. Let m be ((-2)/(-10))/((-6)/(-12)) - 8/(-5). Suppose 9/4*d - 1/4*d**m - b = 0. Calculate d.
1, 8
Let g = 251 - 292. Let r(y) = y**3 + 45*y**2 + 165*y + 43. Let f be r(g). Let 4/15*d**4 - 4/15*d**f + 2/15*d**5 - 2/15*d + 0*d**3 + 0 = 0. What is d?
-1, 0, 1
Let r(p) be the second derivative of 0*p**2 + 2 + 1/6*p**4 - 1/20*p**5 - 1/6*p**3 + 19*p. Factor r(x).
-x*(x - 1)**2
Factor 104*x - 63*x**2 - 48 - 178*x**4 - 153*x**4 + 6*x**3 + 332*x**4.
(x - 4)*(x - 1)**2*(x + 12)
Factor 14125/6*s + 2975/3*s**2 + 4375/2 + 5/6*s**5 + 205*s**3 + 125/6*s**4.
5*(s + 3)*(s + 5)**3*(s + 7)/6
Let o(x) be the second derivative of x**6/150 - 19*x**5/100 + 11*x**4/12 + 5*x**3/2 + 1832*x. Factor o(n).
n*(n - 15)*(n - 5)*(n + 1)/5
Let w = -219 - -242. Factor -9*o**2 - 27*o**4 - 45*o**3 - 26*o**5 + w*o**5 - 12*o**2.
-3*o**2*(o + 1)**2*(o + 7)
Let z = 139172 - 974159/7. Factor 27/7*m**5 - 17/7*m**2 - 27/7*m**4 - z*m**3 + 0 - 2/7*m.
m*(m - 2)*(3*m + 1)**3/7
Suppose 10*a = -13*a - 2*a. Suppose -2*n + 8 = -a*n. Let -136/5*c**3 - 84/5*c**n + 18/5*c**5 - 48/5*c**2 + 0 + 0*c = 0. What is c?
-2/3, 0, 6
Let v(t) be the third derivative of t**6/1080 + 11*t**5/36 + 3025*t**4/72 - 53*t**3/2 + 78*t**2. Let k(b) be the first derivative of v(b). Factor k(j).
(j + 55)**2/3
Let p(l) be the first derivative of l**5/12 + 55*l**4/24 + 25*l**3/3 + 11*l**2 + l - 32. Let i(n) be the second derivative of p(n). Let i(d) = 0. What is d?
-10, -1
Suppose 2*z - 5*n - 24 = 43, 2*z = -5*n + 117. Solve -2*o**2 + 86 - z - 42 - 4*o = 0.
-1
Let i(o) be the third derivative of -o**7/1050 + o**6/40 + 11*o**5/150 - 4*o**4/5 + 37*o**2 - 10*o + 5. Factor i(k).
-k*(k - 16)*(k - 2)*(k + 3)/5
Let j(w) be the third derivative of w**5/210 - 29*w**4/84 - 114*w**3/7 + 7*w**2 + 162. Suppose j(p) = 0. Calculate p.
-9, 38
Suppose 189/2*s - 63/4*s**2 - 3/4*s**3 - 78 = 0. Calculate s.
-26, 1, 4
Let f(o) be the third derivative of -o**5/20 + 47*o**4/8 - 23*o**3 - 298*o**2 + 2*o. Factor f(n).
-3*(n - 46)*(n - 1)
Let b(t) be the first derivative of -t**3 - 309*t**2/2 - 3276*t + 7213. Determine r, given that b(r) = 0.
-91, -12
Let m(z) = -385*z**2 - 40*z + 21. Let i be (2 + -1)*(4 + -13 + 8). Let b(d) = 1. Let k(r) = i*m(r) + b(r). Solve k(f) = 0 for f.
-2/7, 2/11
Factor -5*v**5 - 450*v**3 + 65*v - 358*v + 55*v**4 + 76*v + 27 - 70*v**2 + 564*v**2 + 96*v**4.
-(v - 27)*(v - 1)**3*(5*v - 1)
Determine c so that 1/9*c**3 - 86/9*c**2 + 0*c + 0 = 0.
0, 86
Factor -183/7*a - 540/7 - 1/7*a**2.
-(a + 3)*(a + 180)/7
Suppose 2/3*i - 2/3*i**3 + 44/3 - 44/3*i**2 = 0. What is i?
-22, -1, 1
Let w(n) = 8*n**2 + 3721 + 7*n**2 - 16*n - 112*n + 0*n**2 - 14*n**2. Let o(d) = 2*d**2 - 254*d + 7442. Let q(x) = -3*o(x) + 5*w(x). Factor q(t).
-(t - 61)**2
Let s be (-8 - 282/(-12))/(-1). Let n = -573/38 - s. Factor 6/19*h**3 + 0*h + n - 14/19*h**2.
2*(h - 2)*(h - 1)*(3*h + 2)/19
Let r = 1/101457 - -101455/202914. Factor t + 0 + r*t**2.
t*(t + 2)/2
Let y(o) = o**4 - 3*o**3 - 3*o**2 + 1. Let c(r) = r**5 - 15*r**4 + 120*r**3 - 316*r**2 + 261*r - 75. Let x(h) = c(h) - 6*y(h). Factor x(a).
(a - 9)**2*(a - 1)**3
Let t(m) be the second derivative of m**5/15 - 16*m**4/3 + 62*m**3 + 656*m**2/3 + 1853*m. Factor t(b).
4*(b - 41)*(b - 8)*(b + 1)/3
Suppose 20837*c - 20867*c = 0. Let c - 2*z - 1/2*z**2 = 0. Calculate z.
-4, 0
Let n(h) be the first derivative of h**8/420 + h**7/210 + h**3/3 - 3*h - 5. Let c(g) be the third derivative of n(g). Solve c(i) = 0.
-1, 0
Let h = 46893 + -140659/3. Determine y so that 0*y - 5/3*y**5 - h + 35/3*y**2 + 5/3*y**3 - 5*y**4 = 0.
-2, -1, 1
Let l be 66/77 - ((-13)/(-91)*-85 + 9). Factor 56 - 7*u**3 - 57/2*u**2 - 20*u - 1/2*u**l.
-(u - 1)*(u + 4)**2*(u + 7)/2
Let r = 55758 - 167270/3. Factor -r*l**3 + 0*l + 2/3*l**4 + 0*l**2 + 0.
2*l**3*(l - 2)/3
Let o(p) be the second derivative of -7*p**5/450 - p**4/90 + 15*p**2 + 7*p - 2. Let d(f) be the first derivative of o(f). Determine w, given that d(w) = 0.
-2/7, 0
Let k(j) be the first derivative of -j**4/40 - 139*j**3/15 + 279*j**2/20 - 6457. Find m such that k(m) = 0.
-279, 0, 1
Let c(n) = 5*n**3 - 457*n**2 + 157*n + 2277. Let r be c(91). Suppose 9/4*o**r + 3/4*o**3 + 0 + 0*o = 0. What is o?
-3, 0
Let s be ((26/520)/(6/8))/(72/540). Factor s*z + 1/6 + 1/6*z**3 + 1/2*z**2.
(z + 1)**3/6
Let w(f) = 2*f**3 - 5*f**2 - 6*f + 9. Let m be w(4). Suppose 0*k - m = -11*k. Factor 6*y**2 - 19*y**k + 4*y**3 - 3*y**5 - 65*y**4 + 77*y**4.
-3*y**2*(y - 2)*(y - 1)**2
Let x(y) be the third derivative of 3*y**5/20 - 11*y**4/12 - 7*y**3 - 5*y**2 + 9*y. Let b(j) = 13*j**2 - 23*j - 41. Let r(g) = -2*b(g) + 3*x(g). Factor r(n).
(n - 22)*(n + 2)
Suppose -8*l = -31*l. Let z(a) be the second derivative of -29*a - 7/60*a**5 + 0*a**3 - 1/18*a**4 + l*a**2 + 0. Determine f, given that z(f) = 0.
-2/7, 0
Suppose -58*i + 59*i = 3*c, 0 = -5*c + i + 4. Factor 26/7*l - 4/7 + 2*l**c.
2*(l + 2)*(7*l - 1)/7
Suppose 16/9 + 4/3*x**2 - 10/3*x + 2/9*x**3 = 0. Calculate x.
-8, 1
Let a(x) be the first derivative of x**4/20 - 1811*x**3/15 + 409512*x**2/5 + 820836*x/5 - 7811. Factor a(m).
(m - 906)**2*(m + 1)/5
Suppose 3*o - 31 = -5*z, -4*z + 6 = -3*o + 19. Let l(s) be the first derivative of 2*s + 5/3*s**3 - 30 - 7/