 third derivative of m**5/80 + 53*m**4/32 - 6*m**2 - 564. Factor k(b).
3*b*(b + 53)/4
Let n(y) = -5*y**4 + 75*y**3 + 590*y**2 + 795*y - 1435. Let u(c) = -4*c**3 + c - 1. Let l(b) = n(b) + 5*u(b). Suppose l(s) = 0. Calculate s.
-4, 1, 18
Let s(m) be the second derivative of -1/15*m**3 + 7/60*m**4 - 9/100*m**5 + 0*m**2 - 1/210*m**7 + m + 59 + 1/30*m**6. Factor s(z).
-z*(z - 2)*(z - 1)**3/5
Suppose -3*x - 2*r - 3*r = -4, -5*r = 2*x + 4. Find z such that 509*z - 2*z**2 + x - 507*z + z**2 = 0.
-2, 4
Let c(a) be the third derivative of -19*a**7/630 + a**6/180 + 133*a**5/180 - 16*a**4/9 + 2*a**3/3 + 61*a**2 + 1. Solve c(y) = 0.
-3, 2/19, 1, 2
Factor -1/6*z**3 - 183/2*z - 22/3*z**2 - 351.
-(z + 9)**2*(z + 26)/6
Let g(a) be the second derivative of -49/72*a**4 - 1/18*a**3 + 3 + 0*a**2 + 21*a. Suppose g(d) = 0. Calculate d.
-2/49, 0
Let d(p) = p**2 + 452*p + 51029. Let f be d(-219). Determine b so that 32/13*b + 0 - 2/13*b**3 - 12/13*b**f = 0.
-8, 0, 2
Suppose -30*h - 20 + 50 + 30 = 0. Let z(w) be the second derivative of 1/48*w**3 - 1/8*w**h + 12*w + 0 + 1/96*w**4. Factor z(o).
(o - 1)*(o + 2)/8
Let r(x) = 5*x**4 - 161*x**3 - 670*x**2 - 945*x - 405. Let a(p) = -2*p**4 + 80*p**3 + 336*p**2 + 472*p + 202. Let q(f) = -9*a(f) - 4*r(f). Solve q(n) = 0 for n.
-33, -3, -1
Suppose -4*f + 3*f + 235 = 0. Suppose f = 4*b + 39. What is q in -10*q - 11*q**2 + b*q**2 + 10*q**3 - 3*q**2 - 35*q**4 = 0?
-1, 0, 2/7, 1
Suppose -w = -2*n - 3*n + 49, -26 = -3*n + 4*w. Let p be ((-2)/n + -1)*-10. Factor -10*h**3 - p*h - 8*h**3 + 17*h**3 + 8 + 6*h**2.
-(h - 2)**3
Let r = -1515/286 - -30053/2002. Solve -2/7*m**2 + 10 + r*m = 0.
-1, 35
Let o = -121 + 124. Factor -2*z**o - 3*z**3 - 26*z**3 + z**3 + 3*z**4.
3*z**3*(z - 10)
Let l be ((-16)/195)/4*2097/(-1398). Let d(b) be the first derivative of 7 - 1/13*b**2 - 3/26*b**4 + 0*b + l*b**5 + 2/13*b**3. Find t, given that d(t) = 0.
0, 1
Suppose 29*s - 17*s - 1368 = 0. Suppose -117*a + 9 = -s*a, -4*n = a - 11. Suppose 8/3*u - 2/3*u**n - 2/3*u**3 + 8/3 = 0. Calculate u.
-2, -1, 2
Let h = 1679/1683 + -145/187. Determine x so that h*x**2 + 0 + 8/9*x = 0.
-4, 0
Let v(u) be the third derivative of u**8/6720 + u**7/1120 - u**6/360 - 8*u**3/3 + 39*u**2. Let m(c) be the first derivative of v(c). Solve m(y) = 0.
-4, 0, 1
Let r be (-6)/(-20) - 188/(-40). Determine o, given that 15*o**2 - 37*o**2 + o + 18*o**2 + 6*o**3 - 4*o**4 + o**r = 0.
0, 1
Let a(g) = -g**2 + g + 7. Let u(s) = -1 + 4 + 2 - 4. Let d = -22 - -12. Let q(x) = d*u(x) + 2*a(x). Find v such that q(v) = 0.
-1, 2
Suppose -3*r = -15 - 75. Suppose 0*a = 5*a - r. Factor 4*y**2 - 9*y**4 + 9*y**5 + 5*y**4 + a*y**3 - 15*y**3.
y**2*(y - 1)*(y + 1)*(9*y - 4)
Solve -956/7 - 2/7*q**2 - 482/7*q = 0 for q.
-239, -2
Let n(q) be the first derivative of -3*q**5/25 + 133*q**4/20 + 6*q**3 - 2271. Suppose n(c) = 0. Calculate c.
-2/3, 0, 45
Suppose r + 5 = -0*r + 3*b, 0 = -5*r - b - 41. Let x be (1/(-8))/(r/48). What is j in 0*j**2 + 3/4*j**5 - 3/2*j**4 + x*j**3 + 0*j + 0 = 0?
0, 1
Suppose -113 + 563 = 6*b. Let x = -217/3 + b. Factor 20*k**4 - 8*k**2 - 50/3*k**5 - x*k + 22/3*k**3 + 0.
-2*k*(k - 1)**2*(5*k + 2)**2/3
Let h(i) = i**3 - i - 1. Suppose -x + 11 = -4*u, 2*u - 4*u - 4*x = 28. Let b(d) = -3*d**3 - 3*d**2 - d + 1. Let w(m) = u*h(m) - 2*b(m). Let w(l) = 0. What is l?
-1
Let q(t) = t**3 - 9*t**2 + 4*t + 37. Let a be q(8). Suppose 2*h = 3*g - 6, -2*g + a*g + 3*h = 21. What is f in 2/3*f + 0 + 2*f**2 + 2/3*f**g + 2*f**3 = 0?
-1, 0
Let p(t) be the second derivative of -t**6/6 - 64*t**5 - 40315*t**4/6 + 27520*t**3 - 83205*t**2/2 - 1838*t. Factor p(s).
-5*(s - 1)**2*(s + 129)**2
Let p be (-297)/(-77) - 1/(-7). Suppose -p*c = -84 + 4. Factor -26*x - 7*x**2 + 32*x**4 - c + 80*x**3 + 25*x**2 + 24.
2*(x + 1)*(x + 2)*(4*x - 1)**2
Let h be ((-8080)/38380)/(10/(-171)). Determine j so that 4/5*j**3 + 4*j + 0 - h*j**2 = 0.
0, 2, 5/2
Find u such that -u**3 - 6534 - 55425*u - u**3 + u**3 - 10*u**2 + 54479*u + 3*u**3 = 0.
-11, 27
Let u(n) be the third derivative of 0 - 19/480*n**6 + 108*n**2 + 0*n + 1/280*n**7 - 3/32*n**4 + 0*n**3 + 11/80*n**5. Factor u(s).
s*(s - 3)**2*(3*s - 1)/4
Let k(i) be the second derivative of i**5/35 + 33*i**4/7 + 241*i + 3. Determine r, given that k(r) = 0.
-99, 0
Let u(a) be the second derivative of 0 - 7/2*a**4 - 19/2*a**2 + 1/10*a**5 - 19*a + 7/40*a**6 - 4*a**3. Let h(k) be the first derivative of u(k). Factor h(q).
3*(q - 2)*(q + 2)*(7*q + 2)
Suppose -20*u + 19*u + 8 = 5*m, 0 = -m + u + 4. Factor 2*x**2 + 12*x**3 + 17*x**2 + 4*x**5 - 20*x**4 - 16*x + x**m.
4*x*(x - 4)*(x - 1)**2*(x + 1)
Let w(q) be the second derivative of -q**6/10 - 93*q**5/20 - 109*q**4/2 - 226*q**3 - 396*q**2 - 145*q + 2. Suppose w(r) = 0. What is r?
-22, -6, -2, -1
Let r(b) be the second derivative of -b**5/20 - 29*b**4/12 + b**3/6 + 29*b**2/2 + 7878*b. Factor r(k).
-(k - 1)*(k + 1)*(k + 29)
Let m be -76*(102/24)/1. Let a = m - -325. Factor -10*o - 50 - 1/2*o**a.
-(o + 10)**2/2
Let f(a) = -26*a**2 - 46*a + 48. Let b(q) = 2*q**2 + q - 1. Let r be (-1)/1 - ((-6)/1 - -4). Let c(z) = r*f(z) + 12*b(z). Factor c(t).
-2*(t - 1)*(t + 18)
Let a(d) be the first derivative of d**3/12 + 17*d**2/8 + 4*d + 1165. Suppose a(x) = 0. Calculate x.
-16, -1
Let m(z) be the third derivative of 7*z**6/60 - 169*z**5/15 + 347*z**4/4 - 90*z**3 + 2794*z**2. Let m(p) = 0. Calculate p.
2/7, 3, 45
Let x be (-80)/30*(-3 - 9/(-6)). What is s in -52*s**3 + 0*s + 4*s - x*s**2 - 13*s**5 + 61*s**5 + 4*s**4 = 0?
-1, -1/3, 0, 1/4, 1
Suppose -11*t = -5*o - 6*t + 20, -2*o + 5*t + 20 = 0. Suppose 2*n + 7*n = o. Factor n + 5/4*j - 1/4*j**2.
-j*(j - 5)/4
Let r(d) = -5*d**3 - 5*d**2 - 4*d + 1. Let a be r(-1). Solve -39*t**a - 20*t**3 - 30*t**5 - 108*t**4 + 119*t**2 - 55*t**5 + 104*t**5 + 40*t - 11*t**2 = 0 for t.
-5, -1, -2/5, 0, 1
Let c(k) be the second derivative of -k**4/3 - 148*k**3/3 - 1680*k**2 - 117*k. Factor c(g).
-4*(g + 14)*(g + 60)
Let i(f) be the first derivative of -6/5*f**2 + 55 - 1/5*f**3 - 12/5*f. Find y such that i(y) = 0.
-2
Suppose -5*f + 0*f = -6*f. Suppose v - 18 = -2*v + 2*q, -2*v + 4*q + 20 = f. Factor 4*u**2 + 12*u + 0*u**2 + 3*u**2 - v*u**2.
3*u*(u + 4)
Let o be (-4365)/(-3990) - (23/(-7) + 3). Let v = o - 9/38. Find w such that -4/7*w**2 - v*w - 4/7 = 0.
-1
Solve 334/3*d**2 + 12*d**3 - 2/3*d**4 - 800/3 + 144*d = 0 for d.
-4, 1, 25
Let s(d) = 11*d**2 + 3*d - 8. Let n be s(2). Find z such that z**3 - n + 86*z - z**3 - 46*z**2 + 2*z**3 = 0.
1, 21
Find n such that 12*n - 2/3*n**3 + 2*n**2 + 0 = 0.
-3, 0, 6
Let n(l) be the first derivative of -3*l**2 - 76 + 7*l**2 + 13*l**2 - 12*l - l**3 - 11*l**2. What is o in n(o) = 0?
2
Let f(h) = h**2 + 12*h - 27. Let r be f(-15). Suppose 0 = 4*l + r - 30. Factor 0*t**2 + 0 - 4/3*t + 1/3*t**l.
t*(t - 2)*(t + 2)/3
Let g(n) = n**2 - 19*n + 2. Let a be g(19). Factor 192*i - 2*i**2 - i**a + 96 - 204*i.
-3*(i - 4)*(i + 8)
Let z(g) be the first derivative of g**5/3 - 25*g**4/2 - 325*g**3/9 + 25*g**2 + 320*g/3 + 4741. Suppose z(b) = 0. What is b?
-2, -1, 1, 32
Let u = 22561/2 + -11279. Factor -6*f**2 + u*f + 9*f**3 + 3/2*f**5 + 0 - 6*f**4.
3*f*(f - 1)**4/2
Let c(m) = -3*m**2 - 462*m + 2. Let b be c(0). Determine v so that 2/3*v - 4/3*v**3 - 14/3 + 28/3*v**b + 2/3*v**5 - 14/3*v**4 = 0.
-1, 1, 7
Let m be (-224)/(-14000) - 10071/(-3375). Let -2592/5 + 352*q**m - 10*q**4 - 14768/5*q**2 - 12672/5*q = 0. What is q?
-2/5, 18
Let d(z) = -z + 1. Let i(j) = -9*j - 3907*j**2 + 8 + 3892*j**2 - 4*j. Let q(p) = p**3 - 4*p**2 + 2*p. Let f be q(3). Let m(a) = f*d(a) + i(a). Factor m(l).
-5*(l + 1)*(3*l - 1)
Factor 5561*n**3 - 5558*n**3 + 3*n**2 - 36*n**2 - 180*n.
3*n*(n - 15)*(n + 4)
Let x(n) be the second derivative of -1/48*n**4 + 158*n + 0 + 1/2*n**3 - 11/8*n**2. Solve x(u) = 0 for u.
1, 11
Let s(w) = 5*w**2 - 2*w + 4. Let r be s(3). Let x = 46 - r. Factor -5*q + 5*q**x + 122*q**2 - 122*q**2.
5*q*(q - 1)*(q + 1)
Let g(q) be the third derivative of q**7/1470 + q**6/70 + 37*q**5/420 - 5*q**4/28 - 100*q**3/21 + 39*q**2 + 48. Find y, given that g(y) = 0.
-5, -4, 2
Let g = 169 + -44. Let f = 134 - g. Factor 9*p**2 - 49 - 46 + f*p + 3*p**3 + 98.
3*(p + 1)**3
Let t(p) be the first derivative of -p**5/210 - 5*p**4/28 - 26*p**3/21 + 115*p**2/2 - 127. Let m(d) be the second derivative of t(d). Factor m(v).
-2*(v + 2)*(v + 1