hird derivative of 5*y**2 + 1/20*y**5 + 0 - 1/40*y**6 + 1/2*y**h + 0*y - 2*y**3. Factor j(a).
-3*(a - 2)*(a - 1)*(a + 2)
Let n(v) be the first derivative of v**8/560 + 3*v**7/140 - 7*v**6/120 + 6*v**3 - 29. Let f(y) be the third derivative of n(y). Factor f(t).
3*t**2*(t - 1)*(t + 7)
Suppose 37*z + 43565 = -5571. Let t = -1325 - z. Suppose 1/4*i**2 + 1/2*i**t - 1/4*i**4 + 0 - 1/2*i = 0. What is i?
-1, 0, 1, 2
Let k(f) = -4*f**4 - 13*f**3 + 37*f**2 - 5*f + 5. Let l(g) = -g**3 + g**2 - g + 1. Let a be 1*-2*(-2 + 4)/4. Let c(x) = a*k(x) + 5*l(x). Factor c(b).
4*b**2*(b - 2)*(b + 4)
Let t(p) be the second derivative of -p**6/50 + 9*p**5/20 - 63*p**4/20 + 81*p**3/10 - 1891*p. Factor t(c).
-3*c*(c - 9)*(c - 3)**2/5
Let y(g) be the second derivative of -11/15*g**6 - 17/5*g**5 - 7*g**2 - 1/21*g**7 - 17 - 29/3*g**3 - 23/3*g**4 - 3*g. Factor y(o).
-2*(o + 1)**4*(o + 7)
Let w(l) = -l**2 - 16*l + 18. Let m be (-3)/(3/(1 - -14)). Let i be w(m). Determine o, given that 17*o**3 + 8*o**2 - 4*o - i*o**3 + 14*o**3 - 2*o = 0.
0, 1, 3
Let j(h) be the third derivative of h**7/42 + 247*h**6/12 - 124*h**5 + 3725*h**4/12 - 2485*h**3/6 + 16*h**2 - 36*h. Let j(z) = 0. Calculate z.
-497, 1
Let k(d) be the second derivative of -d**7/105 - 4*d**6/75 + d**5/10 + 6*d**4/5 + 12*d**3/5 + 435*d - 2. Let k(w) = 0. Calculate w.
-3, -2, 0, 3
Suppose 15*i = 8*i + 7. Let s(x) = 26*x**3 + 2*x**2 + 42*x + 6. Let m(z) = -2*z**3 + z**2 - z + 1. Let d(t) = i*s(t) + 12*m(t). Factor d(y).
2*(y + 1)*(y + 3)**2
Let w(t) be the third derivative of 0 - 1/21*t**4 + 1/420*t**5 + 2/7*t**3 + 2*t**2 - 6*t. Let w(d) = 0. Calculate d.
2, 6
Let k = 182952 - 182952. Solve 1/2*c**3 - 3/2*c**2 - 1/2*c + 3/2*c**4 + k = 0 for c.
-1, -1/3, 0, 1
Let r(z) = -4*z**3 + 115*z**2 - 6*z - 130. Let s(x) = -x**3 - 4*x**2 - x + 1. Let k(h) = 2*r(h) - 10*s(h). Suppose k(j) = 0. Calculate j.
-135, -1, 1
Let t = -248093/2 + 124048. Factor 3*d + t*d**2 + 3/2.
3*(d + 1)**2/2
Let t(q) be the first derivative of q**5/120 + q**4/16 + q**3/6 + q**2/2 - 7*q + 3. Let f(p) be the second derivative of t(p). Factor f(k).
(k + 1)*(k + 2)/2
Suppose 8*w + 114 = 458. Let c be (-102)/(-117)*w + (-2)/13. Factor -2*p - c*p**3 + 0 + 32/3*p**4 + 50/3*p**2.
2*p*(p - 3)*(4*p - 1)**2/3
Let z = 34430 + -34428. Factor 8/5 + 18/5*x + 12/5*x**z + 2/5*x**3.
2*(x + 1)**2*(x + 4)/5
Let y = 34927 - 314341/9. Let r = 308/9 - 34. Factor r*m**3 - y*m - 2/9*m**4 + 2/9*m**2 + 0.
-2*m*(m - 1)**2*(m + 1)/9
Let o(f) be the third derivative of -f**7/315 - f**6/20 - 11*f**5/90 + 7*f**4/12 - 2177*f**2. Factor o(l).
-2*l*(l - 1)*(l + 3)*(l + 7)/3
Let i(t) be the third derivative of 0 + 0*t + 7/8*t**4 - 42*t**2 - 1/20*t**5 - 3*t**3. Determine p so that i(p) = 0.
1, 6
Let b = 4/91 + -5/273. Let w(m) be the second derivative of 0*m**2 + 0 - 1/195*m**6 + 1/78*m**4 - 6*m + b*m**3 - 1/130*m**5. Let w(d) = 0. Calculate d.
-1, 0, 1
What is r in 44/3*r**3 + 1648/3*r + 2060/3*r**2 - 368/3 = 0?
-46, -1, 2/11
Let s(b) = 8*b**2 - 97*b. Let q(t) be the third derivative of t**5/4 - 65*t**4/8 + 170*t**2. Let x(z) = -3*q(z) + 5*s(z). Suppose x(p) = 0. Calculate p.
0, 20
Let h(n) = -n**2 - 14*n - 24. Let u(v) = 17*v - 73. Let d be u(4). Let a(j) = -3*j**2 - 30*j - 48. Let m(p) = d*h(p) + 3*a(p). Let m(b) = 0. What is b?
-3, -2
Let s(r) be the second derivative of 118*r**4/3 - 78*r**3 - 2*r**2 - 58*r - 1. Factor s(q).
4*(q - 1)*(118*q + 1)
Let i(s) = 4*s**3 + 96*s**2 - 186*s + 86. Let d(c) = 7*c**3 + 192*c**2 - 372*c + 173. Let r(m) = 6*d(m) - 11*i(m). Factor r(a).
-2*(a - 46)*(a - 1)**2
Factor 407/3*j**3 + j**5 + 242/3*j**2 + 0*j + 68/3*j**4 + 0.
j**2*(j + 11)**2*(3*j + 2)/3
Let g(u) = 5*u**4 + 1990*u**3 - 4060*u**2 + 2015*u + 5. Let m(k) = 5*k**4 + 1994*k**3 - 4055*k**2 + 2016*k + 4. Let c(b) = -4*g(b) + 5*m(b). Factor c(t).
5*t*(t - 1)**2*(t + 404)
Let a(d) be the second derivative of 3/20*d**5 + 18*d**2 - 11/2*d**3 + 0 - 25*d - 1/2*d**4. Factor a(y).
3*(y - 4)*(y - 1)*(y + 3)
Let i = -1187/6 - -198. Let y(f) be the third derivative of i*f**5 + 16*f**2 + 0*f**3 + 1/42*f**7 + 0*f**4 - 1/8*f**6 + 0*f + 0. Find o such that y(o) = 0.
0, 1, 2
Let p(s) be the third derivative of -s**8/504 + 2*s**7/105 - s**6/60 - 13*s**5/45 + 2*s**4/3 - 795*s**2. Let p(w) = 0. What is w?
-2, 0, 1, 3, 4
Suppose 3*n = -3*v + 159, 76 = v + v - 4*n. Suppose 0 = 7*j - 29 - v. Find k, given that j*k - 35*k**2 - 8 - 161*k**2 + 3*k + 70*k = 0.
1/7, 2/7
Let w = 14336 + -47509/3. Let g = w + 1503. Let g - 8/3*r + 2/3*r**2 = 0. Calculate r.
2
Suppose 0 = 5*u - b - 3*b - 763, -6 = 3*b. What is v in 144*v**2 + 3*v**3 + u*v**2 - 280*v**2 = 0?
-5, 0
Let y(d) = 3122*d**2 - 6*d - 6. Let r be y(-2). What is j in -12464 + 3*j**2 + r - 16*j - j**2 = 0?
3, 5
Let n(z) be the second derivative of z**6/1620 + z**5/135 - 7*z**4/36 + 25*z**3/6 + 2*z**2 - 18*z + 1. Let j(m) be the second derivative of n(m). Factor j(o).
2*(o - 3)*(o + 7)/9
Let x be (3/2 - -40) + -41. Factor 3/2*y**2 - x*y - 3/2 + 1/2*y**3.
(y - 1)*(y + 1)*(y + 3)/2
Let t = -3562802/13 - -274062. Suppose 0 + 6/13*s**3 - 2/13*s**5 - t*s + 2/13*s**2 - 2/13*s**4 = 0. What is s?
-2, -1, 0, 1
Let n(k) = k**3 + 5*k**2 - k - 3. Let u be n(-5). Factor 148*m**2 - 214 - 110 - 72*m - 152*m**u.
-4*(m + 9)**2
Let p(d) be the first derivative of 2*d**3/9 - 113*d**2/3 - 76*d + 294. Solve p(r) = 0 for r.
-1, 114
Let t(l) = l**2 - 82225*l - 411147. Let b be t(-5). Solve -9/4*j + 0 + 3/4*j**2 + 9/4*j**b - 3/4*j**4 = 0 for j.
-1, 0, 1, 3
Let j = 642/49 - 1235/98. Let a(r) be the first derivative of 1/3*r**3 + 17 + 7/8*r**2 - j*r. Suppose a(x) = 0. What is x?
-2, 1/4
Let q(j) be the second derivative of 43*j**4/15 + 23*j**3/2 + j**2/5 - 5*j + 6. Factor q(u).
(u + 2)*(172*u + 1)/5
Let i(q) be the second derivative of 2/15*q**6 + 11/10*q**5 - 1/3*q**3 + 2*q**4 - 4*q**2 + 0 + 51*q. Determine w so that i(w) = 0.
-4, -1, 1/2
Suppose 103*x - 1288 = 33*x - 252*x. Factor -13/3*n**2 - x*n - 1/3*n**3 + 0.
-n*(n + 1)*(n + 12)/3
Let v(u) = u**3 + 9*u**2 - 9*u + 11. Let p be v(-10). Suppose 15 = 4*n - p. Determine a, given that -2*a**2 + 2 + n*a + 4 + 6*a**2 - 6*a**2 = 0.
-1, 3
Let f be (154 + -150)*(-3554)/8. Let v = f + 1780. Solve 0 - 12/5*a**v + 4/5*a**4 - 36/5*a**2 - 4*a = 0.
-1, 0, 5
Let l(f) be the third derivative of -22*f**2 + 51/20*f**5 - 49/4*f**4 - 7/40*f**6 + 0*f - 3 + 12*f**3. Solve l(j) = 0 for j.
2/7, 3, 4
Suppose -159*s - 109 = -181*s - 21. Let t(g) be the third derivative of 1/42*g**s + 15*g**2 - 1/210*g**6 + 0*g**5 + 0 + 0*g**3 + 0*g. Solve t(p) = 0 for p.
-1, 0, 1
Factor -94/3*g - 1/3*g**2 - 31.
-(g + 1)*(g + 93)/3
Let m be (-304215)/(-7140) - 6/56. Factor -50 - 27/2*u**2 - 19/10*u**3 - m*u - 1/10*u**4.
-(u + 4)*(u + 5)**3/10
Let a be (-7)/(-3)*((-8)/1 + 276/21). Let k be 0 + (-5)/(-2) - -2. Factor k*x**3 - 29/2*x**2 - 2 + a*x.
(x - 2)*(x - 1)*(9*x - 2)/2
Suppose 31*o - 803 = 4560. Factor 38*j - 270*j**2 - 56 + 28*j**5 + o*j + 161*j - 538*j**2 - 288*j**4 + 752*j**3.
4*(j - 7)*(j - 1)**3*(7*j - 2)
Suppose -90 + 1/2*k**2 + 179/2*k = 0. Calculate k.
-180, 1
Let s(d) = d**2 + 2*d - 5. Let j be s(-3). Let t be j/(((-18)/348)/(6/8)). Factor z - z**5 - 3*z**3 - 5*z**2 + 3*z + t - 29 + 5*z**4.
-z*(z - 4)*(z - 1)**2*(z + 1)
Suppose 8 = -p - 4*h, 4*p + 3*h - 25 = 6*h. Factor 3786*c**2 + 2*c**3 - p*c**3 - 2*c**3 - 3758*c**2 + 36 - 60*c.
-4*(c - 3)**2*(c - 1)
Let y(f) = f**3 - 20*f**2 - 1058*f + 8046. Let d be y(7). Let -48 + 27/2*w**d + 1/2*w**5 - 7*w**2 + 5*w**4 - 64*w = 0. Calculate w.
-4, -3, -1, 2
Suppose 0*l + m + 147 = 3*l, -49 = -l + m. Let s = l + -40. Factor 7*o**2 - 10*o - o**2 + s - 5.
2*(o - 1)*(3*o - 2)
Factor -15/4*s**5 - 57/2*s**3 + 0*s + 129/4*s**4 + 0 + 0*s**2.
-3*s**3*(s - 1)*(5*s - 38)/4
Let z(w) be the third derivative of -w**5/120 - 2951*w**4/24 - 8708401*w**3/12 - 5*w**2 + 29*w - 3. Let z(u) = 0. Calculate u.
-2951
Suppose 257 + 1463 = 430*o. Solve -7/2*b**2 + 1/2*b**5 - 5/2*b**o + b + 9/2*b**3 + 0 = 0 for b.
0, 1, 2
Let l(s) = -52*s**3 - 676*s**2 + 1592*s - 928. Let y(z) = -18*z**3 - 225*z**2 + 533*z - 310. Let r(t) = 5*l(t) - 16*y(t). Factor r(b).
4*(b - 1)*(b + 10)*(7*b - 8)
Let q(t) be the first derivative of -5*t**3/3 - 475*t**2/2 - 470*t - 4912. Factor q(z).
-5*(z + 1)*(z + 94)
Let t(x) be the second derivative of x**4/4 + 3*x**3 - 405*x**2/2 - 13069*