t h(d) be the third derivative of -14/27*d**4 + 0 + 4/945*d**7 + 7/135*d**6 + d**2 + 11/90*d**5 + 12*d + 16/27*d**3. Factor h(b).
2*(b + 4)**2*(2*b - 1)**2/9
What is t in -70/3*t + 73 - 1/3*t**2 = 0?
-73, 3
Let h = -36936 - -36941. Let x(c) be the first derivative of 18 + 1/9*c**6 - 1/3*c**4 - 8/9*c**3 + 4/15*c**h + 4/3*c + 1/3*c**2. Suppose x(k) = 0. What is k?
-2, -1, 1
Let i = 17 + 45. Suppose 0*w + 11 = w - g, -5*w + i = 2*g. Solve -29*a**3 - 48*a + 14*a**3 - 3*a**2 - w + 60*a**2 = 0 for a.
-1/5, 2
Let d(h) = -6*h**3 - 8*h**2 + 4*h - 4. Let a(o) be the first derivative of -7*o**4/4 - 3*o**3 + 5*o**2/2 - 5*o + 10. Let n(u) = -4*a(u) + 5*d(u). Factor n(t).
-2*t**2*(t + 2)
Let v(t) be the second derivative of t**7/168 + 47*t**3/6 + 63*t. Let y(d) be the second derivative of v(d). Find i such that y(i) = 0.
0
Let w = 49979 + -49977. Let 0 - 3/5*i + 3/5*i**w = 0. What is i?
0, 1
Let n be ((-4)/(-40))/((-8)/32)*(-2 - 1). Let x(t) be the second derivative of 0 - 9/50*t**5 - 13/20*t**4 - n*t**3 - 1/50*t**6 - 6/5*t**2 + 31*t. Factor x(j).
-3*(j + 1)**2*(j + 2)**2/5
Let z = -92/843 + 24064/4215. What is r in -z*r**2 - 24/5 + 2/5*r**3 + 10*r = 0?
1, 12
Factor 0 + 2/9*c**2 + 3092/9*c.
2*c*(c + 1546)/9
Let w(n) = 18*n**2 + n + 2. Let t be w(-1). Let z be (-13)/117 + t/9. Factor -2*b**4 + b**4 - 2*b**4 - 3*b**3 + b + 2*b + 3*b**z.
-3*b*(b - 1)*(b + 1)**2
Let r = 5598 - 5586. Let m(g) be the first derivative of -5/3*g**3 + 5*g**2 + r + 15*g. Find t such that m(t) = 0.
-1, 3
Let d(b) = 32*b**2 + 45613*b - 11407. Let s(u) = 52*u**2 + 68420*u - 17111. Let a(q) = 11*d(q) - 7*s(q). Factor a(l).
-3*(l - 1900)*(4*l - 1)
Let p(m) be the first derivative of m**4/16 - 11*m**3 + 630*m**2 - 10800*m - 3865. Factor p(a).
(a - 60)**2*(a - 12)/4
Let i(l) be the second derivative of -2*l**7/21 - 20*l**6 - 5624*l**5/5 + 50*l**4 + 3750*l**3 + 2216*l. Determine k, given that i(k) = 0.
-75, -1, 0, 1
Suppose 4*i = 3*v + 744, -7*v + 772 = 4*i - 3*v. Let -9*m**5 + 186*m**3 - i*m + 35*m**5 - 12*m**5 - 11*m**5 + 102*m**2 - 147 + 45*m**4 = 0. What is m?
-7, -1, 1
Let x(k) be the third derivative of 126*k**2 + 1/1260*k**6 + 0*k**3 + 1/252*k**4 + 1/315*k**5 + 0 + 0*k. Factor x(g).
2*g*(g + 1)**2/21
Let f(d) = -4418*d**2 + 2253*d - 243. Let q(x) = 4418*x**2 - 2254*x + 258. Let m(k) = -2*f(k) - 3*q(k). Factor m(r).
-2*(47*r - 12)**2
Suppose 0 = 3*l + 3*n - 36, 0 = -4*l - n + 4*n + 76. Factor 9*i**2 - l*i**2 + 8*i + 9*i**2.
2*i*(i + 4)
Let l(u) = -7*u**4 + 6*u**3 + 27 + 7*u**2 + 3*u**2 - 33. Let b(c) = 20*c**4 - 17*c**3 - 29*c**2 + 17. Let s(a) = 6*b(a) + 17*l(a). Let s(f) = 0. What is f?
-2, 0, 2
Let u be (-3 + 3)/5 - -4. Let i = -21733/9 + 2415. Suppose 1/3*z**3 - 1/9*z**u - 4/3*z + 8/9 + i*z**2 = 0. Calculate z.
-2, 1, 2
Let y(l) = -2*l**2 + 9*l + 23. Let g be y(6). Factor -i**g + 15*i**2 + 268*i**4 - 35*i**3 - 4*i**5 - 243*i**4.
-5*i**2*(i - 3)*(i - 1)**2
Let p = -1/113373 - -340124/566865. Factor 0 + p*r**2 + 4/5*r.
r*(3*r + 4)/5
Let f(m) = m**3 + 15*m**2 + 15*m + 16. Let q be f(-14). Let 2*t**2 + 8*t**3 - 8*t**2 - 7*t**3 + q*t**3 = 0. What is t?
0, 2
Let b be 0/38 + (-6)/(-9). Let m(x) be the first derivative of 1/9*x**3 - 28 - b*x - 1/6*x**2. Factor m(r).
(r - 2)*(r + 1)/3
Let b(k) be the third derivative of -1/12*k**4 - 1/630*k**7 + 57*k**2 + 1/180*k**5 + 0*k**3 + 0 + 0*k + 1/60*k**6. Factor b(o).
-o*(o - 6)*(o - 1)*(o + 1)/3
Let v be (((-6006)/78)/(-616))/((-1)/((-8)/6)). Let v*j**2 - 5/6*j + 1 = 0. What is j?
2, 3
Suppose -u = h, -5*h = 4*u - 10*u. Let w(m) be the second derivative of -1/15*m**6 + h + 8/3*m**3 + 2/3*m**4 - 1/5*m**5 + 0*m**2 - 15*m. Factor w(f).
-2*f*(f - 2)*(f + 2)**2
Let k(o) be the third derivative of o**6/1260 - 43*o**5/630 - 23*o**4/42 - 752*o**2. Determine p, given that k(p) = 0.
-3, 0, 46
Let x = -7/26 - -713/2600. Let i = 1577/4600 + x. Solve 2/23*l**2 - i*l + 6/23 = 0.
1, 3
Let n(s) be the first derivative of -1/12*s**3 - 34 - 6*s**2 - 144*s. Factor n(j).
-(j + 24)**2/4
Let w(b) = b**3 + 8*b**2 + b + 4. Let o be w(-7). Suppose s = -44 + o. Factor -2/3*f + 2*f**s + 0 + 8/3*f**3.
2*f*(f + 1)*(4*f - 1)/3
Let u = -34777/12 + 9313/4. Let l = -569 - u. Suppose 1/6*o**2 + l*o + 1/2 - 1/6*o**3 = 0. What is o?
-1, 3
Let x be (4 - 774/81)*828/(-345). What is t in 100/3*t**2 + 0 + 4/3*t**4 + x*t**3 + 0*t = 0?
-5, 0
Suppose v - 2*v = 5*z - 207, -5*v + 3*z + 979 = 0. Let -15 - 41 + 53*b**4 + 94*b**2 - 276*b - 24 - 10 + 4*b**5 + 18 + v*b**3 = 0. Calculate b.
-6, -2, -1/4, 1
Let q = -6130 - -55171/9. Let k(s) be the first derivative of -1 - 4/9*s**2 + q*s**4 - 2/45*s**5 + 2/9*s**3 - 8/9*s. Suppose k(x) = 0. What is x?
-1, 2
Let j(o) = 7*o**5 + o**4 + 5*o**3 + 11*o**2 + 18. Let m(q) = 15*q**5 + 3*q**4 + 11*q**3 + 23*q**2 + 39. Let t(s) = 13*j(s) - 6*m(s). Find r such that t(r) = 0.
-1, 0, 1, 5
Let h(g) be the second derivative of 5*g**4/24 - 115*g**3/12 + 255*g**2/2 - 189*g. Determine x so that h(x) = 0.
6, 17
Let q(o) be the first derivative of 3/16*o**4 - 62 + 0*o - 3/2*o**2 + 3/4*o**3. Factor q(m).
3*m*(m - 1)*(m + 4)/4
Let w(r) = 185*r**4 + 9755*r**3 + 121104*r**2 - 44*r - 22. Let n(a) = -46*a**4 - 2439*a**3 - 30276*a**2 + 12*a + 6. Let y(i) = 22*n(i) + 6*w(i). Factor y(v).
2*v**2*(7*v + 174)**2
Let k(j) be the third derivative of j**6/48 + 34*j**5/3 + 1345*j**4/12 + 1340*j**3/3 + 2*j**2 - 64*j - 2. Solve k(w) = 0.
-268, -2
Suppose -39 = -377*v + 364*v. Let u(g) be the second derivative of -g + 1/2*g**4 + 2/5*g**5 + 1/15*g**6 - 4*g**2 - 4/3*g**v + 0. What is y in u(y) = 0?
-2, -1, 1
Suppose 0 = 2*k + k. Let l = 230800 + -230800. Factor k*a**2 + 1/7*a**3 + l + 0*a.
a**3/7
Let j be (10/(-3))/(12/(-360)). Suppose 5*r**3 - 7*r**3 + 2*r**5 - 104*r**2 - 4*r**3 + j*r**2 = 0. Calculate r.
-1, 0, 2
Let l(f) = -2*f - 1. Let v(q) = 10*q**2 + 49*q + 41. Let s(o) = 7*o**2 + 48*o + 40. Let n(g) = 3*s(g) - 2*v(g). Let y(i) = -28*l(i) - 4*n(i). Factor y(u).
-4*(u + 1)*(u + 31)
Let f(o) be the second derivative of -o**6/30 - 7*o**5/15 - 7*o**4/3 - 16*o**3/3 - 2*o**2 + 53*o. Let h(w) be the first derivative of f(w). Factor h(a).
-4*(a + 1)*(a + 2)*(a + 4)
Let p(t) = -8*t**4 + 270*t**3 + 1889*t**2 + 4375*t + 3312. Let r(y) = 7*y**4 - 267*y**3 - 1888*y**2 - 4376*y - 3312. Let z(u) = 4*p(u) + 5*r(u). Factor z(h).
3*(h - 92)*(h + 2)**2*(h + 3)
Suppose 11*n - 6*n = 80. Let b(d) = -220*d**2 - 12*d - 16. Let k(h) = -73*h**2 - 4*h - 5. Let a(t) = n*k(t) - 5*b(t). Factor a(u).
-4*u*(17*u + 1)
Let x(y) = -y**3 - 2*y**2 + 3*y. Let j(t) = -5*t**3 + 6730*t**2 + 6840*t + 1690. Let w(k) = -j(k) + 25*x(k). Determine n, given that w(n) = 0.
-338, -1/2
Suppose -3*z - 30 = -13*z. Solve -64*o + 60 - 56*o**2 + 184*o**4 + 194*o**4 + 64*o**z - 382*o**4 = 0.
-1, 1, 15
Let o(d) be the first derivative of -d**3/4 - 111*d**2/4 + 693*d/4 + 674. Factor o(z).
-3*(z - 3)*(z + 77)/4
Let f(x) = -3*x - x**2 + 17*x + x - 2*x**3 + 8*x + 29 + 4*x. Let i be f(-1). What is u in 0*u**2 - 1 + 3/2*u - 1/2*u**i = 0?
-2, 1
Suppose 365447 - 499403 = -4950*y + 1539144. Suppose 0 + 1/2*h**3 - 26*h**2 + y*h = 0. Calculate h.
0, 26
Let t(p) = 54*p**2 + 4*p + 7. Let n be t(-2). Suppose -o**3 - 4*o**3 + 942*o**2 - 962*o**2 + n + 105 + 80*o = 0. Calculate o.
-4, 4
Suppose 16*s - 22*s = -12. What is u in 6*u + 14 + 12*u**s - 8*u - 14 - 18*u**3 = 0?
0, 1/3
Factor 30*l + 31 + 27/4*l**2 - 1/4*l**3.
-(l - 31)*(l + 2)**2/4
Let c(m) = -6*m**3 - 13*m**2 - 17*m + 30. Let a(d) = -5*d**3 - d**2. Let q(l) = 4*a(l) - 4*c(l). Factor q(v).
4*(v - 1)*(v + 3)*(v + 10)
Let h(v) = -32*v**2 + 287*v + 26. Let j(o) = -4*o**2 + 34*o + 3. Let m(r) = -2*h(r) + 17*j(r). Factor m(c).
-(2*c - 1)**2
Suppose 108 = -19*c + 7*c. Let f be 20/(-30)*3/12*c. Factor -f*k**3 - 15/2*k**2 - 6 - 12*k.
-3*(k + 1)*(k + 2)**2/2
Suppose -5*k - 8 = -28. Suppose -k*s = 2*t - 26, -4 + 5 = 2*t - s. Find f, given that -4*f**4 + 0*f**3 - 1075*f**2 - t*f + f**5 + 2*f**3 + 1079*f**2 = 0.
-1, 0, 1, 3
Let m(w) be the second derivative of 15/2*w**3 + 5/4*w**4 + 1/12*w**5 + 10*w**2 + 0 - 6*w. Let p(q) be the first derivative of m(q). Factor p(g).
5*(g + 3)**2
Let z(r) = -56*r**4 - 626*r**3 - 2784*r**2 + 34. Let o(f) = -5*f**4 - 57*f**3 - 253*f**2 + 3. Let d(k) = 68*o(k) - 6*z(k). Factor d(v).
-4*v**2*(v + 5)*(v + 25)
Let u = -433299 + 433304. Solve 20/13*k**2 - 10/13*k**3 + 2/13*k**