 Let f(m) = m**5 + 7*m**4 - 9*m**3 + 8*m**2 - m. Let j(l) = n*f(l) - 15*c(l). Determine x, given that j(x) = 0.
0, 1/2, 1
Let w(q) be the second derivative of -q**5/20 - q**4/4 + q**3/6 + 3*q**2/2 - 19*q - 2. Find t, given that w(t) = 0.
-3, -1, 1
Let h(k) be the third derivative of 2*k**7/105 - k**6/15 - 7*k**5/15 - 2*k**4/3 + 138*k**2. Suppose h(d) = 0. Calculate d.
-1, 0, 4
Let d(s) be the third derivative of -11*s**7/63 + 173*s**6/45 - 1873*s**5/90 + 76*s**4/3 - 12*s**3 - 291*s**2. Let d(c) = 0. What is c?
2/11, 2/5, 3, 9
Let a(q) be the first derivative of q**3/9 + 25*q**2/6 + 46*q/3 + 142. Suppose a(r) = 0. Calculate r.
-23, -2
Let j(s) be the second derivative of 0*s**2 + s**3 - 9/10*s**5 - 4/15*s**6 + 0 - 21*s + 5/3*s**4. Factor j(t).
-2*t*(t - 1)*(t + 3)*(4*t + 1)
Let d(x) be the third derivative of 0 + 1/24*x**4 - 1/40*x**5 + 0*x**3 + 1/140*x**7 + 8*x**2 + 0*x - 1/120*x**6. Factor d(s).
s*(s - 1)*(s + 1)*(3*s - 2)/2
Let q(m) be the first derivative of m**4/2 + 8*m**3/3 + 4*m**2 - 413. Factor q(w).
2*w*(w + 2)**2
Let i be (70/(-315))/(80/(-18)). Let q(h) be the second derivative of i*h**5 - 1/6*h**3 + 1/6*h**4 - h**2 - 4*h + 0. Factor q(l).
(l - 1)*(l + 1)*(l + 2)
Factor 0*l - 4/3*l**2 + 8/9*l**3 - 1/9*l**4 + 0.
-l**2*(l - 6)*(l - 2)/9
Suppose 2*n - 11 = -3*f, -f - 4*n + 2*n + 5 = 0. Determine w, given that 7*w**4 + 6*w**2 - 40*w**3 + 56*w**3 - 39*w**f = 0.
0, 2/7, 3
Let u(j) be the third derivative of 49*j**6/150 - 371*j**5/75 + 16*j**4 + 120*j**3 - 506*j**2. Determine y so that u(y) = 0.
-1, 30/7
Let m(w) be the first derivative of w**3 + 18*w**2 + 96*w - 46. Solve m(t) = 0.
-8, -4
Let n be (-221)/(-129) - 2 - (-5)/15. Let r = 49/129 - n. Factor r*o - 1/3*o**2 + 0.
-o*(o - 1)/3
Suppose 2*w - 8 = -m - 3*m, 4*w - 4*m = 28. Let b be (w/(-16)*-4)/12. Find s, given that -9/8*s**2 + b*s + 1/8 + 11/8*s**3 - 1/2*s**4 = 0.
-1/4, 1
Let p(y) = y**2 + 7*y - 5. Let u(h) = h**2 + 3*h - 3. Let a be 1*10*1/(-2). Let x(w) = a*u(w) + 3*p(w). Factor x(s).
-2*s*(s - 3)
Suppose 0*q + 12 = -2*l + 3*q, 3*l - 2*q = -13. Let p(m) = -3*m**3 + 9*m + 6. Let r(b) = -4*b**3 + 10*b + 6. Let c(u) = l*p(u) + 2*r(u). Factor c(k).
(k - 3)*(k + 1)*(k + 2)
Let 200 + 2*x**2 - 39*x + 23*x + 66*x = 0. What is x?
-20, -5
Suppose 8*r + 6055 = 6079. Let i(s) be the first derivative of 1/30*s**6 + 2/15*s**3 + 0*s + 0*s**2 - r - 2/25*s**5 - 1/20*s**4. Factor i(u).
u**2*(u - 2)*(u - 1)*(u + 1)/5
Let p be (-16)/6*18/(-8). Suppose -p*m + 20 = -m. Solve 47*r**3 + r**4 + 2*r**m - 44*r**3 = 0.
-1, 0
Let m(r) be the first derivative of 48 - 1/5*r**5 - 1/2*r**4 + r**2 + 0*r**3 + r. Find j, given that m(j) = 0.
-1, 1
Let b = 383/21 - 123/7. Solve -2/3*l + 2/3*l**3 - b + 2/3*l**2 = 0 for l.
-1, 1
Suppose -17*n + 55 = -438. Factor x + 6*x**2 - 6*x**4 - x - n*x**3 + 26*x**3 + 3*x**5.
3*x**2*(x - 2)*(x - 1)*(x + 1)
Let z = 11 - 6. Let w(b) = -3*b**3 + 3*b**2 + 2*b - 4. Let s(k) = k**2 - 1. Let y(o) = z*w(o) - 20*s(o). Find r such that y(r) = 0.
-1, 0, 2/3
Let g(n) = -7*n**2 + 27*n - 32. Let m(b) = -155*b**2 + 595*b - 705. Let f = -106 + 108. Let o(u) = f*m(u) - 45*g(u). Let o(d) = 0. Calculate d.
2, 3
Let i(r) be the first derivative of r**4/22 - 20*r**3/33 + r**2 + 140*r/11 + 527. Factor i(f).
2*(f - 7)*(f - 5)*(f + 2)/11
Let m = 2516/3759 - 10/3759. Determine x, given that 5/6*x**3 - m + 13/6*x**2 + 2/3*x = 0.
-2, -1, 2/5
Let n = 12 + -10. Let m(f) = -f**2 + f + 1. Let t(a) = 3*a**2 + 2*a - 2. Let p(l) = n*m(l) + t(l). Solve p(g) = 0 for g.
-4, 0
Let i = -28 + 31. Factor 12*b + 0*b**2 - 12 + 0*b**i + 3*b**2 - 3*b**3.
-3*(b - 2)*(b - 1)*(b + 2)
Let w(p) = -1. Let z(k) = -k**2 - k + 12. Let l(q) = 2*q**2 + 2*q - 36. Let f(y) = 2*l(y) + 7*z(y). Let u(m) = f(m) + 6*w(m). Determine g, given that u(g) = 0.
-2, 1
Let z = -65 - -68. Let l(j) = 6*j**2 + 144*j + 871. Let o(c) = 3*c**2 + 72*c + 435. Let v(f) = z*l(f) - 7*o(f). Let v(s) = 0. What is s?
-12
Let r(z) be the second derivative of -11*z + 0*z**4 + 0 - 1/9*z**3 + 0*z**6 + 0*z**2 - 1/63*z**7 + 1/15*z**5. Suppose r(x) = 0. What is x?
-1, 0, 1
Let w(q) = -2*q - 115. Let g be w(-59). Let z(u) be the first derivative of 2*u**2 + 1/3*u**6 + 9/2*u**4 - 4 + 2*u**5 + 0*u + 14/3*u**g. Factor z(y).
2*y*(y + 1)**3*(y + 2)
Let u be ((-1)/(-3))/((-12)/(-144)). Let f = 2 + u. Solve -3*d**2 + 5*d**2 + f*d - 6*d + 4*d**3 + 2*d**4 = 0 for d.
-1, 0
Let a = 70 - 75. Let j be (-1)/(-2)*(a + 5). Solve 1/4*v**3 + 0*v**2 - 1/4*v + j = 0 for v.
-1, 0, 1
Suppose 7/4*b**2 + 0 - 5/4*b**3 - 1/2*b = 0. What is b?
0, 2/5, 1
Let d(z) be the third derivative of 0*z + z**3 - 5*z**2 + 1/40*z**6 - 1/8*z**4 - 3/20*z**5 + 1/70*z**7 + 0. Factor d(g).
3*(g - 1)**2*(g + 1)*(g + 2)
Let h be 90/20*(-28)/(-63). Factor 0 + 0*j**h + 1/6*j**3 - 1/6*j.
j*(j - 1)*(j + 1)/6
Suppose -4*k - 5*g = -16, 0*g = 5*g. Factor 0*q**5 + 13*q**k + 4*q**5 - 15*q**4 - 2*q**3.
2*q**3*(q - 1)*(2*q + 1)
Suppose -1/9*m**2 + 62*m - 8649 = 0. What is m?
279
Let -8*n**3 - 7*n**4 - n - 8*n**2 + 4*n**5 + 4 + 9*n**4 + 9*n**4 + 5*n - 7*n**4 = 0. Calculate n.
-1, 1
What is k in -48/5*k + 54/5*k**4 + 3*k**5 + 0 - 54/5*k**2 + 33/5*k**3 = 0?
-2, -8/5, -1, 0, 1
Factor -26 + 6 + 12*d**2 + 8*d**2 - 67*d - 29*d.
4*(d - 5)*(5*d + 1)
Let u(l) be the third derivative of 0 + 0*l + 23*l**2 + 3/10*l**5 - 27/8*l**4 - 1/120*l**6 + 0*l**3. Factor u(g).
-g*(g - 9)**2
Let d(n) = -n**3 - 88*n**2 + 74*n - 1331. Let v be d(-89). Determine x, given that -x**v + 1/2*x**5 - 7/2*x**3 + 0*x - 2*x**2 + 0 = 0.
-1, 0, 4
Suppose -4/3 + 8/3*o**3 - 4*o + 4*o**4 + 4/3*o**5 - 8/3*o**2 = 0. What is o?
-1, 1
What is n in 3/7*n**2 + 192/7 - 48/7*n = 0?
8
Determine h, given that -4/7*h**5 + 174/7*h**2 - 6/7*h**4 + 64/7*h**3 + 108/7*h + 0 = 0.
-3, -2, -1, 0, 9/2
Let v(m) be the second derivative of -m**4/3 - 280*m**3/3 - 9800*m**2 + 2*m - 81. Factor v(k).
-4*(k + 70)**2
Let j = -23/724 + 51/181. Let -j*h**4 + 9/4*h**3 + 6 - h - 9/2*h**2 = 0. What is h?
-1, 2, 6
Let j = 417/2 + -208. Let w(l) be the second derivative of -3/4*l**4 - j*l**3 + 0 - 2*l + 0*l**2. Factor w(v).
-3*v*(3*v + 1)
What is z in 3304/5*z**3 + 1226/5*z**2 + 184/5*z + 1372/5*z**5 + 8/5 + 3626/5*z**4 = 0?
-1, -2/7, -1/14
Let h(g) = -3*g + 2. Let j(u) = u - 1. Let r(v) = -h(v) - 2*j(v). Let s(f) be the first derivative of -2*f**3/3 + 1. Let a(k) = 4*r(k) - s(k). Factor a(y).
2*y*(y + 2)
Factor -64/3*t - 64/3*t**2 - 2/3*t**4 + 0 - 20/3*t**3.
-2*t*(t + 2)*(t + 4)**2/3
Let b = 97 + -95. Suppose 0 = 5*s - 10, 0 = b*h - 4*s - 0*s + 2. Determine f so that 3/2 - f + f**h - 2*f**2 + 1/2*f**4 = 0.
-3, -1, 1
Let u = -31 - -37. Let c(b) be the second derivative of 0*b**2 + 0*b**4 + 1/165*b**6 + 0*b**3 - 1/110*b**5 - u*b + 0. Find h, given that c(h) = 0.
0, 1
Let y(p) = -4*p**2 - 48*p - 142. Let k = 96 + -94. Let h(i) = -1. Let a(o) = k*h(o) + y(o). Factor a(b).
-4*(b + 6)**2
Determine r, given that 28*r - 7*r**2 + 10*r**2 - 3949 + 15481 + 160*r + 184*r = 0.
-62
Let k = 58969/2 + -29484. Let 0 - k*r**3 + 0*r**2 + 1/2*r = 0. What is r?
-1, 0, 1
Let u(d) = d**3 - d**2 + d - 1. Let r(v) be the second derivative of 0 + 1/2*v**4 + v - 9/20*v**5 + 3*v**2 - 1/2*v**3. Let o(w) = r(w) + 6*u(w). Factor o(y).
-3*y*(y - 1)*(y + 1)
Let c(o) be the first derivative of 11*o**5/20 - o**4/8 + 19. Factor c(a).
a**3*(11*a - 2)/4
Let z(c) be the second derivative of 1/3*c**3 - 5*c + 0 - 1/6*c**4 - 1/3*c**2 + 1/30*c**5. Solve z(h) = 0.
1
Let 0 - 73*f + 4 + 694*f + 42388*f**2 + 351*f + 16661*f**2 = 0. Calculate f.
-2/243
Let t(l) = 3*l**2 + l - 1. Let h be t(1). Let r be (1/h)/(2/12). Find f such that 0*f**r - f - 2*f**3 + 0*f**2 + 3*f**3 = 0.
-1, 0, 1
Let p(v) be the third derivative of v**7/42 + 3*v**6/4 + 17*v**5/12 - 5*v**2 - 17*v. Factor p(z).
5*z**2*(z + 1)*(z + 17)
Let i = -84 - -87. Suppose 0*k - 12 = -3*k + i*v, -2*k - 4*v = 4. Suppose -2/7*y + 52/7*y**4 - 4/7 + 2*y**5 + 32/7*y**k + 68/7*y**3 = 0. What is y?
-1, 2/7
Suppose -5*m + 20 = -2*b, -4*m - 4*b - 12 = -0*m. Suppose 0 = 2*n + 119 - 125. Let i**m + n*i**2 - 3*i - 2*i**2 + i**2 = 0. What is i?
0, 1
Let a = -4/10673 - -42720/74711. Solve 2/7*c**3 + 0*c**2 + a - 6/7*c = 0.
-2, 1
Let x be 490/14*(-2)/(-5). Suppose 5*u - 30 = -5*j, 8 = 2*u + 2*j - j. Factor -8 + 44*m - 4*m**u - 119*m**3 - x*m**2 - 16*m**4 - 33*m**4.
-(m + 1)*(m + 2)*(7*m - 2)**2
Let g(m) 