1)**3*(7*r + 2)/4
Let y(m) be the third derivative of m**5/18 - 2*m**4/9 - 182*m**2. Determine i, given that y(i) = 0.
0, 8/5
Factor 0*i + 2/3*i**2 + 2/9*i**3 - 8/9.
2*(i - 1)*(i + 2)**2/9
Let o = 224 + -1567/7. Let g(p) be the first derivative of 1/42*p**6 - 3/35*p**5 + 1/7*p**3 + 1/28*p**4 + 3 - o*p**2 + 0*p. Factor g(x).
x*(x - 2)*(x - 1)**2*(x + 1)/7
Let 0 - 39/2*m**2 - 33*m - 3/2*m**3 = 0. What is m?
-11, -2, 0
Let z(o) = 4*o**4 - 544*o**3 - 4344*o**2 - 9744*o + 14580. Let m(c) = c**4 - 109*c**3 - 869*c**2 - 1949*c + 2916. Let p(h) = -24*m(h) + 5*z(h). Factor p(r).
-4*(r - 1)*(r + 9)**3
Solve 16/5*a**2 + 4/5*a**3 + 4*a + 8/5 = 0.
-2, -1
Let a(r) be the first derivative of 14/15*r**4 - 15 + 196/15*r**3 + 2/75*r**5 + 4802/15*r + 1372/15*r**2. Let a(f) = 0. Calculate f.
-7
Let l = -28442 + 16257. Let f = 97605/8 + l. Factor 225/8*w**2 + f*w**3 + 135/8*w + 27/8.
(5*w + 3)**3/8
Determine m, given that -4/3*m**2 - 4*m + 0 = 0.
-3, 0
Determine u, given that -66*u**2 + 67*u**2 - u - 18 - 2*u = 0.
-3, 6
Let a(r) be the first derivative of r**5 - 5*r**4 + 10*r**3/3 + 10*r**2 - 15*r - 39. Find l, given that a(l) = 0.
-1, 1, 3
Let f = -4 + 7. Suppose -m + 7*m = 24. Let 34*p**m + 30*p**2 + 8*p**5 - 4*p**2 + 64*p**f + 4*p - 16*p**3 = 0. What is p?
-2, -1, -1/4, 0
Let -10/23*u**2 - 18/23*u**3 - 2/23*u - 4/23*u**5 + 0 - 14/23*u**4 = 0. What is u?
-1, -1/2, 0
Let f(o) = -29*o - 174. Let w be f(-6). Solve -8/17*a - 2/17*a**2 + w = 0.
-4, 0
Let c(q) be the second derivative of -10*q - 10*q**2 + 0 + 5/4*q**4 + 1/4*q**5 + 0*q**3. Factor c(n).
5*(n - 1)*(n + 2)**2
Suppose 3*m - 4*m = -4. Suppose 0 = -2*b - m*b + 48. Determine p so that -64*p**4 + 72*p**2 + 16*p**5 + 10*p + 20*p**5 - b - 16*p**3 - 30*p = 0.
-1, -2/9, 1
Let n(i) be the second derivative of -i**4/12 - 7*i**3/6 - 3*i**2 + 49*i. Determine q so that n(q) = 0.
-6, -1
Let n(c) = c - 15. Let o be n(-13). Let h be (-136)/o + -5 + (-4)/(-14). Factor 1/7*t**3 + 1/7*t**2 - h*t - 1/7.
(t - 1)*(t + 1)**2/7
Suppose 4*m - g = 68, 2*g + 60 = 4*m - g. Let n be ((-54)/252)/(m/(-14)). Factor -1/2 - 2/3*v - n*v**2.
-(v + 1)*(v + 3)/6
Let i be (153/612 + (-1)/(-2))*8/18. Solve 0 - 1/3*b**3 + 0*b**2 + i*b = 0.
-1, 0, 1
Let a(p) be the third derivative of p**5/210 - p**4/63 + p**3/63 + 214*p**2. Factor a(g).
2*(g - 1)*(3*g - 1)/21
Let j(c) = 4*c**2 - 3*c + 1. Let p be j(1). Find t, given that -2 - t**2 + 3 + 2*t - p = 0.
1
Let q(f) be the second derivative of -f**6/195 + 4*f**5/65 - 19*f**4/78 + 4*f**3/13 - 48*f. Find w such that q(w) = 0.
0, 1, 3, 4
Let x(y) be the first derivative of -y**4 - 48*y**3 - 768*y**2 - 4096*y - 721. Suppose x(m) = 0. Calculate m.
-16, -4
Factor -2/5 - 6/5*a**2 + 6/5*a + 2/5*a**3.
2*(a - 1)**3/5
Let q(l) = 10*l**3 + 10*l**2 - 4. Let j(u) = -9*u**3 - 8*u**2 + u + 3. Let s(g) = 4*j(g) + 3*q(g). Factor s(v).
-2*v*(v + 1)*(3*v - 2)
Let p be 47/((-1)/(-2)*1). Find t such that 180*t**2 + 8 - 2*t**3 - p*t**2 - 92*t**2 = 0.
-2, 1
Let x(k) be the third derivative of 1/6*k**4 + 0*k + 2*k**2 + 1/3*k**3 + 1/30*k**5 + 0. Factor x(j).
2*(j + 1)**2
Let q(x) be the second derivative of 1/16*x**2 - 13/48*x**3 - 7/10*x**5 + 5/8*x**4 - 13*x + 0 + 4/15*x**6. Factor q(p).
(p - 1)*(4*p - 1)**3/8
Let b(f) be the first derivative of f**7/21 + 4*f**6/15 + 3*f**5/5 + 2*f**4/3 + f**3/3 - 2*f - 1. Let d(j) be the first derivative of b(j). Factor d(v).
2*v*(v + 1)**4
Let r(s) = s**2 + 5*s + 9. Let l be r(-4). Let j be (-1)/l - 26/(-65). Suppose 0 + j*b**3 + 0*b + 1/5*b**2 - 1/5*b**5 - 1/5*b**4 = 0. Calculate b.
-1, 0, 1
Factor 6/7*s**2 - 1/7*s**3 - 8/7 + 4/7*s - 1/7*s**4.
-(s - 2)*(s - 1)*(s + 2)**2/7
Let s = 902/15 - 60. Let o(z) be the first derivative of -6/5*z**2 - s*z**3 - 3 - 18/5*z. Factor o(r).
-2*(r + 3)**2/5
Let h(m) be the second derivative of 0 + 0*m**2 - 7*m + 2/21*m**3 + 1/84*m**4. Suppose h(f) = 0. Calculate f.
-4, 0
Let j = 67 - 86. Let n be (79 - 22)*j/(-5). Find m, given that -24/5 - 978/5*m**2 - 96*m**4 + 15*m**5 + 276/5*m + n*m**3 = 0.
1/5, 2
Let u(c) = 2*c**2 + 1. Let q(h) = 44*h**2 - 16*h - 64. Let b(j) = -q(j) + 20*u(j). Factor b(o).
-4*(o - 7)*(o + 3)
Let j(t) be the first derivative of 2*t**3/15 - 7*t**2/5 - 36*t/5 - 88. Factor j(i).
2*(i - 9)*(i + 2)/5
Let z(s) be the third derivative of -s**6/210 + 8*s**5/105 - 3*s**4/14 - 12*s**3/7 + 99*s**2. Factor z(v).
-4*(v - 6)*(v - 3)*(v + 1)/7
Factor 59/8*i**2 - 1/4 - 57/8*i.
(i - 1)*(59*i + 2)/8
Let b be ((-2)/(-4)*6 - -1) + 33 + -37. Factor -1/2*k**2 + 2 + b*k.
-(k - 2)*(k + 2)/2
Let 32/3*s - 7/3*s**3 + 32/3 - 1/3*s**4 - 2*s**2 = 0. What is s?
-4, -1, 2
Let q be (9*8/6)/1. Determine j, given that -3*j**5 + 24*j - q*j**2 + 16*j**3 - 14*j**3 - 20*j**3 + 15*j**4 = 0.
-1, 0, 2
Factor -d - 7/2*d**2 + 0 + 3/2*d**4 - d**3.
d*(d - 2)*(d + 1)*(3*d + 1)/2
Suppose 0 = -2*v + s - 3, 4*s - 2*s - 2 = 3*v. Let g(o) = -o**3 + 3*o**2 + 4. Let z(b) = b**3 - 4*b**2 + b - 4. Let j(i) = v*z(i) - 5*g(i). Factor j(k).
(k - 2)*(k + 1)*(k + 2)
Let q(x) = -10*x**2 + 118*x - 778. Let a(m) = 9*m**2 - 117*m + 779. Let p(k) = -6*a(k) - 5*q(k). Factor p(s).
-4*(s - 14)**2
Find o such that 5/8 + 33/8*o + 7/2*o**2 = 0.
-1, -5/28
Let k(w) be the third derivative of 0*w**3 + w**4 + 0*w + 0 + 14*w**2 - 3/10*w**5 + 1/40*w**6. Factor k(t).
3*t*(t - 4)*(t - 2)
Suppose -3*h = -2*h + 5*s - 32, -5*h + 56 = -s. Suppose -5*p + 40 = x, p = x - 2*x + h. Factor -2*r**2 - p*r + 6*r + 2 + r**2.
-(r - 1)*(r + 2)
Let o(u) be the third derivative of u**8/151200 + u**7/12600 - 3*u**5/10 - 8*u**2. Let f(j) be the third derivative of o(j). Find w such that f(w) = 0.
-3, 0
Let w(n) be the first derivative of 2*n**3/3 - 5*n**2 + 8*n + 55. Suppose w(m) = 0. What is m?
1, 4
Let b(r) be the third derivative of -r**6/120 - r**5/12 - r**4/6 - 96*r**2. Factor b(q).
-q*(q + 1)*(q + 4)
Let a = 89 + -349/4. Let c = 13/14 + -3/7. Find d, given that 5/4*d**3 + 1/2 + 5/4*d**2 - a*d + c*d**5 - 7/4*d**4 = 0.
-1, 1/2, 1, 2
Suppose f = 4*b - 20, 2*b + 4 = -3*f - 0. Let c(u) = 19*u + 120. Let x be c(-6). Let h + 3*h**2 + 3*h**3 - 2*h - x*h**3 + h**b = 0. Calculate h.
0, 1
Let t = 9383 - 9380. Factor 4/13 - 2/13*w + 2/13*w**t - 4/13*w**2.
2*(w - 2)*(w - 1)*(w + 1)/13
Suppose -4*z + 3*c = -c, z + 2*c - 12 = 0. Let l be -5*(-5 + z) + -3. Factor -2/5*u**l + 8/5*u - 6/5.
-2*(u - 3)*(u - 1)/5
Suppose -4*j - 4*h = -0*h, j - h - 4 = 0. Let w(g) be the second derivative of -4*g + 0 + 9/10*g**5 - 13/4*g**4 + 6*g**3 - 1/10*g**6 - 6*g**j. Factor w(q).
-3*(q - 2)**2*(q - 1)**2
Let -160/3 + 1/6*l**4 - 7/6*l**3 - 2*l**2 + 88/3*l = 0. Calculate l.
-5, 4
Let s(u) = -3*u - 46. Let l be s(-15). Let m be l - (-1 + 1) - (-11)/7. Factor m*h - 2*h**4 + 32/7*h**3 + 0 - 22/7*h**2.
-2*h*(h - 1)**2*(7*h - 2)/7
Let q be (((-360)/(-35))/(-6))/(15 - (-2628)/(-168)). Determine y so that -2/3*y**2 - 8/3*y - q = 0.
-2
Let i(y) = -18*y**3 + 170*y**2 - 114*y + 22. Let v(c) = -36*c**3 + 341*c**2 - 227*c + 43. Let h(t) = 7*i(t) - 4*v(t). Let h(g) = 0. What is g?
1/3, 9
Let w(q) = -2*q**2 + 24*q + 2. Let m be w(12). Factor -2*g**3 + 316 + m*g**4 - 10*g**2 - 316 - 6*g.
2*g*(g - 3)*(g + 1)**2
Let a(c) be the first derivative of 0*c + 0*c**3 + 0*c**4 + 2/3*c**6 + 0*c**2 - 21 - 4/5*c**5. Factor a(p).
4*p**4*(p - 1)
Let t(o) = -24*o**3 + 28*o**2 + 4*o - 12. Let p(x) = 47*x**3 - 58*x**2 - 9*x + 21. Let m(n) = 4*p(n) + 7*t(n). Factor m(q).
4*q*(q - 2)*(5*q + 1)
Let s = -6 - -12. Let g be s/(1 + -3)*-1. Determine r so that -3*r**2 + r**4 + g*r**5 + 2*r**4 + 0*r**3 - 3*r**3 = 0.
-1, 0, 1
Let d = -62 - 30. Let k be d/(-28) + (-4)/14. What is c in 2*c + 2*c**2 - 4*c**2 + 6*c**2 - k*c**2 = 0?
-2, 0
Suppose -4*h + 2*f + 40 = 0, 4*f + 17 = 1. Let g be h/(-32) + 1 + 3/(-4). Determine n, given that -1/4*n**2 + g*n + 0 = 0.
0
Let q(f) be the third derivative of f**6/30 + 6*f**5/5 + 11*f**4/2 + 32*f**3/3 + 26*f**2. Factor q(u).
4*(u + 1)**2*(u + 16)
Factor 3 + 17*o**2 + 4*o**4 + 1/2*o**5 + 23/2*o + 12*o**3.
(o + 1)**3*(o + 2)*(o + 3)/2
Let x(n) be the second derivative of -n**6/20 - 3*n**5/10 - 3*n**4/8 + 4*n + 1. What is y in x(y) = 0?
-3, -1, 0
Let c = 289748/15 - 19316. Suppose 2/15*v**2 - c + 2/5*v = 0. Calculate v.
-4, 1
Find t such that -24 - 2/7*t**2 + 50/7*t = 0.
4, 21
Factor 3*o**4 + 0 - 56/3*o + 172/3*o**2 - 46*o**3.
o*(o - 14)*(3*o - 2)**2/3
Suppose -22*w + 32*