) be the first derivative of -49*p**4/8 + 91*p**3/6 - 51*p**2/4 + 9*p/2 + 66. Suppose x(t) = 0. Calculate t.
3/7, 1
Let j(p) = 3*p**4 - 2*p**3 - 3*p**2 + 7*p - 15. Let z(l) = -4*l**4 + 3*l**3 + 4*l**2 - 10*l + 21. Let y(d) = -7*j(d) - 5*z(d). Factor y(b).
-b*(b - 1)*(b + 1)**2
Let x(m) = -9*m**3 - 27*m**2 + 21*m + 406. Let h(d) = -4*d**3 - 13*d**2 + 10*d + 202. Let k(c) = -14*h(c) + 6*x(c). Solve k(n) = 0.
-7, 4
Suppose -4*x - 4 = 0, -5*x = 2*r - 6*x - 5. Let m be ((-22)/55)/((-11)/5 + r). Suppose -2/3*s**m + 0 + 4/3*s = 0. Calculate s.
0, 2
Let g(n) be the third derivative of n**7/4200 - n**5/150 + 7*n**3/3 + 3*n**2. Let i(x) be the first derivative of g(x). Factor i(u).
u*(u - 2)*(u + 2)/5
Suppose 58*b = 52*b + 4*w + 20, -2*b + 3*w = -10. Factor 24/5 + 8/5*l + 2/15*l**b.
2*(l + 6)**2/15
Solve -2/3*c**2 + 26/3*c + 28/3 = 0 for c.
-1, 14
Let q = -18 - -20. Factor -4*a**4 - a**3 + q*a**2 + 10*a**4 - 9*a**4.
-a**2*(a + 1)*(3*a - 2)
Let f(h) be the first derivative of h**4/4 + 9*h**3/5 - 12*h**2/5 + 14*h + 3. Let w(x) be the first derivative of f(x). Factor w(r).
3*(r + 4)*(5*r - 2)/5
Let h = 2898 - 20284/7. Determine d so that -h + 4/7*d - 2/7*d**2 = 0.
1
Let x(b) be the second derivative of b**5/20 - 11*b**4/6 - 25*b**3/6 + 23*b**2 + 4*b + 31. Determine l, given that x(l) = 0.
-2, 1, 23
Let t be 3/2*14/(-21). Let n = t + 9. Find f, given that 6*f + 0 + 2 + 4*f**2 - n*f**3 - 6 + 2*f**5 = 0.
-2, -1, 1
Let b(f) = -f - 5. Let t be b(-5). Suppose t = -2*h + 8 - 2. Suppose 3*m - h*m**3 + 3 + 2 + 1 - 6*m**2 = 0. What is m?
-2, -1, 1
Let j = -154 - -157. Let z(l) be the second derivative of -1/15*l**4 - 4/15*l**j + 9*l + 0 + 0*l**2. Factor z(w).
-4*w*(w + 2)/5
Let f(k) = k**2 - 14*k - 28. Let m be f(17). Let r = -19 + m. Determine g, given that 36/5*g**r + 0 + 84/5*g**3 + 16/5*g + 64/5*g**2 = 0.
-1, -2/3, 0
Let m = -229702 - -2522337/11. Let w = m + 399. Determine i, given that 2/11*i + 2/11*i**5 - 2/11 - 4/11*i**3 + w*i**2 - 2/11*i**4 = 0.
-1, 1
Let f(y) = -39*y**2 - 4*y**3 - 2*y + 45*y**2 - 15 + 3*y**3. Let u be f(5). Find m such that -6/7*m**3 - 2/7*m - 2/7*m**4 - 6/7*m**2 + u = 0.
-1, 0
Let k(j) be the third derivative of j**5/180 - j**4/6 + 197*j**2. What is i in k(i) = 0?
0, 12
Let p be (1 - 6)*59/295 - -1. What is b in 1/5*b**4 + 1/5*b**3 + 0 + 0*b + p*b**2 = 0?
-1, 0
Let p(o) be the first derivative of -2*o**5/35 - 2*o**4/7 - 10*o**3/21 - 2*o**2/7 - 29. Factor p(r).
-2*r*(r + 1)**2*(r + 2)/7
Let p(n) = n**3 - 3*n**2 - n - 1. Let k(b) = -4*b**3 + b**2 + b + 4. Let i(w) = -2*k(w) - 4*p(w). Factor i(y).
2*(y + 1)*(y + 2)*(2*y - 1)
Let n be 96/(-1152) - 34/(-120). Solve 8/5 - 28/5*y - n*y**5 - 5*y**3 + 8/5*y**4 + 38/5*y**2 = 0.
1, 2
Let z(s) be the second derivative of -s**5/10 - 7*s**4/3 + 87*s - 3. Find d such that z(d) = 0.
-14, 0
Let h(y) be the second derivative of -y**7/126 + y**6/90 + y**5/60 - y**4/36 - 2*y + 40. Factor h(w).
-w**2*(w - 1)**2*(w + 1)/3
Let h(g) = g**3 + 27*g**2 + 10*g + 1064. Let a be h(-28). Let f be (1/(-2))/(1/(-6)). Factor -3/5*s + a*s**2 + 3/5*s**f + 0.
3*s*(s - 1)*(s + 1)/5
Let t(h) be the second derivative of -h**8/1176 + h**7/735 + h**6/420 - h**5/210 - 7*h**2 - 3*h. Let z(w) be the first derivative of t(w). Factor z(d).
-2*d**2*(d - 1)**2*(d + 1)/7
Let k(f) = -f + 10. Let b be k(8). Find n, given that -29*n - 12*n**b - 41*n - 16 + 38*n = 0.
-2, -2/3
Let f(l) be the third derivative of 9/40*l**6 - 1/70*l**7 + 9/20*l**5 + 1/4*l**4 + 0 - 40*l**2 - 3/112*l**8 + 0*l + 0*l**3. Determine v, given that f(v) = 0.
-1, -1/3, 0, 2
Factor -5*c**3 + 6 + c**3 + 16*c - 8*c**2 + 30*c + 138 + 14*c.
-4*(c - 4)*(c + 3)**2
Let k(m) be the second derivative of -1/4*m**4 - 3/10*m**5 + 0*m**2 + 0 - 10*m + m**3 + 1/10*m**6. What is w in k(w) = 0?
-1, 0, 1, 2
Let q(r) = -152*r**2 + 436*r - 132. Let o(t) = -22*t**2 + 62*t - 19. Let j(s) = 20*o(s) - 3*q(s). What is a in j(a) = 0?
1/4, 4
Let m be (-24)/(-7) - (-144 + 146). Factor -2/7*y**5 + m*y**4 + 6/7*y**2 + 0 - 2*y**3 + 0*y.
-2*y**2*(y - 3)*(y - 1)**2/7
Let v = 1337/1665 - 1/333. Solve 16/5 + v*h**2 - 16/5*h = 0 for h.
2
Suppose 16*o = -0 + 32. Factor 0 + 0*g - 4/7*g**4 + 4/7*g**o + 0*g**3.
-4*g**2*(g - 1)*(g + 1)/7
Factor 81/4 + 3/4*o**2 + 9*o.
3*(o + 3)*(o + 9)/4
Let y(o) be the first derivative of 125/2*o - 75/4*o**2 - 1/8*o**4 + 5/2*o**3 - 9. Factor y(b).
-(b - 5)**3/2
Let s(f) be the second derivative of 2*f**6/15 - 14*f**5/5 - 31*f**4/3 - 32*f**3/3 - 126*f + 2. Factor s(g).
4*g*(g - 16)*(g + 1)**2
Let w(t) = t**3 + 87*t**2 - 681*t + 1074. Let g(n) = -n**3 - 3*n**2 + n - 2. Let z(f) = -3*g(f) + w(f). Factor z(k).
4*(k - 3)**2*(k + 30)
Factor 1/2*x**2 - 68 - 33*x.
(x - 68)*(x + 2)/2
Let z(u) be the second derivative of u**7/11340 - u**6/1620 + 5*u**4/6 + 5*u. Let x(k) be the third derivative of z(k). Factor x(f).
2*f*(f - 2)/9
Let t be 15 + -21 + -2 + 10. Let j be (0/(-8))/6*2/(-4). Factor 0*y**3 + j - 3/4*y**4 + 0*y**t + 0*y.
-3*y**4/4
Let s(a) = -a**3 + a**2 + 4*a - 1. Let t(j) = -4*j**3 - 16*j**2 + 153*j - 228. Let p(g) = -15*s(g) + 5*t(g). Factor p(k).
-5*(k - 3)**2*(k + 25)
Let x = -30 + 32. Factor -12*r**3 - 4*r**3 - x*r - 2*r**5 + 20*r**3.
-2*r*(r - 1)**2*(r + 1)**2
Let u(j) be the second derivative of 1/30*j**4 + 4/3*j**3 + 0 + 20*j**2 - j. Determine o so that u(o) = 0.
-10
Let d(g) be the second derivative of g**6/6 - 15*g**5/4 + 105*g**4/4 - 425*g**3/6 + 90*g**2 - 94*g. Factor d(i).
5*(i - 9)*(i - 4)*(i - 1)**2
Let j = 3 + -1. Factor 4*f - 3*f - 3*f + 2 - 10*f**3 - 2*f**j + 12*f**3.
2*(f - 1)**2*(f + 1)
Factor -10/7*p**4 - 216/7 - 2/7*p**5 + 0*p + 10/7*p**3 + 90/7*p**2.
-2*(p - 2)**2*(p + 3)**3/7
Suppose -f = 1, 5*f - 8 = -5*l + 3*f. Let 63*b**4 - 35*b**4 + 16*b**3 + 16*b - 32*b**4 - 4 - 24*b**l = 0. Calculate b.
1
Let u = -37 - -44. Suppose 0 = 8*o + u - 31. Suppose 1/3*n**o - 1/3*n - 1/3*n**2 + 1/3 = 0. Calculate n.
-1, 1
Let y(z) be the first derivative of z**6/480 + z**5/80 - z**4/96 - z**3/8 + 12*z**2 + 5. Let q(s) be the second derivative of y(s). Factor q(j).
(j - 1)*(j + 1)*(j + 3)/4
Suppose -6*g + 21*g = 30. Suppose 2*a + 20 = 7*a. Let -5*z**3 + 6*z**g - 6*z - z**3 + 2 + a*z**3 = 0. What is z?
1
Determine l, given that 25*l**3 + 1/2*l**5 - 10 - 44*l**2 + 69/2*l - 6*l**4 = 0.
1, 4, 5
Let x = -5 + 8. Let p be (-16 + 2)*-1 - x. Find l such that -3 + 5*l**2 - 4*l - p*l**3 + 1 + 9*l**2 + 3*l**3 = 0.
-1/4, 1
Let w(z) be the third derivative of -z**7/210 + z**6/6 - 28*z**5/15 + 2*z**4 + 120*z**3 + 129*z**2 - 4*z. Find r, given that w(r) = 0.
-2, 6, 10
Let i = 5999 + -5990. Determine j so that 9*j - 81/2 + 1/2*j**4 + 40*j**2 - i*j**3 = 0.
-1, 1, 9
Let w = 28 - 25. Suppose w*i - 5*i = i. Solve i + 0*n - 2/13*n**2 + 2/13*n**3 = 0.
0, 1
Let h(r) be the second derivative of 0*r**3 - 11*r + 0 - 3/8*r**2 + 1/16*r**4. Determine g, given that h(g) = 0.
-1, 1
Let r(w) be the first derivative of w**6/27 - 2*w**5/15 - 5*w**4/18 + 2*w**3 - 32*w**2/9 + 8*w/3 + 920. Suppose r(f) = 0. What is f?
-3, 1, 2
Let w(y) = y**2 - 10*y - 64. Let a(p) = p**2 + 3*p. Let d(o) = -2*a(o) + w(o). Suppose d(z) = 0. What is z?
-8
Let u(s) = s**3 - 7*s**2 + 6*s + 1. Let m = -20 - -26. Let p be u(m). Solve 2*h + 7 + h**2 + 2*h - p - 2 = 0 for h.
-2
Let v(y) = 786*y + 77621. Let m(j) = 2*j**2 + 2*j - 3. Let b(s) = 2*m(s) + 2*v(s). Factor b(r).
4*(r + 197)**2
Let s(d) be the first derivative of 4*d**5/5 - 3*d**4/2 - 2*d**3 + 2*d**2 - 197. Factor s(c).
2*c*(c - 2)*(c + 1)*(2*c - 1)
Let v = 88 + -246. Let f be v/(-4) - (-15)/(-10). Solve i**2 + f*i - 1 - 38*i = 0 for i.
-1, 1
Let w(f) be the first derivative of 6*f**2 - 21/20*f**5 + 16 - 3*f**4 + 3*f + 3/4*f**3. Solve w(r) = 0 for r.
-2, -1, -2/7, 1
Suppose -4*p**3 - 528/5 - 1856/5*p - 1348/5*p**2 = 0. What is p?
-66, -1, -2/5
Let l = -832 - -832. Let v = 57 - 511/9. Factor -2/3*n**3 + l + v*n**4 - 2/9*n**2 + 2/3*n.
2*n*(n - 3)*(n - 1)*(n + 1)/9
Let w = 47/1770 + 2/295. Let a(g) be the third derivative of 0*g**4 + 0*g**3 - 1/210*g**7 + 0 - 1/120*g**6 + w*g**5 + 5*g**2 + 0*g. Factor a(o).
-o**2*(o - 1)*(o + 2)
Let k(j) = j**2 + 2*j - 6. Let p be k(-4). Suppose 2*t - 10 = p*f, -3*f - f + 5*t - 25 = 0. Solve f - 4/5*g**2 + 2/5*g + 2/5*g**3 = 0.
0, 1
Suppose -4*j - f + 10 = 0, 10*j + 3*f = 8*j - 10. Factor -2/3 - y + 1/3*y**2 + 1/3*y**j + y**3.
(y - 1)*(y + 1)*