q**3 + 0*q - 1/2*q**4 + 5/2*q**2. Find d, given that x(d) = 0.
-1/2, 0, 5
Suppose -f + 8 = 3*t, -3*t - 6*f + f = -4. Suppose t*w + i = 5, 5*w - i - i = 12. Suppose 3*y**w + 5 - 5*y**2 - 3 = 0. What is y?
-1, 1
Suppose 2/3*p**2 + 0 + 6*p = 0. Calculate p.
-9, 0
Let c(p) be the second derivative of p**5/18 - 16*p**4/27 + 37*p**3/27 - 10*p**2/9 + p + 15. Let c(g) = 0. Calculate g.
2/5, 1, 5
Let a be (-45)/27*(-6)/5. Find m, given that 45*m**a + 163*m - 388*m - 2*m**3 + 375 - m**3 = 0.
5
Let r(l) be the first derivative of 5*l**7/63 + 5*l**6/36 + l**5/24 - 27*l + 31. Let x(i) be the first derivative of r(i). Factor x(a).
5*a**3*(a + 1)*(4*a + 1)/6
Let c(q) = -3*q**5 + 2*q**4 - 11*q**3 + 4. Let b(w) = -w**5 + w**4 - w**3 + w**2 + 1. Let l(x) = 4*b(x) - c(x). Find p, given that l(p) = 0.
-1, 0, 4
Let n be (-7)/(7/(-4)) - 1. Factor 20*d**2 + 13*d**3 + 11*d**n - 29*d**3 - 20*d.
-5*d*(d - 2)**2
Suppose -5*k - 405 = -5*t, -t - 429 = k + 4*k. Let y = 159 + k. Factor -16 + 32*c - 75*c**3 + y*c**2 + 74*c**2 - 5*c**3.
-4*(c - 2)*(4*c - 1)*(5*c + 2)
Factor -9*k + 14*k + 5*k**2 - 2*k**2 - 8*k.
3*k*(k - 1)
Let q(b) be the first derivative of -2*b**7/21 + 8*b**6/15 - 6*b**5/5 + 4*b**4/3 - 2*b**3/3 + 8*b + 10. Let l(a) be the first derivative of q(a). Factor l(v).
-4*v*(v - 1)**4
Let t be 4 + 13/((-52)/16). Let g(k) be the third derivative of -1/40*k**6 + t*k + 1/10*k**5 + k**2 - k**3 + 0 + 1/8*k**4. Suppose g(x) = 0. Calculate x.
-1, 1, 2
Let l(v) be the first derivative of 5*v**7/42 + v**6/6 + 4*v + 12. Let n(k) be the first derivative of l(k). Factor n(f).
5*f**4*(f + 1)
Let x(t) be the first derivative of t**6 - 21*t**5/2 + 297*t**4/8 - 81*t**3/2 - 81*t**2/4 - 19. Find g such that x(g) = 0.
-1/4, 0, 3
Let z(g) be the second derivative of -7*g**5/150 - 19*g**4/15 - 32*g**3/3 - 128*g**2/15 + 42*g. Factor z(v).
-2*(v + 8)**2*(7*v + 2)/15
Let j(t) be the first derivative of 0*t + 18 + 3*t**5 - 5*t**3 + 5/4*t**4 - 5/2*t**2. Find x such that j(x) = 0.
-1, -1/3, 0, 1
What is q in 253*q**2 - 15*q - 51*q - 160 + 62*q**2 - 24*q + 260*q**3 + 15*q**4 = 0?
-16, -1, 2/3
Let o(m) be the first derivative of -2*m**6/3 + 36*m**5/5 - 20*m**4 + 292. Find u, given that o(u) = 0.
0, 4, 5
Factor -14/9*n**2 + 14/9 + 2/9*n - 2/9*n**3.
-2*(n - 1)*(n + 1)*(n + 7)/9
Suppose 5*q - 5*n = 9 + 21, 0 = -4*q + n + 15. Solve 3/2*u**4 + 0*u - 3*u**2 + 0 - 3/2*u**q = 0 for u.
-1, 0, 2
Let v(t) be the first derivative of -t**3/2 - 9*t**2/2 + 21*t/2 + 62. Find c such that v(c) = 0.
-7, 1
Let f(v) = -20*v**5 - 32*v**4 - 104*v**3 - 80*v**2 - 20*v + 16. Let i(o) = -o**5 - o**3 + o**2 + o + 1. Let t(x) = f(x) - 16*i(x). Solve t(r) = 0 for r.
-3, -1, 0
Let -22*n - 25*n - 37*n - 2*n**2 - 160 = 0. Calculate n.
-40, -2
Let h(v) = 58*v + 4587. Let c be h(-79). What is s in -10*s + 14*s**c - 68/3*s**4 - 4*s**3 + 64/3*s**2 + 4/3 = 0?
-1, 2/7, 1/3, 1
Let 2*t**3 - 34/7*t**2 - 12/7 + 34/7*t - 2/7*t**4 = 0. What is t?
1, 2, 3
Let d = -21 - -37. Let 4*i**4 + 84*i**5 - 76*i**3 - 72*i**3 + 0 + 64*i + 12*i**2 - d = 0. Calculate i.
-1, 2/7, 2/3, 1
Let c(h) be the first derivative of -h**6/39 + h**4/13 - h**2/13 + 93. Factor c(k).
-2*k*(k - 1)**2*(k + 1)**2/13
Let o = -6/67 + 554/201. Let b = -113 + 115. Find f such that -b*f**2 - 8/9 - o*f = 0.
-2/3
Suppose -4*b = 0, 3*b - 26 + 6 = -5*w. Let x(k) be the second derivative of 1/30*k**5 + 4/3*k**3 + 3*k + 0 + 1/3*k**w + 8/3*k**2. Find z, given that x(z) = 0.
-2
Let d(h) be the second derivative of -29*h - 8/105*h**7 - 22/75*h**6 + 0 + 13/15*h**4 - 4/5*h**2 - 1/25*h**5 + 2/3*h**3. Determine v so that d(v) = 0.
-2, -1, 1/4, 1
Let f(y) = -y**3 - 4*y**2 + 2*y + 7. Let b be f(-5). Let t = b + -13. Factor 27*g**2 + 2*g**4 - g**4 + 27*g + t*g**3 + 0*g**4.
g*(g + 3)**3
Suppose 3*v + 36 = 4*v. Suppose v = -5*n + 61. Determine l, given that 26*l**2 + 49/2*l**n - 77/2*l**4 + 0 - 33*l**3 - 4*l = 0.
-1, 0, 2/7, 2
Let p(b) be the second derivative of 0 - 9*b - 1/600*b**6 + 0*b**4 - 7/2*b**2 + 0*b**3 + 1/300*b**5. Let k(w) be the first derivative of p(w). Factor k(t).
-t**2*(t - 1)/5
Let l(n) be the first derivative of 11*n**3 - 377*n**2/2 + 104*n - 4. Let w(q) = 50*q**2 - 566*q + 156. Let v(b) = -8*l(b) + 5*w(b). Factor v(y).
-2*(y - 13)*(7*y - 2)
Let a be (-1)/(((-20)/(-68))/(-5)). Suppose -4*f + 5*p = a, 4*p - 29 - 1 = -5*f. Factor n + n**3 - 4*n + f*n + 0*n**3.
n*(n - 1)*(n + 1)
Let n(i) = 7*i**2 - 10*i + 12. Let u be n(1). Suppose g + 2*g - u = 0. Factor 8/15*d**g - 4/5*d**2 - 2/15 + 8/15*d - 2/15*d**4.
-2*(d - 1)**4/15
Let m be ((-216)/126)/(17/(-119)). Determine a so that -m*a**2 + 96*a - 256 + 1/2*a**3 = 0.
8
Let y(u) = 47*u - 41. Let b be y(6). What is p in -36*p**2 - 54 + 108*p - 243*p**4 + 20*p**3 - 36*p**2 + b*p**4 = 0?
1, 3
Suppose 5 = 2*m - 3, -4*u + 28 = 5*m. Factor 2*x**2 - u*x**2 - 33 - x - 3*x**2 + 37*x.
-3*(x - 11)*(x - 1)
Let i(l) = -l**5 + l**3 + 1. Let o be 4/32 - (-36)/(-32). Let v(h) = 6*h**5 - 11*h**3 + 5*h - 1. Let a(q) = o*v(q) - i(q). Suppose a(b) = 0. What is b?
-1, 0, 1
Let u(j) = -6*j**2 - 3*j - 3. Let p be u(4). Let i = 445/4 + p. Solve -3/4*n - 1/4*n**4 + 1/2 - i*n**2 + 3/4*n**3 = 0.
-1, 1, 2
Let o be -1*(2 + 20/15*(-30)/20). Factor o + 0*g**2 + 0*g - 3/5*g**3 + 3/5*g**4.
3*g**3*(g - 1)/5
Let q be (-13 + 41)*1/4. Let t(y) = y**3 - 6*y**2 - 6*y - 5. Let z be t(q). Factor 3*c**2 - c**2 + 3*c**z - c**3 - 2*c**2.
-c**2*(c - 3)
Let u(h) = 18*h**2 + 70*h - 33. Let k(c) = -5*c**2 - 18*c + 8. Let p(l) = 22*k(l) + 6*u(l). Factor p(r).
-2*(r - 11)*(r - 1)
Suppose -60 - 80 = -5*o + 5*g, 3*g = 15. Suppose 25 = -4*j + o. Let 1/3*x**j + 1/3 - 2/3*x = 0. What is x?
1
Let k(m) be the third derivative of -m**5/330 - 7*m**4/66 - 49*m**3/33 + 64*m**2. Factor k(o).
-2*(o + 7)**2/11
Let h be 2/(-15) - 5/(450/(-13)). Let s(b) be the third derivative of 0 + 1/12*b**4 + 0*b**3 + b**2 + h*b**5 + 0*b. Factor s(p).
2*p*(p + 3)/3
Let x(l) be the third derivative of l**7/630 - l**6/90 + l**5/30 - l**4/18 + l**3/18 + 112*l**2 + 2. Suppose x(t) = 0. What is t?
1
Suppose -64*x + 110 = -112 + 94. Solve 32/9*o - 14/9*o**x - 8/9 = 0 for o.
2/7, 2
Let t(d) = -5*d**3 + 8*d**2 - 3*d. Let w(u) be the third derivative of -u**6/24 + 7*u**5/60 - u**4/12 - 14*u**2. Let h(y) = 3*t(y) - 2*w(y). Factor h(k).
-5*k*(k - 1)**2
Suppose -276*i = -207*i - 138. Factor -8/9*r + 52/9*r**i - 32/9 - 4/3*r**3.
-4*(r - 4)*(r - 1)*(3*r + 2)/9
Let t(w) be the second derivative of w**8/1680 + w**7/420 - w**6/120 - w**5/30 - 8*w**4/3 + 29*w. Let b(m) be the third derivative of t(m). Factor b(q).
2*(q - 1)*(q + 2)*(2*q + 1)
Let y(m) = -18*m**4 + 60*m**3 + 15*m**2 - 84*m - 24. Let z(t) = -19*t**4 + 59*t**3 + 16*t**2 - 84*t - 24. Let c(i) = 2*y(i) - 3*z(i). Let c(q) = 0. Calculate q.
-1, -2/7, 2
Let a(s) be the second derivative of -22/15*s**3 - 1/30*s**4 + 0 - 121/5*s**2 + 27*s. Factor a(x).
-2*(x + 11)**2/5
Let u(l) = -5*l**2 + 86*l + 88. Let d(h) = -h**2. Let w(j) = 3*d(j) - u(j). Find f such that w(f) = 0.
-1, 44
Let o = -373534/2167 + 1896/11. Let q = o + 802/1379. Find n such that 4/7 - q*n**2 + 0*n = 0.
-1, 1
Let u(y) = -y**4 - 18*y**3 - 15*y**2 + 120*y. Let b(o) = o**4 + o**2. Let p(i) = -2*b(i) + 2*u(i). Let p(x) = 0. What is x?
-6, -5, 0, 2
Let z = -2/11699 - -280786/58495. Suppose 0 + z*t**2 + 16/5*t + 9/5*t**3 = 0. Calculate t.
-4/3, 0
Let t be 852/330 + 0 + ((-60)/(-33) - 2). Factor -9/5*v**2 + 3/5*v**4 - 12/5*v + t + 6/5*v**3.
3*(v - 1)**2*(v + 2)**2/5
Let j(g) be the third derivative of g**6/20 - 13*g**5/60 + g**4/3 - g**3/6 + 50*g**2. Factor j(c).
(c - 1)**2*(6*c - 1)
Let l be 22*-4*1/(-8). Suppose 0 = 7*w - l*w - 3*c + 24, -5*w = 4*c - 31. Factor 0*u**2 + 1/5*u**w - 1/5*u**4 + 0 + 0*u.
-u**3*(u - 1)/5
Suppose t + 3*t = 11*t. Let z(q) be the second derivative of -1/48*q**4 + 1/8*q**2 + 1/80*q**5 + t + 9*q - 1/24*q**3. Solve z(u) = 0 for u.
-1, 1
Factor 22/7*j**3 - 6/7*j**4 - 4/7 - 30/7*j**2 + 18/7*j.
-2*(j - 1)**3*(3*j - 2)/7
Find x, given that 679 - 128*x + 1362 - 51 + 58 + 2*x**2 = 0.
32
Let n(d) be the second derivative of d**5 + 0 + 1/6*d**6 + 0*d**2 + 0*d**3 + 24*d + 5/3*d**4. Factor n(m).
5*m**2*(m + 2)**2
Let s = 20 - 54. Let b = -31 - s. Solve 0 + 2/3*d + 0*d**2 - 2/3*d**b = 0 for d.
-1, 0, 1
Let w be 1*-8*2/(-12). Suppose 6*b - b = 5, 4*z + 4*b = 12. Factor -w*s - 2/3*s**2 + z.
-2*(s - 