 that n(b) = 0.
-1, 1, 2
Factor -3/2*p**3 - 1/4*p**4 - 3/4 - 5/2*p - 3*p**2.
-(p + 1)**3*(p + 3)/4
Let u(n) be the first derivative of -2*n**5/5 - n**4/2 + 4. Solve u(c) = 0 for c.
-1, 0
Suppose -1 - 2 = -m. Let k(i) be the second derivative of -1/42*i**4 + 0*i**m - 2*i + 1/105*i**6 + 0*i**5 + 0*i**2 + 0. Let k(c) = 0. What is c?
-1, 0, 1
Let b = -5 + 8. Suppose -4*y + 19 - b = 0. Let 2/7*v**5 - 16/7*v**y - 76/7*v**2 + 8*v - 16/7 + 50/7*v**3 = 0. Calculate v.
1, 2
Let g be (-510)/17*2/(-12). Factor -2/5*f + 2/5 - 4/5*f**2 - 2/5*f**g + 4/5*f**3 + 2/5*f**4.
-2*(f - 1)**3*(f + 1)**2/5
Let i(k) be the third derivative of k**8/70560 - k**7/4410 + k**6/630 + k**5/60 + 7*k**2. Let o(r) be the third derivative of i(r). Factor o(v).
2*(v - 2)**2/7
Let l(d) be the third derivative of -3*d**6/20 - 2*d**5/5 - d**4/3 - 7*d**2. Determine z so that l(z) = 0.
-2/3, 0
Let w(i) be the first derivative of 3*i**5/20 - 3*i**4/4 + i**3 + 4*i + 3. Let l(f) be the first derivative of w(f). Factor l(y).
3*y*(y - 2)*(y - 1)
Let u(p) be the third derivative of -1/480*p**6 + 0*p**3 + 0 + 3*p**2 + 0*p**4 + 0*p**5 + 1/420*p**7 + 0*p - 1/1344*p**8. Factor u(t).
-t**3*(t - 1)**2/4
Let i(h) be the first derivative of -h**7/280 + h**6/180 + h**5/40 - h**4/12 + h**3 + 5. Let f(b) be the third derivative of i(b). Factor f(c).
-(c - 1)*(c + 1)*(3*c - 2)
Let s(t) be the first derivative of 1/5*t**5 - 1/2*t**2 + 0*t + 1 - 1/3*t**3 + 1/4*t**4. Find m, given that s(m) = 0.
-1, 0, 1
Suppose 0 = 4*t + 10 + 54. Let o = -12 - t. Factor 0*u - 2/7*u**o - 2/7*u**3 + 2/7*u**2 + 2/7*u**5 + 0.
2*u**2*(u - 1)**2*(u + 1)/7
Let j(r) be the first derivative of 14*r**5/15 - 5*r**4/6 - 4*r**3/9 - 6. Factor j(c).
2*c**2*(c - 1)*(7*c + 2)/3
Let j(u) be the first derivative of -u**8/1176 + u**6/420 + u**2 - 2. Let f(c) be the second derivative of j(c). Solve f(r) = 0.
-1, 0, 1
Let g(k) be the second derivative of k**5/5 - 2*k**4 + 8*k**3 - 16*k**2 - 4*k. Suppose g(x) = 0. Calculate x.
2
Let m = 137 + -136. Factor m + 1/2*q**3 - q**2 - 1/2*q.
(q - 2)*(q - 1)*(q + 1)/2
Let s = 2/1339 - -1331/5356. Factor 0*i + 1/4*i**2 - 1/4*i**5 + 0 - 1/4*i**4 + s*i**3.
-i**2*(i - 1)*(i + 1)**2/4
Let d = 0 - 7. Let p = d + 9. Determine i, given that 4/3*i + 2/3 + 2/3*i**p = 0.
-1
Let z = 45 - 41. Let w(q) be the second derivative of -1/2*q**2 + 1/16*q**z - 1/6*q**3 - 2*q + 0. Factor w(i).
(i - 2)*(3*i + 2)/4
Let 2/15*d**5 + 0*d - 2/15*d**3 + 0 + 2/15*d**2 - 2/15*d**4 = 0. What is d?
-1, 0, 1
Let y(a) be the third derivative of 25*a**8/126 - a**7/3 + a**6/5 - 2*a**5/45 + 7*a**2. Suppose y(j) = 0. Calculate j.
0, 1/4, 2/5
Let -9*t - t - t**2 + 2*t - 4*t**5 + 5*t**3 + 3*t**5 + t**4 - 4 = 0. Calculate t.
-1, 2
Let b be (-48)/(-20) - ((-6)/(-15) - 1). Factor -t + 1/2*t**4 + 0*t**2 - 1/2 + t**b.
(t - 1)*(t + 1)**3/2
Suppose -2*x + 7 = -t - 0, 2*t = 10. Let n = -2 + x. Factor 4/3*v**3 + 0*v**n - 2/3*v**5 - 2/3*v + 0*v**2 + 0.
-2*v*(v - 1)**2*(v + 1)**2/3
Let i(y) be the second derivative of -y**5/20 - y**4/12 + 2*y**3/3 + 2*y**2 + 39*y. Factor i(q).
-(q - 2)*(q + 1)*(q + 2)
Let 20/3*v**5 - 28/3*v**4 - 80/3*v + 124/3*v**2 - 52/3*v**3 + 16/3 = 0. Calculate v.
-2, 2/5, 1
Let x(z) be the third derivative of -z**8/2520 - 8*z**7/1575 - 11*z**6/450 - 4*z**5/75 - z**4/20 + z**2 - 2*z. What is h in x(h) = 0?
-3, -1, 0
Determine u, given that 16/3*u + 32/3 + 2/3*u**2 = 0.
-4
Let y(a) be the first derivative of a**6/15 + 2*a**5/15 - a**4/30 - 2*a**3/9 - 2*a**2/15 + 12. Suppose y(f) = 0. What is f?
-1, -2/3, 0, 1
Suppose 17 = -2*z + 3*z - 3*w, -4*z + 33 = -5*w. Solve 2/5 - 1/5*g**3 + 3/5*g + 0*g**z = 0.
-1, 2
Let l(w) = 4*w**3 - 9*w**2 + w + 2. Let i(h) = -11*h**3 + 28*h**2 - 3*h - 7. Let q(c) = -2*i(c) - 7*l(c). Factor q(p).
-p*(p - 1)*(6*p - 1)
What is q in -3*q - 22/3*q**3 + 8*q**2 - 1/3*q**5 + 8/3*q**4 + 0 = 0?
0, 1, 3
Let q(k) be the third derivative of -k**6/180 - k**3/3 - k**2. Let i(b) be the first derivative of q(b). Factor i(t).
-2*t**2
Suppose 5*j - 4 = j. Let r be 4*(-2)/(-20)*j. Suppose r*o**3 + 8/5 + 16/5*o + 2*o**2 = 0. What is o?
-2, -1
Let 0*r**4 + 4/11*r**3 - 2/11*r + 0 + 0*r**2 - 2/11*r**5 = 0. Calculate r.
-1, 0, 1
Let w(t) be the second derivative of -1/50*t**6 + 0*t**4 + 0 + 0*t**5 + 0*t**3 + 1/70*t**7 + 0*t**2 + 6*t. Let w(r) = 0. What is r?
0, 1
Let w(c) be the first derivative of -c**4 + 4*c**3/3 + 2*c**2 - 4*c - 22. What is z in w(z) = 0?
-1, 1
Let v(x) be the third derivative of -x**7/945 + x**5/270 - 11*x**2 - 2. Factor v(s).
-2*s**2*(s - 1)*(s + 1)/9
Let x(w) be the second derivative of w**5/130 + w**4/26 + 2*w**3/39 + 6*w. Let x(z) = 0. Calculate z.
-2, -1, 0
Let i be 13*(0 + 3/144). Let o = i + -1/48. Find y such that -y - o*y**2 - 1 = 0.
-2
Let q(v) = -4*v**3 + v**2 + 2*v + 3. Let h(b) = b**3 - 1. Let d = -16 - -22. Let g(u) = d*h(u) + 2*q(u). Factor g(z).
-2*z*(z - 2)*(z + 1)
Let j be (2 - 6/(-5)) + -2. Suppose -3*l + 0 = -6. Factor -4/5 - 2/5*y**l + j*y.
-2*(y - 2)*(y - 1)/5
Find m such that 0*m**4 - 5*m**2 + 6*m**3 + 3*m**2 + 3*m**4 + 5*m**2 = 0.
-1, 0
Suppose -v + 4 = 4*n - 5*v, 0 = 3*v. Let q = 3 - n. Factor f - f + 0 + 4 - 2*f - q*f**2.
-2*(f - 1)*(f + 2)
Let s(n) be the second derivative of 0 + 1/6*n**3 - 1/8*n**4 + n**2 + 2*n + 1/30*n**5. Let u(l) be the first derivative of s(l). Solve u(j) = 0 for j.
1/2, 1
Let d(l) be the third derivative of -l**8/112 - l**7/70 + l**6/20 + l**5/10 - l**4/8 - l**3/2 + 26*l**2. Suppose d(o) = 0. Calculate o.
-1, 1
Let s(g) be the second derivative of -g**5/60 - g**4/12 + 2*g**3/9 - g. What is h in s(h) = 0?
-4, 0, 1
Suppose w - 28 = -3*c, 5*w - 55 = 4*c + 66. Suppose 0 = -5*g - w, 0*z + 4*z - 31 = -5*g. Find l such that -8 - 2 - 6*l**3 + 1 + 1 + z*l**2 = 0.
-2/3, 1, 2
Let s(m) be the third derivative of -6*m**2 - 1/6*m**4 + 0*m + 1/3*m**3 + 0 + 1/30*m**5. Factor s(n).
2*(n - 1)**2
Suppose 0 = 2*d + 1 - 5. Factor -2*c**5 - 9*c + d*c**3 + 9*c.
-2*c**3*(c - 1)*(c + 1)
Suppose -82*j = -75*j - 21. Solve 0*h + 2/7*h**2 + 0 - 1/7*h**j = 0.
0, 2
Let x(j) = -j**2 - 4*j + 7. Let n be x(-5). What is g in -n*g**2 - g**2 + 5*g**2 + 28*g - 30*g = 0?
0, 1
Suppose 4*w - 2 = -2*l + 16, 0 = w + l - 6. What is h in 1/3*h - 1/3*h**2 - 1/3*h**w + 1/3 = 0?
-1, 1
Let t(p) = p**2 - p + 1. Let j be t(2). Find c such that -j*c**3 + 4*c**2 + 4*c**3 - 5*c**2 = 0.
0, 1
Let q(a) = -a**2 + 4*a + 2. Let n be q(4). Suppose -12 + 2 = -2*v. Let 0*m**2 - 4*m**n + v*m**2 = 0. What is m?
0
Let l(z) = -z**2 + 12*z + 16. Let b be l(13). Let a(x) be the first derivative of 1/4*x**2 - 2 + 0*x**4 - 1/3*x**b + 1/5*x**5 + 0*x - 1/12*x**6. Factor a(t).
-t*(t - 1)**3*(t + 1)/2
Let g(m) = m**4 + m**3 + m**2 + m - 2. Let k be (-3)/(-1) - 3 - -5. Let p(b) = -2*b**4 - 3*b**3 - 3*b**2 - 2*b + 5. Let v(n) = k*g(n) + 2*p(n). Factor v(d).
d*(d - 1)**2*(d + 1)
Let l(b) be the second derivative of -b**5/60 + 5*b**4/18 + 2*b + 19. Suppose l(z) = 0. What is z?
0, 10
Factor 3/5*b**2 - 24/5*b + 0.
3*b*(b - 8)/5
Let n = 0 - 0. Determine o, given that -9*o**3 + 12*o**2 + n + 2*o**4 - 8*o + 2 + o**3 = 0.
1
Let w = -76/7 + 78/7. Solve -w*t**2 - 2/7 - 4/7*t = 0.
-1
Suppose 2*a + 6 = 4*c, 5*a = 3*c - 5 + 4. Suppose -c*i = 2*i + k - 14, -3*i + 18 = -3*k. Let -16*s**i + 0*s**3 + 3*s**3 - 7*s**3 + 2*s**4 = 0. What is s?
-2/7, 0
Let b(m) = -5*m**3 + 7*m**2 - 10*m - 4. Let k(n) = -n**3 - n - 1. Let r(c) = -3*b(c) + 12*k(c). Determine i, given that r(i) = 0.
0, 1, 6
Let d = -17/11 - -107/55. Let g be 1/4*144/180. Determine j so that d*j + 1/5*j**2 + g = 0.
-1
Let s(o) be the second derivative of o**6/180 - o**5/120 + 8*o. What is z in s(z) = 0?
0, 1
Let i(v) be the third derivative of -v**5/15 - 7*v**4/6 + 25*v**2 + v. Suppose i(c) = 0. Calculate c.
-7, 0
Let o(s) be the second derivative of -s**4/3 + 2*s**2 + 5*s. Suppose o(t) = 0. Calculate t.
-1, 1
Let r(b) be the third derivative of b**6/20 - b**5/15 - 5*b**2. Determine h, given that r(h) = 0.
0, 2/3
Let s(c) be the third derivative of -c**6/70 + 3*c**5/140 + c**4/56 + 32*c**2. Find n, given that s(n) = 0.
-1/4, 0, 1
Let g(j) be the third derivative of 1/108*j**4 + 0*j**3 - 2/135*j**5 - 2/945*j**7 - 2*j**2 + 1/108*j**6 + 0*j + 0. Find s such that g(s) = 0.
0, 1/2, 1
Let w = -8 - -13. Suppose 5*q + 2 - 7 = w*y, 2*q - 2 = 4*y. Suppose y + 0*h + 1/5*h**2 = 0. Calculate h.
0
Let r(o