 -f**8/3360 - f**7/1260 + f**6/360 + f**5/60 + f**4/12 - 3*f**2. Let m(u) be the second derivative of v(u). Factor m(b).
-2*(b - 1)*(b + 1)**2
Let s(v) be the second derivative of v**6/10 + 3*v**5/5 - v**4/2 - 6*v**3 + 27*v**2/2 - 16*v. Find n, given that s(n) = 0.
-3, 1
Let x(i) = 6*i**2 + 6*i - 12. Let o(f) = 2*f**2 + 2*f - 4. Suppose 3*m - 7*m = 8. Suppose -k - 3*k + 28 = 0. Let g(h) = k*o(h) + m*x(h). Factor g(w).
2*(w - 1)*(w + 2)
Let h(i) be the first derivative of 1/240*i**5 - 1/24*i**3 + 1/480*i**6 + i**2 - 1/96*i**4 + 1 + 0*i. Let b(q) be the second derivative of h(q). Factor b(v).
(v - 1)*(v + 1)**2/4
Let g(q) = -20*q**5 - 21*q**4 + 23*q**3 + 9*q**2 - 3*q - 3. Let b(n) = -n**4 - n**3 - n**2 - n - 1. Let l(s) = 3*b(s) - g(s). Determine r, given that l(r) = 0.
-3/2, -2/5, 0, 1
Let u = -88 - -88. Factor 5/4*j**4 + u*j + 0*j**2 - 1/4*j**3 - j**5 + 0.
-j**3*(j - 1)*(4*j - 1)/4
Let d = -10 - -10. Let f(j) be the first derivative of 2 + 1/18*j**4 + d*j**3 - 1/3*j**2 - 4/9*j. Find i such that f(i) = 0.
-1, 2
Let r(k) be the second derivative of -k**4/30 - 2*k**3/15 - k**2/5 - 8*k. Let r(g) = 0. What is g?
-1
Suppose -8*g = -3*g - 10. Solve 5*c**3 - c**3 - 2*c**3 + g*c**2 = 0 for c.
-1, 0
Let k be 0 - (-16)/114*5. Let l = k - 2/57. Factor l + 2/3*y**3 - 2/3*y - 2/3*y**2.
2*(y - 1)**2*(y + 1)/3
Suppose -7*r - 6*r = 0. Find a such that 1/2*a**3 + r + 0*a + 1/2*a**4 + 0*a**2 = 0.
-1, 0
Let b(i) be the second derivative of 3*i**5/4 - 2*i**4 - 2*i**3 + 8*i. Factor b(u).
3*u*(u - 2)*(5*u + 2)
Let j(w) be the first derivative of w**5/60 + w**4/12 + w**3/6 + w**2/6 - w + 5. Let s(o) be the first derivative of j(o). Let s(h) = 0. What is h?
-1
Let x be 18/(-24)*(-4)/42. Let o(c) be the first derivative of 0*c**3 + 0*c - 4/35*c**5 + 0*c**2 + 1 + x*c**4. Factor o(k).
-2*k**3*(2*k - 1)/7
Let d(r) = 7*r**2 + 5*r + 5. Let y be (-7)/(-2) + 2/(-4). Let g(s) = -4*s**2 - 3*s - 3. Let j(x) = y*d(x) + 5*g(x). What is b in j(b) = 0?
0
Let a(u) be the third derivative of u**8/504 + 2*u**7/315 - u**6/90 - 2*u**5/45 + u**4/36 + 2*u**3/9 + 9*u**2. Let a(n) = 0. What is n?
-2, -1, 1
Suppose 2*m + 2 = -4*k, -5*m = 2*k - 6*k + 33. Factor 2 - 4 - 2 - 2*z**k + 6*z.
-2*(z - 2)*(z - 1)
Let t = -1/143 + 293/1001. Let f(g) = g**3 + 2*g**2 - g - 2. Let y be f(-2). Suppose t*x**3 + y + 0*x + 2/7*x**2 = 0. Calculate x.
-1, 0
Factor 3*c**2 - 5*c + 13*c + 6 - c**2 + 0.
2*(c + 1)*(c + 3)
Let p(g) be the third derivative of -1/30*g**5 + 3*g**2 + 0*g + 0*g**4 + 0*g**3 - 1/30*g**6 + 0 - 1/105*g**7. Factor p(q).
-2*q**2*(q + 1)**2
Suppose -6/11*y - 8/11*y**2 + 2/11 = 0. Calculate y.
-1, 1/4
Suppose 2*t = -4*t. Let q(a) be the second derivative of 1/15*a**3 - 1/50*a**5 + 0*a**4 - 2*a - 1/10*a**2 + t + 1/150*a**6. Factor q(o).
(o - 1)**3*(o + 1)/5
Let c(g) be the second derivative of -g**8/5040 + g**6/1080 - 5*g**3/6 - g. Let n(o) be the second derivative of c(o). Factor n(i).
-i**2*(i - 1)*(i + 1)/3
Let o(z) be the first derivative of 9*z**4/28 - z**3/7 - 5*z**2/14 - z/7 - 1. Factor o(v).
(v - 1)*(3*v + 1)**2/7
Let j(w) be the first derivative of 2*w**6/3 - w**4 - 5. Factor j(p).
4*p**3*(p - 1)*(p + 1)
Let j(q) be the third derivative of -q**8/23520 + q**6/840 + q**5/210 - q**4/12 + 2*q**2. Let p(y) be the second derivative of j(y). Factor p(m).
-2*(m - 2)*(m + 1)**2/7
Let n(f) be the first derivative of -7*f**6/15 - 124*f**5/75 - 13*f**4/6 - 56*f**3/45 - 4*f**2/15 + 3. Suppose n(x) = 0. Calculate x.
-1, -2/3, -2/7, 0
Let u = -86 - -260/3. Let r(x) be the first derivative of -3*x**2 + 3/2*x**4 + 2*x - u*x**3 - 3. Factor r(b).
2*(b - 1)*(b + 1)*(3*b - 1)
Let r(z) be the third derivative of z**7/70 - z**6/40 - z**5/20 + z**4/8 + z**2. Suppose r(o) = 0. What is o?
-1, 0, 1
Let r(a) be the first derivative of -2 + 1/9*a**3 - 4/3*a + 0*a**2. Factor r(s).
(s - 2)*(s + 2)/3
Let h be 22/21 - (1 - (-27)/(-21)). Solve h*s**4 - s**5 - 2*s**2 + 4/3*s**3 - 1/3*s + 2/3 = 0.
-1, -2/3, 1
Suppose -1 = -h - 1. Let q(l) be the first derivative of h*l**2 - 4/15*l**5 - 1/9*l**6 - 1/6*l**4 + 0*l**3 - 3 + 0*l. Solve q(a) = 0 for a.
-1, 0
Factor 2/5*t**5 + 0*t**2 + 0*t + 4/5*t**4 + 2/5*t**3 + 0.
2*t**3*(t + 1)**2/5
Factor 0 - 8/5*n + 2/5*n**3 + 6/5*n**2.
2*n*(n - 1)*(n + 4)/5
Let w be ((-3)/4)/(36/(-16)). Factor -w*o**4 + 0 + 1/3*o - o**2 + o**3.
-o*(o - 1)**3/3
Let w = -865/3 - -289. Factor w*g + 1/3 - 2/3*g**3 - 1/3*g**2.
-(g - 1)*(g + 1)*(2*g + 1)/3
Find r, given that 2*r**4 - 3*r**2 + 2*r**5 + r**2 - 2*r - 2*r**2 + 2*r**4 = 0.
-1, 0, 1
Let q(l) be the second derivative of 7*l**6/24 + l**5 + 55*l**4/48 + 5*l**3/12 - 2*l. Determine a so that q(a) = 0.
-1, -2/7, 0
Let k = -6 - -21. Let g be 1/5 + 42/k. Factor g*n**2 - n**2 - 5*n**3 + 3*n**4 + 5*n**5 - 5*n**4.
n**2*(n - 1)*(n + 1)*(5*n - 2)
Let o(t) be the first derivative of 1/12*t**3 + 1/4*t**2 + 1/4*t + 2. Suppose o(y) = 0. What is y?
-1
Let d be ((-52)/(-40))/13*2/12. Let j(s) be the third derivative of 0*s - 1/12*s**4 + d*s**6 - 1/3*s**3 - 2*s**2 + 0 + 1/30*s**5. Factor j(f).
2*(f - 1)*(f + 1)**2
Let c = -7 + 9. Let 0*y + 8 + c*y**2 + y + 7*y = 0. What is y?
-2
Let k(s) be the first derivative of -s**3 - 9*s**2/2 - 6*s + 5. Factor k(y).
-3*(y + 1)*(y + 2)
Let b be (-78)/(-180) - 6/(-90). Find k, given that 0 - 1/4*k**5 + 0*k**2 + b*k**3 - 1/4*k + 0*k**4 = 0.
-1, 0, 1
Let c(f) = 2*f**3 + 28*f**2 + 58*f + 34. Let z(t) = t**3 + 28*t**2 + 57*t + 33. Let g(r) = -3*c(r) + 2*z(r). Solve g(b) = 0 for b.
-3, -1
Suppose 0 = -0*w - w - 5*w. Factor -3/2*f**3 + 1/2*f + w + f**2.
-f*(f - 1)*(3*f + 1)/2
Let x(c) be the first derivative of -c**4/4 + 7*c**3/3 + 3*c + 5. Let q be x(7). Find i, given that -2*i + i**3 - i + 2*i**q = 0.
-1, 0, 1
Let c(f) be the third derivative of -5*f**8/336 - f**7/42 + f**6/4 - f**5/6 - 25*f**4/24 + 5*f**3/2 - 3*f**2. Factor c(d).
-5*(d - 1)**3*(d + 1)*(d + 3)
Suppose -2 = -4*k + 6. Let u = -1 + 3. Suppose 5*w**k - 5*w**u - w**2 = 0. Calculate w.
0
Let d(k) be the second derivative of k**9/6048 - k**7/1680 - 5*k**3/6 + 4*k. Let a(p) be the second derivative of d(p). Factor a(t).
t**3*(t - 1)*(t + 1)/2
Factor -9*m**3 - 6*m**2 + 141*m - 141*m + 3*m**5.
3*m**2*(m - 2)*(m + 1)**2
Let q(g) = -2*g - 12. Let l be q(-7). Let i be 2 + l/(-8)*7. Factor -3/4*y**2 + i*y + 3/4*y**3 - 1/4*y**4 + 0.
-y*(y - 1)**3/4
Let x(c) be the second derivative of 5*c**7/14 - 17*c**6/10 + 63*c**5/20 - 11*c**4/4 + c**3 + 5*c. Factor x(k).
3*k*(k - 1)**3*(5*k - 2)
Suppose 1/3 + 2/3*z + 1/3*z**2 = 0. What is z?
-1
Let i(t) be the first derivative of -1/18*t**3 + 3 + 0*t**2 + 0*t. Factor i(r).
-r**2/6
Let m = -5 + 7. Suppose 3*z + 0*z = 5*p + 12, 2*p = 0. Find t, given that -6*t**2 - 5*t**4 + m*t**z + t**4 + 6*t**3 + 2*t = 0.
0, 1
Let a(t) be the first derivative of -5*t**3/9 + 5*t**2/3 - 5*t/3 + 7. Let a(i) = 0. What is i?
1
Let c(p) be the second derivative of -p**9/60480 - p**8/26880 + p**7/10080 + p**6/2880 + p**4/6 - p. Let t(h) be the third derivative of c(h). Solve t(l) = 0.
-1, 0, 1
Suppose -5*w = -4*z - 23, -3*z + 3 = 5*w - 6. Let t = z + 2. Find r such that t*r**3 - r**2 - r**3 + 0*r**3 = 0.
-1, 0
Let g(h) be the second derivative of h**6/120 - h**5/20 + h**4/8 + 2*h**3/3 - 3*h. Let i(d) be the second derivative of g(d). Factor i(f).
3*(f - 1)**2
Let m(j) be the third derivative of -1/60*j**6 - 1/70*j**7 + 0*j - 1/336*j**8 + 0 + 0*j**5 + 0*j**3 + 0*j**4 + j**2. Solve m(q) = 0.
-2, -1, 0
Let i(d) be the first derivative of -1 - 1/4*d**2 + d - 1/2*d**3. Suppose i(g) = 0. Calculate g.
-1, 2/3
Let x(z) be the third derivative of z**8/336 - z**6/60 + z**4/24 - 4*z**2. Solve x(k) = 0 for k.
-1, 0, 1
Let f(b) be the second derivative of -5*b**4/12 + 20*b**3/3 + 45*b**2/2 - 7*b. Let f(p) = 0. What is p?
-1, 9
Let t(f) be the third derivative of 0*f - 1/30*f**4 - 1/60*f**6 + 1/120*f**8 - 3/175*f**7 + 0*f**3 - 3*f**2 + 0 + 3/50*f**5. What is q in t(q) = 0?
-1, 0, 2/7, 1
Let -3*h**5 + 36/5*h**3 + 9/5*h**4 + 0*h + 12/5*h**2 + 0 = 0. What is h?
-1, -2/5, 0, 2
Let h(l) be the third derivative of -1/455*l**7 - 5*l**2 - 1/60*l**6 - 11/156*l**4 - 2/39*l**3 + 0*l + 0 - 19/390*l**5. Determine u, given that h(u) = 0.
-2, -1, -1/3
Let w = 178/9 - 154/9. Let f be (6/(-4))/(0 + 54/(-24)). Factor -2/3*m**3 + 1/3*m**5 - 7/3*m - f + 2/3*m**4 - w*m**2.
(m - 2)*(m + 1)**4/3
Let 0*q**5