*3. Factor o(u).
-u*(u - 2)*(u - 1)/3
Let f(t) be the second derivative of -27*t**2 - 3/2*t**4 + 0 + 1/10*t**5 + 9*t**3 + 8*t. What is r in f(r) = 0?
3
Find p such that -26/17*p**2 - 2/17*p**4 - 8/17 - 12/17*p**3 - 24/17*p = 0.
-2, -1
Let 42*x**3 - 40*x - 210*x - 2*x**3 - 25*x**2 - 2*x**4 - 3*x**4 = 0. What is x?
-2, 0, 5
Let k(h) be the first derivative of -1 + 0*h**2 + 2/9*h**4 + 0*h + 8/27*h**3 + 2/45*h**5. Factor k(v).
2*v**2*(v + 2)**2/9
Let h(b) = -b**2 - 11*b - 30. Let f be h(-6). Factor -1/9*v**2 - 2/9*v**3 + f - 1/9*v**4 + 0*v.
-v**2*(v + 1)**2/9
What is h in -h**3 + 5*h**4 - h**4 - 8*h**2 + 0*h**2 - 3*h**3 = 0?
-1, 0, 2
Solve 2/3 - 2/9*z - 16/3*z**2 = 0 for z.
-3/8, 1/3
Let g(z) = -2*z**2 + 14*z - 6. Let x(n) = -3*n**2 + 29*n - 11. Let i(j) = 5*g(j) - 2*x(j). Find v such that i(v) = 0.
1, 2
Let h(c) = 9*c**2 + 10*c - 19. Let g(o) = -55*o**2 - 60*o + 115. Let l(p) = 4*g(p) + 25*h(p). Let l(q) = 0. What is q?
-3, 1
Factor 12*j + 2*j + j**2 - 12*j.
j*(j + 2)
Find i such that 1/4*i - 1/4*i**2 + 0 = 0.
0, 1
What is d in 20*d**3 - 32 - 4*d**5 + 39*d**2 - 22*d + 27*d**2 + 6*d - 8*d**4 - 26*d**2 = 0?
-2, -1, 1, 2
Let g = -60 - -62. Let o(r) be the first derivative of -3/2*r**3 + 1/8*r**4 + 27/4*r**g + 4 - 27/2*r. Factor o(s).
(s - 3)**3/2
Determine p, given that 3*p**3 - p - p**2 - 3*p**4 + 2*p - 4*p + 4*p**2 = 0.
-1, 0, 1
Let y(c) be the first derivative of 2*c**3/27 - c**2/9 - 19. What is n in y(n) = 0?
0, 1
Let v(g) = -g**3 - 26*g**2 + 31*g - 4. Let q(z) = -z**3 - z**2 + z + 1. Let l(d) = -6*q(d) + v(d). Determine r, given that l(r) = 0.
1, 2
Let p(z) be the third derivative of 1/24*z**4 + 0 + 0*z + z**2 - 1/105*z**7 + 0*z**3 - 1/40*z**6 + 0*z**5. Find l such that p(l) = 0.
-1, 0, 1/2
Factor 0 + 1/4*j - 1/4*j**2.
-j*(j - 1)/4
Suppose -m = -4*q - 5*m + 64, -84 = -5*q - 3*m. What is n in 5*n + q + 2*n**2 + n + 7*n - n = 0?
-3
Let i(n) = -42*n**3 - 298*n**2 - 998*n - 1248. Let z(f) = f**4 - 43*f**3 - 297*f**2 - 997*f - 1247. Let o(w) = 3*i(w) - 2*z(w). Solve o(s) = 0.
-5
Let q be 1*(0/(-2))/(-3). Suppose -5*f - 6 = -2*w + 23, q = 2*f + 10. Find g, given that 0*g**2 + 4*g**3 - 6*g**w + 4*g**2 - 2*g = 0.
-1/2, 0, 1
Suppose 1/2*g**4 + 1/2 + 5/4*g**5 - g**2 - 5/2*g**3 + 5/4*g = 0. Calculate g.
-1, -2/5, 1
Let i(x) be the first derivative of 4*x**3/3 + x**2 + 2*x - 5. Let w be i(-1). Determine r so that 0 + 2/3*r**2 - 2*r**5 - 2/3*r**w + 0*r + 2*r**3 = 0.
-1, -1/3, 0, 1
Suppose -5*j = -7*j. Let q(z) be the third derivative of -2/45*z**5 + z**2 + 0 + 0*z + j*z**3 + 1/36*z**4. Factor q(i).
-2*i*(4*i - 1)/3
Suppose -7*n = -18 - 3. Let o(b) be the third derivative of 0*b + 0*b**n - 1/120*b**4 - 2*b**2 + 1/300*b**5 + 0. Factor o(t).
t*(t - 1)/5
Factor 0*v**4 + 3*v**3 - 3/2*v - 3/2*v**5 + 0 + 0*v**2.
-3*v*(v - 1)**2*(v + 1)**2/2
Let o(u) be the second derivative of -u**6/660 - u**5/330 + u**2 + 7*u. Let d(s) be the first derivative of o(s). Solve d(i) = 0.
-1, 0
Let d = 12 + -7. Let p(w) = -5*w**d + 3*w**5 + 2*w**4 + w**4 + 2*w**3 - 3. Let c(b) = -b**4 + 1. Let o(z) = 3*c(z) + p(z). Factor o(t).
-2*t**3*(t - 1)*(t + 1)
Let a(l) be the second derivative of 0 + 0*l**3 + 0*l**4 - 2*l + 1/30*l**5 - l**2. Let c(d) be the first derivative of a(d). Let c(u) = 0. What is u?
0
Let p(z) be the second derivative of z**4/6 + 2*z**3/3 - 3*z**2 - 5*z. Find b, given that p(b) = 0.
-3, 1
Let c(s) be the second derivative of s**5/20 + s**2/2 + 2*s. Let p(f) = -4*f**3 + 2*f**2 + 4*f - 2. Let n(h) = -2*c(h) - p(h). Factor n(k).
2*k*(k - 2)*(k + 1)
Solve -15*o**2 + 2*o + 7*o**2 + 9*o**2 = 0 for o.
-2, 0
Let s be (-3)/(-12)*0 - (1 - 3). Let a(g) be the second derivative of -1/6*g**4 - 3*g + 0 + 1/3*g**3 + 0*g**s. Suppose a(c) = 0. What is c?
0, 1
Let w(m) be the third derivative of m**2 + 0 + 1/600*m**6 + 1/24*m**4 + 1/75*m**5 + 0*m + 1/15*m**3. Factor w(o).
(o + 1)**2*(o + 2)/5
Let b(n) be the first derivative of n**8/2016 - n**6/360 + n**4/144 - n**2/2 - 3. Let s(v) be the second derivative of b(v). Let s(l) = 0. Calculate l.
-1, 0, 1
Let j(u) be the second derivative of -u**6/80 - 3*u**5/16 - 3*u**4/4 - 11*u**3/8 - 21*u**2/16 + 28*u. Factor j(a).
-3*(a + 1)**3*(a + 7)/8
Let w(k) be the first derivative of -3/2*k**4 + 12*k**2 - 12*k - 3*k**3 + 3 + 3/5*k**5. Factor w(v).
3*(v - 2)*(v - 1)**2*(v + 2)
Let c(h) = -9*h - 7. Let o be c(8). Let j = -867/11 - o. Factor j - 2/11*x**2 + 0*x.
-2*(x - 1)*(x + 1)/11
Factor 2*s**2 - 13*s + 10*s + 23*s + 2*s**2 + 16.
4*(s + 1)*(s + 4)
Suppose -11 = 3*t + 5*b, -4*b + 3 = 5*t - b. Let g(i) = -5*i**3 + 3*i**2 + 3*i. Let y(a) = 9*a**3 - 5*a**2 - 5*a. Let c(k) = t*y(k) + 5*g(k). Factor c(n).
2*n**3
Let s(g) = 15*g**2 - 7*g - 5. Let q(t) = 16*t**2 - 8*t - 6. Let k(n) = -5*q(n) + 6*s(n). Determine r, given that k(r) = 0.
0, 1/5
Let u(i) be the second derivative of 0*i**2 + 1/90*i**6 + 3*i - 1/30*i**5 + 0 + 0*i**3 + 1/36*i**4. Factor u(h).
h**2*(h - 1)**2/3
Let k = 0 - -2. Let n(h) be the first derivative of 2 + 1/5*h**5 + 0*h**k + 1/4*h**4 + 0*h - 2/3*h**3. Suppose n(o) = 0. Calculate o.
-2, 0, 1
Suppose -m - 3 - 2 = 2*t, 5*m + 3*t - 3 = 0. Solve m + 6*n**3 + 4*n**2 + 9*n**4 - 10*n**2 - 9*n + 0*n**5 + 3*n**5 - 6 = 0.
-1, 1
Suppose 2*z + 3*l - 2 = 0, -l = l + 4. Let n(w) be the second derivative of -1/12*w**z - 1/3*w**3 - 1/2*w**2 + 0 - 3*w. Factor n(d).
-(d + 1)**2
Let d be 12/30 + (-13)/(-5). Let i(s) be the third derivative of 0*s**d + 0*s + 0*s**5 - 1/360*s**6 + 1/72*s**4 + 0 + 2*s**2. Factor i(l).
-l*(l - 1)*(l + 1)/3
Let t(y) be the second derivative of -y**5/4 - 25*y**4/12 - 20*y**3/3 - 10*y**2 - 8*y + 3. Find x such that t(x) = 0.
-2, -1
What is c in -9/2*c + 11/2*c**2 - 1 = 0?
-2/11, 1
Let r(k) be the third derivative of 0 + 1/10*k**5 + 1/4*k**4 + 0*k + 1/60*k**6 + 1/3*k**3 + 4*k**2. Factor r(z).
2*(z + 1)**3
Solve -2*s**4 + 5*s**3 - 4*s**2 - 6*s + s**3 + 0 + 2*s**2 + 4 = 0 for s.
-1, 1, 2
Let o(a) be the first derivative of -a - 3/2*a**2 - 4 - 2/3*a**3. Factor o(i).
-(i + 1)*(2*i + 1)
Let f(d) be the second derivative of d**5/110 - d**4/66 - 2*d**3/33 + d. Find g such that f(g) = 0.
-1, 0, 2
Let l(x) = 3*x**3 - 11*x**2 + 10. Let w be 14/42*(-1 + -5). Let a(u) = 39*u**3 - 144*u**2 + 129. Let j(z) = w*a(z) + 27*l(z). What is o in j(o) = 0?
-1, 2
Let s(r) = -6*r**2 + 15*r - 9. Let z(b) = -7*b**2 + 16*b - 8. Let k(p) = 4*s(p) - 3*z(p). Factor k(o).
-3*(o - 2)**2
Suppose -4*m + 8*m = 68. Factor 2*t + 3 + t**2 - m*t + 11*t.
(t - 3)*(t - 1)
Suppose 4*b = 2*u + 3*u, 0 = -4*b + 4*u + 4. Suppose -b*d + 32 = 2. Solve 2*o**2 - d*o**2 + 2*o - o + 2*o**3 + o = 0.
0, 1
Let z = -1 + 5. Factor 13*h**3 + 1 - 14*h**3 - 2*h**z - h**5 - 1.
-h**3*(h + 1)**2
Let d(f) = -f**3 + 5*f**2 - 5*f + 3. Let b be d(3). Let s be 0/(-3)*(-2)/b. Solve 1/3*v**2 + 2/3*v + s = 0 for v.
-2, 0
Suppose 7*k + 20 = 11*k. Solve 31*p - 27*p + 13*p**2 - k*p**2 - 5*p**3 = 0 for p.
-2/5, 0, 2
Let i(f) be the first derivative of -2*f**3/5 + 4*f**2/5 + 8*f/5 - 6. Factor i(h).
-2*(h - 2)*(3*h + 2)/5
Let q(f) be the second derivative of -3*f**5/160 + 3*f**3/16 + 3*f**2/8 + 12*f. Factor q(u).
-3*(u - 2)*(u + 1)**2/8
Factor 2/9*n + 0 - 2/9*n**2.
-2*n*(n - 1)/9
Let d(h) be the third derivative of -h**6/40 + h**4/8 - 43*h**2. Determine g so that d(g) = 0.
-1, 0, 1
Let s(u) be the first derivative of 3*u**4/32 + u**3 + 9*u**2/4 + 8. Factor s(i).
3*i*(i + 2)*(i + 6)/8
Let j(u) = 13*u**4 - 43*u**3 + 45*u**2 + 5*u - 5. Let l(b) = -6*b**4 + 22*b**3 - 22*b**2 - 2*b + 2. Let r(p) = -2*j(p) - 5*l(p). Factor r(m).
4*m**2*(m - 5)*(m - 1)
Let w(v) be the second derivative of -v**10/5040 - v**9/1680 - v**8/2240 - v**4/3 - 3*v. Let z(d) be the third derivative of w(d). Factor z(h).
-3*h**3*(h + 1)*(2*h + 1)
Solve -2*w**2 - 1/3*w**4 - 5/3*w**3 + 4/3*w + 8/3 = 0.
-2, 1
Let a(o) = -13*o**3 + 29*o**2 - 47*o + 17. Let k(w) = 4*w**3 - 10*w**2 + 16*w - 6. Let b(i) = 4*a(i) + 14*k(i). Suppose b(m) = 0. What is m?
1, 4
Suppose -2*n = -5*o + 342, o = -0*o + n + 66. Let x be 3/(-7) + 72/o. Suppose x*g + 0 - 12/5*g**2 = 0. What is g?
0, 1/4
Solve -3*g**5 + 22*g**3 - g**5 + 12*g**4 - 6*g**3 = 0.
-1, 0, 4
Let b(h) be the first derivative of h**6/6 + 7*h**5/10 + 3*h**4/8 - 4*h**3/3 - h**2 + 13. Determine l so that b(l) = 0.
-2, -1/2, 0, 1
Let z be (-3)/((-9)/6) + 0. Find s such that -3*s**3 - 10*s + 5*s**3 + z*s