rivative of -1/20*r**5 - 1/2*r**3 - 3*r + 1/2*r**i + 0 + 1/4*r**4. Factor z(b).
-(b - 1)**3
Let i(y) be the second derivative of -2/15*y**3 + 0 - 3*y + 1/5*y**2 + 1/30*y**4. Factor i(d).
2*(d - 1)**2/5
Let g = 17730/301 + -412/7. Let p = 39/86 + g. Factor -p + 3/2*o - o**2.
-(o - 1)*(2*o - 1)/2
Suppose -2*b + 3*b = -3*m + 6, 5*m - 10 = -4*b. Let u(r) be the second derivative of 1/48*r**4 + b - r + 0*r**3 - 1/8*r**2. Factor u(y).
(y - 1)*(y + 1)/4
Let i = 718/665 + 6/95. Let h = 7 + -5. Suppose -h*w - i*w**2 + 4/7 = 0. What is w?
-2, 1/4
Let f be (20/(-30))/(24/(-27)). Factor 3/2*n**2 + 0 + f*n + 3/4*n**3.
3*n*(n + 1)**2/4
Suppose -r = -15*r + 56. Let t(o) be the third derivative of 0*o**5 - 1/120*o**6 + 1/24*o**4 + 0 + 0*o**3 - r*o**2 + 0*o. Let t(s) = 0. Calculate s.
-1, 0, 1
Let h = 1541/4 + -382. Let -21/4*b**3 + 9/4*b**4 + h*b**2 + 1/4*b - 1/2 = 0. What is b?
-1/3, 2/3, 1
Let a = 1189/7 - 169. Factor -2/7*n**5 - 6/7*n**4 - a*n**3 + 0*n + 0 - 2/7*n**2.
-2*n**2*(n + 1)**3/7
Suppose -13*d - 18*d**2 - 81*d - 222 - 14*d - d**3 + 6 = 0. Calculate d.
-6
Let h(u) be the third derivative of -u**7/42 - u**6/60 + u**5/4 - u**4/6 - 2*u**3/3 + 8*u**2. Solve h(l) = 0.
-2, -2/5, 1
Let l(s) = 3*s - 60. Let g be l(20). Let o(i) be the first derivative of -1/10*i**4 + 4 + 0*i**2 + g*i + 2/15*i**3. Factor o(f).
-2*f**2*(f - 1)/5
Suppose -3*i - 6 = -4*i. Suppose -4*u = -u - i. Suppose u*o + 2/3*o**3 + 2/3 + 2*o**2 = 0. What is o?
-1
Factor 1/6*p**3 + 0 + 1/6*p - 1/3*p**2.
p*(p - 1)**2/6
Let s(k) = 7*k**2 + 7. Let x(m) = 11*m**2 + 11. Let h(v) = -8*s(v) + 5*x(v). Let t(w) = w**2 + 6*w + 1. Let q(n) = 2*h(n) - t(n). Factor q(d).
-3*(d + 1)**2
Let s be (-3)/((9/(-8))/(9/36)). Determine g so that -s*g**2 - 2/3*g + 0 = 0.
-1, 0
Suppose 6*x = x. Let f(h) be the second derivative of -1/100*h**5 + x*h**2 + 1/60*h**4 + 0 + 2*h + 0*h**3. Factor f(d).
-d**2*(d - 1)/5
Factor -23*i + 6*i**4 - 28*i**2 + 5 - 7*i**4 - 21 - 13*i - 9*i**3.
-(i + 1)*(i + 2)**2*(i + 4)
Let x(b) be the second derivative of b**6/180 - 7*b**5/300 + b**4/30 + b**3/2 - 7*b. Let h(v) be the second derivative of x(v). Factor h(g).
2*(g - 1)*(5*g - 2)/5
Factor -2*x - 2*x + 5*x**2 - 5*x**3 - x + 15*x.
-5*x*(x - 2)*(x + 1)
Let q(h) = 5*h**5 - 7*h**4 + h**3 + 7*h**2. Let r(p) = 6*p**5 - 8*p**4 + 2*p**3 + 8*p**2 + p. Let f(z) = 3*q(z) - 2*r(z). Factor f(l).
l*(l - 1)**2*(l + 1)*(3*l - 2)
Determine d, given that 9*d**3 - 7*d**2 + 9*d**2 + 3*d**2 - 3*d**5 + d**2 = 0.
-1, 0, 2
Let i = -1/4 + 13/20. Factor 2/5*b - i*b**2 + 0.
-2*b*(b - 1)/5
Let x = 0 + 0. Let x*q**4 - q**4 - 2*q**3 - q**4 = 0. Calculate q.
-1, 0
Factor -3/2 - 5/4*k - 1/4*k**2.
-(k + 2)*(k + 3)/4
Let z be 94/(-56) + (-1 - -1). Let v = -10/7 - z. Suppose -1/4*s**2 - v - 1/2*s = 0. Calculate s.
-1
Let y(i) be the first derivative of -2/3*i**3 - 2*i - 2*i**2 - 2. Factor y(p).
-2*(p + 1)**2
Let q be (11/6 - 0) + 67/402. Let -3/2*z**q - 3*z - 3/2 = 0. Calculate z.
-1
Determine c, given that -125/2 - 1/2*c**3 - 75/2*c - 15/2*c**2 = 0.
-5
Suppose -24 = -11*y + 7*y. Let u(r) be the second derivative of 0*r**y - 1/80*r**5 + 0 - r + 0*r**4 + 0*r**2 + 1/168*r**7 + 0*r**3. Solve u(o) = 0 for o.
-1, 0, 1
Let r = 8 - 5. Suppose -5*b = -5*o - 25, 2*b - 7 = r*b + 5*o. Factor -w**2 - b*w**2 + 3*w**2.
-w**2
Suppose 0 = 9*b - 94 + 58. Factor 0*n**b + 1/4*n**3 + 0*n**2 + 0*n - 1/4*n**5 + 0.
-n**3*(n - 1)*(n + 1)/4
Let l(x) be the first derivative of 3*x**6/10 - 21*x**5/20 + 4*x**4/3 - 2*x**3/3 - 5*x + 1. Let d(h) be the first derivative of l(h). Factor d(c).
c*(c - 1)*(3*c - 2)**2
Let l(c) be the first derivative of c**6/57 + 2*c**5/19 + 9*c**4/38 + 14*c**3/57 + 2*c**2/19 + 18. Determine s so that l(s) = 0.
-2, -1, 0
Let w(c) be the second derivative of -c**8/1176 + c**7/735 - 2*c**2 - 5*c. Let p(i) be the first derivative of w(i). Factor p(u).
-2*u**4*(u - 1)/7
Let s = -11/13 - -68/65. Factor s*c**3 + c**2 + 4/5 + 8/5*c.
(c + 1)*(c + 2)**2/5
Let s = 1 + 1. Factor -3*c**2 - c**3 + 8 - 4*c**s - c**3 + c**2.
-2*(c - 1)*(c + 2)**2
Let j = 402 - 400. Factor -2/3*l**4 - 2/3*l**3 + 0 + 2/3*l + 2/3*l**j.
-2*l*(l - 1)*(l + 1)**2/3
Suppose -2*a - 17 + 1 = 3*c, -5*a - 29 = 2*c. Let s = a + 7. Suppose 4*d + 3*d**s - 2*d - 4*d**2 = 0. Calculate d.
0, 2
Suppose -17*a = -14*a - 6. Factor 8/5 + 2/5*f**a + 8/5*f.
2*(f + 2)**2/5
Let c(d) = d**4 + d**3 + d - 1. Let l(h) = -h**4 - 7*h**3 + 6*h**2 - 2*h + 2. Let q(x) = 2*c(x) + l(x). What is b in q(b) = 0?
0, 2, 3
Let x = -14 - -47/3. Solve x*i + 1/3*i**3 - 2/3 - 4/3*i**2 = 0 for i.
1, 2
Factor 2/5*z + 2/25*z**2 + 8/25.
2*(z + 1)*(z + 4)/25
Let s(d) be the first derivative of -98*d**5/45 - 14*d**4/9 - 8*d**3/27 + 1. Suppose s(y) = 0. Calculate y.
-2/7, 0
Let o(x) = -x - 2. Let s be o(-6). Suppose 3*m + m - 39 = 3*n, 44 = 4*m - s*n. Factor 4*t - m*t + t**4 + 3*t**2 + t - 3*t**3.
t*(t - 1)**3
Factor -3/2*m - 1/4*m**2 - 9/4.
-(m + 3)**2/4
Let u(r) = 16*r**2 - 16*r. Let i(l) = 3*l**2 - 3*l. Let h(g) = -g**3 - 5*g**2 + 4. Let q be h(-5). Let j(t) = q*u(t) - 22*i(t). Let j(p) = 0. What is p?
0, 1
Let u(d) = d**3 + 17*d**2 + 26*d - 56. Let j be u(-15). What is w in 0*w + 0*w**2 - 1/3*w**j + 0 + 2/3*w**3 = 0?
0, 2
Let 2/3*z**5 + 8/3*z**2 - 2*z**3 - 8/9*z + 0 - 4/9*z**4 = 0. Calculate z.
-2, 0, 2/3, 1
Let l(b) be the first derivative of -b**6/8 + 3*b**5/10 - b**3/2 + 3*b**2/8 - 5. Determine a so that l(a) = 0.
-1, 0, 1
Let o be (-6)/9 - 200/(-12). Find w such that -4*w**5 + 8*w**3 + o*w**2 - 8*w**4 - 8 - 16*w + 22*w - 10*w = 0.
-2, -1, 1
Let o(q) be the third derivative of -q**6/160 - q**5/160 + 2*q**3/3 + 5*q**2. Let w(s) be the first derivative of o(s). Let w(i) = 0. Calculate i.
-1/3, 0
Let n(q) be the third derivative of q**5/20 - q**4/24 - 8*q**2. Find h such that n(h) = 0.
0, 1/3
Suppose 2*p = -0 - 2, -5*p - 5 = f. Let g = 989/7 + -141. Let f*h**2 - g*h**5 + 0*h + 4/7*h**4 - 2/7*h**3 + 0 = 0. What is h?
0, 1
Let n(m) = -2*m**2 + 19*m - 37. Let r be n(6). Let 0 + 1/6*v**2 + 2/3*v**r + 11/6*v**4 + 3/2*v**3 - 1/6*v = 0. What is v?
-1, 0, 1/4
Let h(a) = -a**2 - 23*a - 19. Let u be h(-22). Factor 0*r + 0*r**2 + 2*r**5 - 1/2*r**u + 3/2*r**4 + 0.
r**3*(r + 1)*(4*r - 1)/2
Let n(y) = -9*y**2 + 21*y - 9. Let g(d) = 9*d**2 - 21*d + 8. Let x(z) = -3*g(z) - 2*n(z). Factor x(u).
-3*(u - 2)*(3*u - 1)
Let w = -76 - -305/4. Factor 1/4 + w*y - 1/4*y**3 - 1/4*y**2.
-(y - 1)*(y + 1)**2/4
Let k(v) be the first derivative of 0*v**2 - 1/18*v**4 + 0*v**3 + 0*v - 2/45*v**5 + 4. What is h in k(h) = 0?
-1, 0
Let q(f) be the second derivative of f**6/480 - f**5/120 + f**4/96 + 3*f**2/2 + 3*f. Let r(t) be the first derivative of q(t). Suppose r(n) = 0. What is n?
0, 1
Solve 6*p + 0*p**2 + 3*p**2 - 18*p**3 + 15*p**3 = 0 for p.
-1, 0, 2
Suppose -w = 6*w - w. Let 0*z**4 + 0 + 1/5*z**3 - 1/5*z**5 + w*z + 0*z**2 = 0. What is z?
-1, 0, 1
Factor -2/5*o**4 + 1/5*o + 0 + 2/5*o**2 + 0*o**3 - 1/5*o**5.
-o*(o - 1)*(o + 1)**3/5
Let a = 907/5 + -182. Let u = 1/15 - a. Determine h, given that -2/3 + 0*h + u*h**2 = 0.
-1, 1
Let v(u) = 10*u**2 + 7*u - 12. Let m(k) = -3*k**2 - 2*k + 4. Let o(l) = -21*m(l) - 6*v(l). Factor o(x).
3*(x - 2)*(x + 2)
Let n be 45/27 - (-4)/(11 - -1). What is l in -3/2*l**n - l - l**3 - 1/4 - 1/4*l**4 = 0?
-1
Let l(j) = j**3 + 2*j**2 + j + 2. Let t be l(-2). Factor -2*y**3 - 8/3*y**2 + 4/3*y**4 + 8/3*y + 2/3*y**5 + t.
2*y*(y - 1)**2*(y + 2)**2/3
Suppose -6 + 8 = r. Factor 3*d**3 - r - 4 - 3*d**2 - 3*d + 6*d**2 + 3.
3*(d - 1)*(d + 1)**2
Suppose -2*l + 9 = 2*i - l, -4*l + 12 = 0. Let r(n) be the second derivative of n + 1/30*n**4 + 1/15*n**i + 0 + 0*n**2. Factor r(z).
2*z*(z + 1)/5
What is c in 2/5*c**3 + 2/5*c**2 - 2/5*c**4 + 0 - 2/5*c = 0?
-1, 0, 1
Let v(a) be the third derivative of -a**6/280 + 3*a**5/140 - a**4/28 + 15*a**2. Let v(t) = 0. Calculate t.
0, 1, 2
Solve -4*l**2 - 20*l + 6*l**2 + 0*l**2 - 50 - 4*l**2 = 0.
-5
Let i = -1 - -5. Factor l**3 - 4*l - 5*l - i*l**3 - 4*l**2 - 3 - 5*l**2.
-3*(l + 1)**3
Let z(a) = -a**2 + a + 20. Let h be z(-4). Let q(m) be the second derivative of 2*m - 2/5*m**5 + m**2 - 4/3*m**3 + m**4 + h + 1/15*m**6. Solve q(k) = 0.
1
Suppose -2 = -5*v - 5*m - 7, 0 = -5*m - 25. Let u = 4 + -2. Let 5*g**3 - 6*g**2 - g**3 + v - 3*g**3 + 3*g**u = 0. Calculate g.
-1, 2
Let u(o) be the second derivative of -o**7/105 - o**6/25 - o**5/