Let s be k(-3). Let v(r) = 4*r**2 + 2*r. Let g(m) = s*d(m) + 8*v(m). Determine y, given that g(y) = 0.
-2, 0
Factor 2 - 2/3*g**2 - 4/3*g.
-2*(g - 1)*(g + 3)/3
Let j(l) be the third derivative of 3*l**8/448 + l**7/70 - l**6/96 - l**5/20 - l**4/24 + 8*l**2. Suppose j(i) = 0. Calculate i.
-1, -2/3, 0, 1
Let m(x) = x**2 + 2*x + 7. Suppose 3*k = -i + 23, 3*k - 3 = -2*i + 5*i. Suppose -2*l + 20 = -k*l. Let s(z) = -z - 1. Let w(c) = l*s(c) - m(c). Factor w(t).
-(t - 2)*(t - 1)
Find r such that -13*r**2 + 25*r**4 - 13*r**5 + 21*r**2 - 10*r - 45*r**3 + 8*r**5 + 27*r**2 = 0.
0, 1, 2
Let a(f) = 3*f**3 - 9*f**2 + 3*f + 9. Let v(n) be the first derivative of n**4/2 - 8*n**3/3 + 3*n**2/2 + 8*n - 3. Let p(u) = -5*a(u) + 6*v(u). Factor p(r).
-3*(r - 1)*(r + 1)**2
Let o = 16 - 10. Let a(k) = -k**2 + 7*k - 6. Let b be a(o). Let b + 0*y + 1/4*y**4 + 1/2*y**2 - 3/4*y**3 = 0. What is y?
0, 1, 2
Let a(c) be the third derivative of c**8/504 + 2*c**7/315 - c**6/90 - 4*c**5/45 - 7*c**4/36 - 2*c**3/9 - 9*c**2. Let a(z) = 0. What is z?
-1, 2
What is g in 3/4*g + 9/4*g**3 + 0 + 3/4*g**4 + 9/4*g**2 = 0?
-1, 0
Let s be 12/9 - 4/(-6). Suppose 42 = s*o + 4*c, 3*o - 19 = -5*c + 39. Let o*k**2 + 4*k**2 + 33*k + 0 + 6 + 12*k**2 = 0. Calculate k.
-1, -2/9
Let w(q) = q**2 - 2*q - 5. Let j be w(4). Suppose 4*u = z + 5, -j*u + 2 = -2*u. Let -g**3 - g**2 + g**z + g**4 = 0. Calculate g.
-1, 0, 1
Let v = 2 + 0. Let m(q) be the first derivative of v*q - 3*q**2 + 3 + 4/3*q**3. Suppose m(c) = 0. Calculate c.
1/2, 1
Factor -26*q + 7 + 8*q**3 - 4*q**3 + 4*q**2 - 2*q**3 + 13.
2*(q - 2)*(q - 1)*(q + 5)
Suppose -z + 5 = 3*x, -x + 6*x + 5*z = 25. Find b, given that -2/3*b**3 + 0 - 2/3*b**2 + x*b = 0.
-1, 0
Suppose s - 3 - 3 = -h, 2*s + 3*h = 15. Factor -1/4*p - 1/4*p**s + 0 - 1/2*p**2.
-p*(p + 1)**2/4
Let o = 20 - 18. Factor 0 + 1/5*i + 4/5*i**o.
i*(4*i + 1)/5
Factor -1 + 3/2*x + 0*x**2 - 1/2*x**3.
-(x - 1)**2*(x + 2)/2
Let l = 2 - 0. Let u(z) = z**2 + 2*z + 2. Let v be u(-2). Factor 2*q**2 - v*q - q + l - q.
2*(q - 1)**2
Let z(p) be the second derivative of -p**7/210 + p**6/60 - p**4/12 + p**3/6 + 3*p**2/2 + 3*p. Let f(o) be the first derivative of z(o). Factor f(t).
-(t - 1)**3*(t + 1)
Suppose 2*a - 10 = -0. Factor 2 + 7*w**3 - 4*w - a*w**4 - 3*w - w**2 + 4*w**2.
-(w - 1)**2*(w + 1)*(5*w - 2)
Let o = 13/2 - 6. Let a(w) = -2*w**2 - 4*w + 9. Let m be a(-3). What is r in 0 + r**2 - 1/2*r - o*r**m = 0?
0, 1
Suppose 2*w - 3*w - 8 = -5*b, 0 = 4*b - 4*w. Factor 1/3*g**b + 0*g + 0.
g**2/3
Let i(v) be the second derivative of 0 + 0*v**2 + 1/6*v**3 + 1/6*v**4 + 1/20*v**5 - 4*v. Factor i(r).
r*(r + 1)**2
Let k = -9/2 + 103/22. Let y be (-8)/44*(-1 - 0). Suppose 0 + k*j**2 + y*j = 0. What is j?
-1, 0
Solve 10*i**4 + 80/3*i**2 + 10/3 + 5/3*i**5 + 70/3*i**3 + 15*i = 0 for i.
-2, -1
Factor -2/5*p - 1/5 - 1/5*p**2.
-(p + 1)**2/5
Factor -4/7*c**2 + 0*c + 0.
-4*c**2/7
Let w be 2/(6/(-3)) + 5. Suppose -4*u + 5 = 5*g + 1, -w*u = -5*g - 4. Factor 2/3*o**2 - 10/3*o**4 + g*o - 2*o**5 + 0 - 2/3*o**3.
-2*o**2*(o + 1)**2*(3*o - 1)/3
Suppose 3*f + 5*j + 14 = -0*f, -2*j = 8. Factor a**4 - 8*a**3 - 2 - 3*a**4 + 2*a**4 - f*a**4 - 12*a**2 - 8*a.
-2*(a + 1)**4
Let h(p) = -5*p + 25. Let r be h(5). What is d in 1/2*d + 0*d**3 - 1/2*d**5 - d**4 + d**2 + r = 0?
-1, 0, 1
Let r be ((-144)/1710)/((-2)/(-5)). Let b = 65/38 + r. Factor -3/2*q**2 - 3/2*q**3 + 0*q + 3/2*q**4 + b*q**5 + 0.
3*q**2*(q - 1)*(q + 1)**2/2
Let a(v) be the second derivative of -3*v**7/70 - 7*v**6/40 - v**5/4 - v**4/8 + 3*v**2/2 + 4*v. Let b(n) be the first derivative of a(n). Solve b(l) = 0.
-1, -1/3, 0
Suppose v - 28 = -5*t, -v = -t - 4*t + 22. Let i(l) be the second derivative of 1/8*l**2 - 2*l + 0 + 1/48*l**4 - 1/12*l**v. Factor i(w).
(w - 1)**2/4
Suppose -3*q = -y - 8, 5*y = 3*y - 4. Let -8*u**2 + 2 + 16*u - 7 - 3 + q*u**2 = 0. What is u?
2/3, 2
Factor -4/3*q**5 + q**3 + 4/3*q**4 - 2/3*q**2 - 1/3*q + 0.
-q*(q - 1)**2*(2*q + 1)**2/3
Let m be (-4)/(-48)*2 - -8. Let w = -8 + m. What is q in -1/6*q**5 - 1/3*q**2 + 1/3*q**4 + 0 + 0*q**3 + w*q = 0?
-1, 0, 1
Let z(g) be the third derivative of 2/45*g**6 + 1/36*g**4 + 4/315*g**7 + 0*g**3 + 1/18*g**5 + 0*g + 3*g**2 + 0. Find s such that z(s) = 0.
-1, -1/2, 0
Let u(h) = -3*h**2 - 11*h + 4. Let t(z) = -2*z**2 - 6*z + 2. Let i = 6 - 11. Let m(y) = i*t(y) + 3*u(y). Factor m(b).
(b - 2)*(b - 1)
Let q(l) be the third derivative of 1/20*l**5 - 1/8*l**4 + 0*l + 0 + 1/40*l**6 + 5*l**2 + 0*l**3 - 1/70*l**7. Factor q(u).
-3*u*(u - 1)**2*(u + 1)
Let w = 577/6 + -96. Find a such that w*a**3 - 1/6*a + 0 + 0*a**2 = 0.
-1, 0, 1
Let a(x) be the second derivative of x**4/48 - x**3/3 + 2*x**2 + 9*x. Factor a(z).
(z - 4)**2/4
Let g(h) be the first derivative of h**3/3 - h**2 + h - 1. Let g(v) = 0. Calculate v.
1
Let s(a) be the first derivative of -2*a**3/3 + 3*a**2 - 4*a + 6. Factor s(w).
-2*(w - 2)*(w - 1)
Let j(a) be the first derivative of 49*a**5/10 - 147*a**4/8 - 100*a**3/3 + 3*a**2 + 8*a + 7. Determine k, given that j(k) = 0.
-1, -2/7, 2/7, 4
Suppose -f + 10 - 56 = 0. Let y = -87/2 - f. Find w, given that 1/2*w + 1/2 + 3/2*w**3 - y*w**2 = 0.
-1/3, 1
Let u(w) be the first derivative of 2 + 0*w**4 + 0*w**5 + 0*w + 1/60*w**6 + 0*w**3 + 1/105*w**7 - w**2. Let l(o) be the second derivative of u(o). Factor l(g).
2*g**3*(g + 1)
Let a(j) = 3*j**3 - j**4 - j**4 - j**2 - 4*j + j. Let r(u) = 49*u**4 + 18*u - 40*u**4 + 4*u**2 - 13*u**3 - 5*u. Let w(i) = -26*a(i) - 6*r(i). Factor w(z).
-2*z**2*(z - 1)*(z + 1)
Let t(d) be the first derivative of 5*d**3/9 - 10*d**2/3 + 3. Find h, given that t(h) = 0.
0, 4
Let i be (-16)/20 + (-16)/(-20). Solve 3/4*c**3 - 3/4*c + i*c**2 + 0 = 0.
-1, 0, 1
Let g(w) = -w**3 - 3*w**2 + w - 2. Let h be g(-4). Let r = 20 - h. Factor 5*u**5 - 13*u**4 + 20*u**3 + 3*u**4 - 2 - 20*u**2 - 3*u**5 + r*u.
2*(u - 1)**5
Factor 32/9*t**2 + 4/9*t**4 + 40/9*t - 4 - 40/9*t**3.
4*(t - 9)*(t - 1)**2*(t + 1)/9
Let u(g) be the first derivative of g**6/3 - 2*g**4 - 4*g**3/3 + 3*g**2 + 4*g + 7. Suppose u(v) = 0. Calculate v.
-1, 1, 2
Let r(b) = -7*b**4 - b**3 + 3*b**2 - 7*b - 4. Let z(c) = 27*c**4 + 3*c**3 - 12*c**2 + 27*c + 15. Let j(u) = 15*r(u) + 4*z(u). Suppose j(g) = 0. Calculate g.
-1, 0, 1
Let j = 71/12 - 17/3. Find z, given that 1/4 + j*z**2 - 1/2*z = 0.
1
Suppose -7 - 2 = -2*x + 3*u, 4*x + 4*u = 8. Factor -9*h + 9*h**2 + 6 + 3 - 6 - x*h**3.
-3*(h - 1)**3
Let h(g) = 4*g**2 + 6. Let m(a) = a**2 + 1. Let i(x) = h(x) - 6*m(x). Factor i(n).
-2*n**2
Let g(l) = l**2 - 2*l - 3. Let i be g(5). Suppose 0 = -s + 4*h - 16, -2*s - i = -0*s - 4*h. Determine b, given that -1/3*b**2 + 0*b**3 + 0*b + 0 + 1/3*b**s = 0.
-1, 0, 1
Let h be (-6)/(-8) + 44/(-176). Let -2 - 4*x + 1/2*x**5 + 7/2*x**3 - h*x**2 + 5/2*x**4 = 0. Calculate x.
-2, -1, 1
Let l(i) = i**2 - 4*i - 2. Let g be l(5). Suppose g*t = 7*t - 8. Factor -n**2 - 2*n + 4*n**t - n**2.
2*n*(n - 1)
Let g(f) = -20*f**3 - 29*f**2 + 11*f - 11. Let v(z) = 7*z**3 + 10*z**2 - 4*z + 4. Let y(h) = 4*g(h) + 11*v(h). Solve y(m) = 0 for m.
-2, 0
Let y be 28/(-30) + 22*(-2)/(-33). Factor -2/5*p**5 + 4/5*p - y*p**4 + 6/5*p**3 + 2*p**2 + 0.
-2*p*(p - 2)*(p + 1)**3/5
Let w(q) be the third derivative of 5*q**8/336 - 2*q**7/21 + q**6/8 + q**5/3 - 5*q**4/6 + 2*q**2. Find h, given that w(h) = 0.
-1, 0, 1, 2
Let n(w) = -w**3 + 14*w**2 - 13*w + 4. Let d(s) = 8*s - 3. Let b be d(2). Let u be n(b). Suppose 1/3*x + 1/3*x**2 - 1/3*x**u - 1/3*x**3 + 0 = 0. What is x?
-1, 0, 1
Solve 255*j**3 - 80*j**2 + 24 + 16*j**5 - 70*j**2 + 23*j**5 - 144*j**4 - 12*j**5 - 12*j = 0 for j.
-1/3, 2/3, 1, 2
Let p(c) be the second derivative of c**7/840 + c**6/120 + c**5/40 + 5*c**4/12 + c. Let y(q) be the third derivative of p(q). Solve y(t) = 0.
-1
Determine l, given that -4*l**2 - 15*l**3 - 1 - 2*l + 1 + 13*l**3 = 0.
-1, 0
Factor -1944/7*t - 2/7*t**3 + 108/7*t**2 + 11664/7.
-2*(t - 18)**3/7
Let f(h) be the first derivative of -4*h**3/3 - 5*h**2 + 6*h - 9. Factor f(x).
-2*(x + 3)*(2*x - 1)
Let c(a) be the first derivative of 14*a**5/45 + 8*a**4/9 - 2*a**3/9 - 16*a**2/9 - 8*a/9 - 5. Let c(x) = 0. What is x?
-2, -1, -2/7, 1
Let v(s) = s**2 - s + 1. Let g be v(2). Let 6*b**2 - 2*b**3 - 4*b - 6*b**g + 6*b**3 = 0. Calculate b.
0, 1, 2
Let c(f) = 4*f - 3 + 2*f**2 + 7*f - 3*f**2 - 3. Let z be c(7). Factor -z*q + q**5 - q**3 + 22*q.
q*