b - 3*b, 3*g = 5*b - 4. Factor -2/5*v - 2/5*v**b + 0.
-2*v*(v + 1)/5
Suppose -9 = -g - 6. Let z(b) be the first derivative of 0*b - 4/9*b**g - 1/3*b**2 + 1/9*b**6 + 0*b**4 + 4/15*b**5 - 1. Find j, given that z(j) = 0.
-1, 0, 1
Let r(i) be the third derivative of 0*i + 0 - 1/15*i**6 + 2*i**2 + 1/3*i**4 + 2/3*i**3 - 2/105*i**7 + 0*i**5. Factor r(d).
-4*(d - 1)*(d + 1)**3
Suppose 4*w - 2*w = 8. Factor 4*v - 14*v**3 - 4*v**4 - 2*v - 4*v**2 + 0*v**4 - w*v**4.
-2*v*(v + 1)**2*(4*v - 1)
Let h(x) = 8*x**3 + 5*x**2 + x - 8. Let b(w) = 23*w**3 + 15*w**2 + 3*w - 23. Let o(t) = -6*b(t) + 17*h(t). Determine v, given that o(v) = 0.
-2, -1, 1/2
Solve -2/23*j**2 + 22/23*j - 20/23 = 0 for j.
1, 10
Let l(t) be the second derivative of -3*t**7/70 - 7*t**6/50 - 13*t**5/100 + t**4/60 + t**3/15 - 3*t. Let l(p) = 0. What is p?
-1, -2/3, 0, 1/3
Let r(p) be the first derivative of -p**3/12 + p/4 + 3. Determine k so that r(k) = 0.
-1, 1
Solve 0 + 18/7*g**3 + 0*g - 54/7*g**4 + 54/7*g**5 - 2/7*g**2 = 0.
0, 1/3
Find l such that 14 - l - 10 - 2*l - l**2 = 0.
-4, 1
Find q, given that 15*q**2 - 14*q - q**3 + 4 - 5*q**3 - 10*q**2 + 11*q**2 = 0.
2/3, 1
Find n, given that n**5 + 23/5*n**4 + 12/5*n**2 - 8*n**3 + 0 + 0*n = 0.
-6, 0, 2/5, 1
Let a(b) be the second derivative of b**6/6 - 5*b**4/4 + 5*b**3/3 + 5*b. Factor a(u).
5*u*(u - 1)**2*(u + 2)
Let c(b) = -b + 4. Let z be c(2). Suppose 0 = -q + 2*q + 4*w - 9, 0 = -z*q - 2*w + 12. Factor -2/9*k**q + 0*k**4 + 0 + 0*k**2 + 4/9*k**3 - 2/9*k.
-2*k*(k - 1)**2*(k + 1)**2/9
Let w be 2/4 + 52/(-8). Let x be (-3)/w + 55/22. Factor -j**2 + j - 1/3 + 1/3*j**x.
(j - 1)**3/3
Let f(t) be the second derivative of t**4/78 - t**3/39 + 31*t. Factor f(g).
2*g*(g - 1)/13
Let h be (12/(-18))/(1/(-3)). Factor 0*d**3 + d**4 + 0*d**2 + d**3 + d**h - 3*d**3.
d**2*(d - 1)**2
Let y be (-1)/((2/4)/(-1)). Suppose 5*g - 3*p = 1 + 25, -3*p = -4*g + 22. Factor y*c**4 - c**2 - c**g + 0*c**2.
c**2*(c - 1)*(c + 1)
Factor 0*a + 0 + 4/11*a**3 - 2/11*a**2.
2*a**2*(2*a - 1)/11
Find h such that 0*h**3 - 11*h**3 - 5*h**2 + 5*h + h**3 = 0.
-1, 0, 1/2
Let w(l) = -l**3 - 6*l**2 + l + 8. Let y be w(-6). Factor 0 + 1/8*t**5 + 1/8*t**3 + 3/8*t**4 - 3/8*t**y - 1/4*t.
t*(t - 1)*(t + 1)**2*(t + 2)/8
Let u(y) = 2*y. Let r(w) = -w**2 - w. Let i(p) = -r(p) - u(p). Let x(t) = t**5 + t**4 - t**3 + 2*t**2 - 3*t. Let c(v) = -6*i(v) + 2*x(v). Factor c(g).
2*g**2*(g - 1)*(g + 1)**2
Let q = 10 - 6. Suppose 5*p + 9 = 4*s + q*p, -10 = 2*p. Factor 2*r**3 - r**4 + s + 2*r**4 - r**5 + r - 2*r**2 - 2*r.
-(r - 1)**3*(r + 1)**2
Let h(o) = -2*o**2 + 14*o - 56. Let i(f) = 4*f**2 - 27*f + 113. Let k(c) = 13*h(c) + 6*i(c). Suppose k(x) = 0. Calculate x.
5
Suppose t = 2*d - 4, -5*t + 7*t - d - 1 = 0. Let s be -2*2/(-4) + 2. Factor 5*l**s - 2*l**t + 0*l**3 - 4*l - 4*l**3 + l**3.
2*l*(l - 2)*(l + 1)
Let z be 81/36 - (-1)/(-4). Let p(i) be the second derivative of 1/42*i**7 + 0*i**z + 1/15*i**6 + 0*i**4 + 0*i**3 + 1/20*i**5 + 0 + 2*i. Factor p(y).
y**3*(y + 1)**2
Let y(d) = d**5 + d**3 + d + 1. Let r(i) = 5*i**5 + 4*i**4 + 5*i**3 + 3*i + 3. Let t(m) = r(m) - 3*y(m). Factor t(h).
2*h**3*(h + 1)**2
Let w = 0 - 5. Let n be 0 - w/(105/6). Suppose n*h**2 - 2/7*h + 0 = 0. What is h?
0, 1
Suppose f - 15 = -4*f. Suppose 3*s + f = 0, -4*s = 5*a - 15 + 4. Let g - 4*g**3 + 3*g**a + 0*g**3 = 0. What is g?
-1, 0, 1
Suppose 0 = -3*t - 4 + 13. Let m(l) be the first derivative of -1 + 1/2*l + 3/8*l**2 + 1/12*l**t. Factor m(v).
(v + 1)*(v + 2)/4
Find x, given that -16 + 8*x**4 + 11*x**3 + 84*x**2 + 4*x**3 + 9*x**3 + 40*x + 22*x**3 = 0.
-2, 1/4
Let d = 323 - 4197/13. Suppose -d*u**2 - 2/13 + 4/13*u = 0. What is u?
1
Let b(i) = 20*i**3 - 12*i**2 + 11*i. Let r(h) = 13*h**3 - 8*h**2 + 7*h. Let w(s) = 2*s - 4. Let z be w(6). Let d(n) = z*r(n) - 5*b(n). Factor d(q).
q*(2*q - 1)**2
Let c = -27 - -29. Let -3 + c*z**3 + 0*z**3 + z**3 + 9*z - 9*z**2 + 0*z**3 = 0. What is z?
1
Let k(a) be the first derivative of -2*a**3/21 + 4*a**2/7 - 8*a/7 - 10. Factor k(b).
-2*(b - 2)**2/7
Let t(a) be the first derivative of -2*a**3/15 - a**2/5 + 7. Factor t(g).
-2*g*(g + 1)/5
Let i(k) = 4*k**2 + 12*k - 12. Let o(j) be the first derivative of j + 1/3*j**3 - 1 + 0*j**2. Let a(q) = i(q) - 6*o(q). Factor a(s).
-2*(s - 3)**2
Let p be 1/(-2) + (-18)/12. Let h be (-1)/3*(p - 1). Solve -4*d**2 - 2*d + 0*d**2 + h + 5*d**2 = 0.
1
Let s be 24/15*(-5)/(-2). Let m be (-1 - 1)/(2/(-3)). Factor b**4 - b**m - s + 4.
b**3*(b - 1)
Let s be 4*(-4)/32*2/(-5). Let h(u) = -u**2 + 5*u + 3. Let a be h(5). Solve 1/5*o**2 + s*o**a + 0 - 2/5*o = 0.
-2, 0, 1
Let v(p) be the first derivative of 0*p + 1/2*p**2 + 9 + 1/3*p**3. Factor v(c).
c*(c + 1)
Let l(f) = 10*f**2 - 12*f - 7. Let q(w) = -6*w**2 + 6*w + 4. Let j(s) = 4*l(s) + 7*q(s). Solve j(r) = 0.
-3, 0
Suppose 2*z + 30 = -4*k, 5*z = 2*k - 0*z - 15. Let q = 7 + k. What is l in -7/3*l**q - 2/3*l + 7/3*l**4 + 2/3*l**3 + 0 = 0?
-1, -2/7, 0, 1
Find v, given that 56*v**4 - 14*v + 170*v**3 + 6*v + 17 - 25 + 114*v**2 = 0.
-2, -1, -2/7, 1/4
Let r = -29 + 34. Suppose -1/2*j**2 - 1/2*j**3 + 1/2*j**4 + 1/2*j**r + 0*j + 0 = 0. What is j?
-1, 0, 1
Find g, given that 6*g - g**2 - 2*g**2 - 5 - 2 + 4 = 0.
1
Let g(q) be the first derivative of -3*q**4 + 5*q**3 - 3*q**2/2 - 1. Find k, given that g(k) = 0.
0, 1/4, 1
Let m(a) = a**2 - a - 17. Let j be m(-4). Let b(c) be the first derivative of -1/3*c**6 + 4 + 4/3*c**j - 2*c + c**4 - 2/5*c**5 - c**2. Factor b(p).
-2*(p - 1)**2*(p + 1)**3
Factor -3*w + 3 + 3/4*w**2.
3*(w - 2)**2/4
Let u(j) be the first derivative of 3*j + 1/70*j**5 + 1/42*j**4 - 1/7*j**2 - 1 - 1/21*j**3. Let q(i) be the first derivative of u(i). Factor q(g).
2*(g - 1)*(g + 1)**2/7
What is l in 264*l - 4 - 270*l + 1 - 3*l**2 = 0?
-1
Let i be (2/(-4))/(2/(-4)). Let o be (i/(-1))/((-4)/8). Factor -1/3 + t + 1/3*t**3 - t**o.
(t - 1)**3/3
Let d(s) be the third derivative of -2*s**7/315 - s**6/72 - s**5/180 - 34*s**2. Factor d(h).
-h**2*(h + 1)*(4*h + 1)/3
Let q(u) = -u**3 + 3*u**2 - 2*u + 2. Let o be q(2). Let k = 167/468 - 7/52. Factor 0 - 4/9*r - k*r**o.
-2*r*(r + 2)/9
Suppose 5*q + 9 - 4 = p, 0 = 5*p + q + 1. Suppose p + 1/2*x**2 - 1/2*x = 0. What is x?
0, 1
Factor 16/9*n + 4/9*n**2 - 20/9.
4*(n - 1)*(n + 5)/9
Let v(g) be the second derivative of g**7/350 - g**6/75 + 7*g**5/300 - g**4/60 + g**2 + 2*g. Let i(n) be the first derivative of v(n). Factor i(r).
r*(r - 1)**2*(3*r - 2)/5
Let p(i) be the first derivative of i**3/9 + 5*i**2/6 + 4*i/3 + 9. Find c such that p(c) = 0.
-4, -1
Suppose 0 = 4*b + b - 15. Let y(p) be the second derivative of -2*p**2 + 1/3*p**4 - 1/10*p**5 + p + 0 + 1/3*p**b. Solve y(v) = 0.
-1, 1, 2
Let n(f) = -3*f**3 + 6*f**2 - f + 2. Let v(k) = 48*k**3 - 96*k**2 + 15*k - 33. Let j(p) = 33*n(p) + 2*v(p). Find w, given that j(w) = 0.
0, 1
Let d(q) be the third derivative of -q**5/75 - 11*q**2. Factor d(a).
-4*a**2/5
Let 3*z**2 + 11*z + 5*z**3 + 12*z**2 - z = 0. What is z?
-2, -1, 0
Let t(s) be the first derivative of -2 - 3/16*s**4 + 0*s - 1/8*s**2 - 9/20*s**5 + 5/12*s**3. What is i in t(i) = 0?
-1, 0, 1/3
Let k = -11 - -18. Factor 36*o + 18*o**3 - k - 3*o**4 - 39*o**2 - 10 + 5.
-3*(o - 2)**2*(o - 1)**2
Let i(b) be the first derivative of 1/4*b + 3/8*b**2 + 1/16*b**4 + 2 + 1/4*b**3. Let i(z) = 0. What is z?
-1
Let k(p) be the first derivative of p**7/1050 + p**6/200 + p**5/100 + p**4/120 + p**2/2 - 3. Let x(g) be the second derivative of k(g). Factor x(h).
h*(h + 1)**3/5
Let t = -2/25 - -61/450. Let j(g) be the second derivative of t*g**4 - 1/18*g**3 + 0 - 1/126*g**7 + 2*g + 1/30*g**5 - 1/6*g**2 - 1/90*g**6. Factor j(c).
-(c - 1)**2*(c + 1)**3/3
Let k(n) = n**2 - 5*n + 2. Let y be k(5). Factor -y*l**4 + l**3 + l**3 + 2*l**2 - l**3 - l**5 + 0*l**2.
-l**2*(l - 1)*(l + 1)*(l + 2)
Let s = 0 + 7. Let v = s - 7. Let 1/2 + v*h - 1/2*h**2 = 0. What is h?
-1, 1
Let f(c) = -5*c**2 + 3*c - 4. Let o(l) = -14*l**2 + 4*l - 12. Let g = 9 + -3. Let t(k) = k. Let p(b) = g*t(b) + o(b). Let u(y) = -8*f(y) + 3*p(y). Factor u(m).
-2*(m - 2)*(m - 1)
Let k(q) be the third derivative of -1/20*q**4 + 1/100*q**6 + 0*q + 0 + 1/525*q**7 + 1/150*q**5 - 2/15*q**3 - 3*q**2. Determine j so that k(j) = 0.
-2, -1, 1
Let n(g) = -15*g**2 + 9*g + 9. Let u(r) = -7*r**2 + 4*r + 4. Let y be (0 + -4 + 1)*3. Let t(p) = y*u(p) + 4*n(p). Solve t(f)