 Let w(r) = -r**4 + r**3 + r**2. Suppose -5*d + 10 = 0, 3*j + 6 = 5*d - 13. Let k(o) = j*m(o) - 12*w(o). Factor k(i).
3*i**2*(i - 1)*(i + 1)
Let m(t) be the second derivative of -t**6/20 + 9*t**5/40 - t**4/8 - 3*t**3/4 + 3*t**2/2 + 6*t. Solve m(z) = 0 for z.
-1, 1, 2
Let w = 200 + -1796/9. Let k(g) be the second derivative of -4/3*g**2 + w*g**3 - 2*g - 1/18*g**4 + 0. Find p such that k(p) = 0.
2
Let h(m) be the third derivative of m**6/6 + 3*m**5/4 - 25*m**4/12 - 5*m**3/2 + 28*m**2. Factor h(v).
5*(v - 1)*(v + 3)*(4*v + 1)
Suppose 2 = -37*o + 38*o. Factor -4/9*b - 2/9 - 2/9*b**o.
-2*(b + 1)**2/9
Find g, given that -12/5 - 2/5*g**2 + 2*g = 0.
2, 3
Determine j so that -34/9*j**2 + 0 + 10/9*j**3 + 4/3*j = 0.
0, 2/5, 3
Suppose -14*u + 5*u**2 + 4*u**5 + 5*u**2 - 2*u**4 - 6*u**3 + 10*u - 2*u**5 = 0. Calculate u.
-2, 0, 1
Find u such that -u**2 + 4 - 2*u - 3 - 2 = 0.
-1
Let x = -8/49 + 138/245. Factor -4/5 + x*w**2 - 2/5*w.
2*(w - 2)*(w + 1)/5
Let q be (36/40)/(3/(-248)). Let n = -74 - q. Find g, given that n*g + 2/5*g**2 + 0 = 0.
-1, 0
Let p(b) = b - 1. Let l(o) = -7*o**2 + 7*o. Let u = 4 - -1. Suppose 2*f = -5*s, u*f = 3*s - 18 - 13. Let z(w) = s*p(w) - l(w). Factor z(m).
(m - 1)*(7*m + 2)
Suppose -5*x = 2*h - 10, -2*x + 3 = -5*h - 1. Suppose 1/2*f**2 - x*f + 2 = 0. What is f?
2
Let k(z) = 3*z**2 - 4*z + 5. Let q(u) = 2*u**2 - 3*u + 4. Let a(d) = -3*k(d) + 4*q(d). Let a(l) = 0. Calculate l.
-1, 1
Let q(v) be the third derivative of 0 + 0*v + 0*v**3 - 1/120*v**6 - 1/210*v**7 + 0*v**4 + 1/30*v**5 + 4*v**2. Factor q(b).
-b**2*(b - 1)*(b + 2)
Let f(b) be the first derivative of -2/15*b**5 - 4/3*b**4 + 0*b**2 + 18*b - 6 - 4*b**3. Determine l so that f(l) = 0.
-3, 1
Let z(m) be the first derivative of -121*m**6/12 + 77*m**5/10 + 161*m**4/8 - 73*m**3/6 - 10*m**2 - 2*m + 9. What is w in z(w) = 0?
-1, -2/11, 1
Let -6/5*u**3 + 26/5*u**4 + 0 + 0*u - 8/5*u**5 + 0*u**2 = 0. What is u?
0, 1/4, 3
Let v = 18 - 7. Let u = v + -7. Find t such that 3*t**4 - 2*t**3 - 5*t**u - t**2 - t**4 + 2*t**4 = 0.
-1, 0
Let p = 2 - 0. Let a be (p/(-5))/((-1)/5). Suppose 1/3*q**a - 1/3*q**5 + 0*q + 0 - q**3 + q**4 = 0. Calculate q.
0, 1
Let k(t) be the first derivative of -3 - 6/5*t + 9/10*t**2 - 9/20*t**4 + 1/5*t**3 + 3/25*t**5. Factor k(g).
3*(g - 2)*(g - 1)**2*(g + 1)/5
Let w(h) be the second derivative of h**4/3 + 4*h**3/3 + h. Factor w(x).
4*x*(x + 2)
Suppose 13 = 3*p - 2*p. Let q = p + -13. Find u such that -2/5*u**2 - 4/5*u**3 + q*u + 6/5*u**4 + 0 = 0.
-1/3, 0, 1
Let z(w) be the first derivative of 1/110*w**5 + 1/33*w**3 + 3 + 1/33*w**4 + 0*w**2 - 2*w. Let m(l) be the first derivative of z(l). Factor m(j).
2*j*(j + 1)**2/11
Suppose -19 = -3*x - 2*n, n = 8*x - 9*x + 8. Find l such that -2/7*l**4 + 0*l - 2/7*l**2 + 4/7*l**x + 0 = 0.
0, 1
Let h(b) be the third derivative of -1/60*b**6 + 0 + 0*b**3 + 0*b + 1/15*b**5 + 2*b**2 - 1/12*b**4. Find z, given that h(z) = 0.
0, 1
Let q = -37/2 + 19. Determine h so that 1/2*h - 1/2*h**2 - q*h**3 + 0 + 1/2*h**4 = 0.
-1, 0, 1
Let i(d) = -3 - 9 - 2*d + 0. Let g be i(-8). Factor 2 - 4*c**3 - 2*c**g + c + 8*c - 5*c.
-2*(c - 1)*(c + 1)**3
Let g(c) = -c**2 - 4*c - 1. Let l be g(-3). Suppose -1 = 2*y + t, 3*y - t + 2 = -3*t. Factor 0*m + 1/4*m**l - 1/4*m**3 + y.
-m**2*(m - 1)/4
Let t be 268/(-18) + (-1)/9. Let k(c) = 2*c + 34. Let i be k(t). Factor 0 - 3/4*b**2 - 1/2*b**3 + 1/2*b + 3/4*b**i.
b*(b - 1)*(b + 1)*(3*b - 2)/4
Let o = -23 - -231/10. Let y(x) be the second derivative of 1/20*x**6 + 0*x**2 - 1/6*x**3 - x + o*x**5 - 1/24*x**4 + 0. Factor y(r).
r*(r + 1)**2*(3*r - 2)/2
Let u(a) be the first derivative of -a**4/4 + a**3/2 + 3*a**2 - 6*a + 9. Let v(l) be the first derivative of u(l). Determine c so that v(c) = 0.
-1, 2
Let x(c) be the second derivative of c**4/30 + 7*c**3/15 + 6*c**2/5 - 30*c. Suppose x(z) = 0. What is z?
-6, -1
Let z(r) = 3*r**2 + 8*r + 10. Let g = -10 - -16. Let c(q) = -3*q**2 - 8*q - 9. Let b(d) = g*c(d) + 5*z(d). Factor b(h).
-(h + 2)*(3*h + 2)
Let x(h) = -10*h - 8. Let q(r) = r**2 - 50*r - 40. Let u(b) = -4*q(b) + 22*x(b). Find w such that u(w) = 0.
-4, -1
Suppose 2*s = 6, 2*s + 26 = 2*a + 8. Suppose a = 4*t - 0. Factor 0 + 0 - 6*z**2 + 11*z**t - 21*z**3 + 4*z.
-2*z*(z + 1)*(5*z - 2)
Find r such that 9*r**4 + 2*r + r - 5*r**4 - 7*r**2 - r - 5*r**3 = 0.
-1, 0, 1/4, 2
Let f(d) be the second derivative of d**6/10 + d**5/5 - d**4/12 - d**3/3 - 6*d. Factor f(k).
k*(k + 1)**2*(3*k - 2)
Let k be (4/6)/(25 - 23). Let r(c) be the first derivative of 1/6*c**2 + 2 + 1/5*c**5 - k*c**3 - 1/12*c**4 + 0*c. Factor r(u).
u*(u - 1)*(u + 1)*(3*u - 1)/3
Let -3 - 2*g**2 - 71*g - 1 + 65*g = 0. What is g?
-2, -1
Let u(b) be the third derivative of 0*b + 1/84*b**4 + 3*b**2 + 0 - 1/84*b**6 - 1/245*b**7 - 1/210*b**5 + 0*b**3. Factor u(a).
-2*a*(a + 1)**2*(3*a - 1)/7
Let a(b) = -b**3 - b**2 - 2*b + 2. Let y(d) = -6*d**3 - 6*d**2 - 11*d + 11. Let k(v) = -11*a(v) + 2*y(v). Factor k(s).
-s**2*(s + 1)
Factor -3/4*w**3 - 1/4*w**2 + 1/2 + 3/4*w - 1/4*w**4.
-(w - 1)*(w + 1)**2*(w + 2)/4
Let g = 5 + -6. Let x = g + 4. Factor 0*n**3 + n**3 - 4*n**3 + x*n**4.
3*n**3*(n - 1)
Let k(l) = -l**2 + 5*l + 9. Let b be k(5). Let i = b + -7. Let 2/9*n - 2/9*n**i + 2/9 - 2/9*n**3 = 0. What is n?
-1, 1
Let c(t) be the third derivative of t**8/336 + t**7/30 + 73*t**6/480 + 43*t**5/120 + 11*t**4/24 + t**3/3 + 18*t**2. Factor c(s).
(s + 2)**3*(2*s + 1)**2/4
Let z = -54 - -57. Let 0*j**4 + 0*j**2 + 0*j + 2/9*j**5 + 0 - 2/9*j**z = 0. Calculate j.
-1, 0, 1
Let y(p) be the third derivative of p**5/40 - p**4/16 - p**3/2 + 11*p**2. Find m such that y(m) = 0.
-1, 2
Let j(o) be the second derivative of -o**4/42 + o**3/21 + 2*o**2/7 + 13*o. Find p, given that j(p) = 0.
-1, 2
Solve 4*h**2 - 4*h**2 + 3*h + 3*h**3 + 2*h**2 + 4*h**2 = 0.
-1, 0
Let q(x) = -x**2 - x + 2. Let m be q(0). Solve -t**2 + 21 - 3*t**4 - m*t**3 - t**3 - t**5 - 21 = 0.
-1, 0
Let q(l) be the second derivative of -l**4/54 + l**3/9 + 19*l. Suppose q(b) = 0. Calculate b.
0, 3
Let d = -781/3 + 261. Factor 2/3*j + 4/3 - d*j**2.
-2*(j - 2)*(j + 1)/3
Let t(b) = 18*b**2 + 2*b - 10*b + 7 - 17*b**2. Let z be t(7). Factor z + 4/5*n**5 + 14/5*n**4 + 2/5*n + 18/5*n**3 + 2*n**2.
2*n*(n + 1)**3*(2*n + 1)/5
Find a such that 3 - 9/2*a + 3/2*a**2 = 0.
1, 2
Determine u so that 0*u - 1/3*u**2 + 0 = 0.
0
Suppose -13*m**2 + 5*m - m + 7*m**2 + 20*m**2 = 0. Calculate m.
-2/7, 0
Let o(g) = g**3 + 5*g**2 - 6*g + 5. Let y be o(-6). Determine v so that -15*v - 103*v**2 - 31*v - 8 - 10*v + y*v**2 = 0.
-2/7
Let w(t) be the second derivative of -3*t + 0 - 1/105*t**6 + 0*t**2 - 3/35*t**5 - 8/21*t**3 - 2/7*t**4. Suppose w(q) = 0. What is q?
-2, 0
Suppose 0 = -3*f + 7 - 1. Suppose s - 2*c - f = 2*s, 0 = -2*s + 5*c + 23. Factor 0 + 9/2*y**3 - 7/2*y**s + 1/2*y + y**5 - 5/2*y**2.
y*(y - 1)**3*(2*y - 1)/2
Determine f, given that -3*f - 6*f**3 + 7*f + 0*f**2 + 4*f**3 - 2*f**2 = 0.
-2, 0, 1
Let h(w) be the third derivative of 5*w**8/336 - 11*w**7/105 + 23*w**6/120 + 7*w**5/30 - 7*w**4/6 + 4*w**3/3 + 4*w**2. Determine l so that h(l) = 0.
-1, 2/5, 1, 2
Let v(f) be the first derivative of 7*f**6/3 + 4*f**5/5 - 7*f**4 - 8*f**3/3 + 7*f**2 + 4*f + 10. Solve v(t) = 0 for t.
-1, -2/7, 1
Let j(p) be the first derivative of -2*p**3/21 + 5*p**2/7 + 12*p/7 - 19. Find d, given that j(d) = 0.
-1, 6
Let k(v) = -2*v - 2 + v + 5 - 2. Let t be k(-2). Solve 2*u**4 - u**5 + 2*u - 4*u**3 - 2 + t*u**5 - 4*u**2 + 4 = 0.
-1, 1
Let k(z) be the first derivative of z**4/24 + 10*z**3/3 + 100*z**2 + 4000*z/3 - 24. Find w, given that k(w) = 0.
-20
Let v(u) be the third derivative of -u**5/240 - u**4/16 - 5*u**3/24 + 22*u**2. Factor v(y).
-(y + 1)*(y + 5)/4
Let y(p) be the third derivative of p**6/40 - 3*p**5/10 + 9*p**4/8 - 68*p**2. Find f, given that y(f) = 0.
0, 3
Let d(r) = r**3 - 41*r**2 + 113*r + 40. Let h be d(38). Factor 0 - 2/7*k**3 - 2/7*k - 4/7*k**h.
-2*k*(k + 1)**2/7
Factor -5 + 2*d**4 + 3*d**4 + 6*d + 7*d - 10*d**3 - 3*d.
5*(d - 1)**3*(d + 1)
Let d = 997/30 - 166/5. Let v(r) be the second derivative of d*r**6 + 0*r**2 - 1/20*r**5 + 1/6*r**3 - 1/12*r**4 + 0 - r. Factor v(y).
y*(y - 1)**2*(y + 1)
Let t(y) be the second derivative of -y**7/140 + y**6/80 + y**5/40 - y**4/16 + 3*y**2/2 - 3*y. Let a(o) be the first derivative of t(o). Factor a(l).
-3*l*(l - 1)**2*(l + 1