erivative of b(r). Let f(g) = 0. Calculate g.
1, 3
Let l(w) be the second derivative of w**7/420 - w**5/60 + w**3/12 - w**2/2 - 2*w. Let i(g) be the first derivative of l(g). Suppose i(c) = 0. Calculate c.
-1, 1
Let q(p) = -21*p**3 + 45*p**2 - 36*p + 3. Let g(k) = -42*k**3 + 89*k**2 - 73*k + 5. Let t(u) = -3*g(u) + 7*q(u). Factor t(j).
-3*(j - 1)**2*(7*j - 2)
Suppose 2*p - 3*y = -2*p + 4, -p - 5*y = -24. Factor -10 + 15*v**2 + p*v**3 - 21*v + 4 + 8*v**3.
3*(v - 1)*(v + 2)*(4*v + 1)
Let k(c) be the third derivative of c**6/120 + c**5/12 - c**4/4 + c**3/2 - 2*c**2. Let a be k(-6). Factor 3*w**4 - w**2 - 4*w - a*w**2 - 5*w**3 + 4*w + 4*w.
w*(w - 2)*(w + 1)*(3*w - 2)
Let k(q) be the third derivative of q**5/60 + q**4/12 + q**3/6 - 10*q**2. Factor k(a).
(a + 1)**2
Let d = 132 - 123. Factor -1/3*m**3 - d - 9*m - 3*m**2.
-(m + 3)**3/3
Let y(w) be the first derivative of -8 + 3/10*w**5 + 0*w**2 + 0*w**3 + 0*w + 3/4*w**4. Factor y(x).
3*x**3*(x + 2)/2
Let m = -18 + 22. Let u**2 + 3 - 4*u**3 - 7 + m = 0. Calculate u.
0, 1/4
Let a(i) be the second derivative of i**5/60 - i**4/6 + 2*i**3/3 + 2*i**2 + 8*i. Let z(s) be the first derivative of a(s). Factor z(m).
(m - 2)**2
Let u(v) be the first derivative of 3*v**4/2 + 5*v**3 + 3*v**2/2 - 6*v + 10. What is l in u(l) = 0?
-2, -1, 1/2
Let y be (-78)/(-12)*3*2. Let r = -77/2 + y. Factor -2*w + 2 + r*w**2.
(w - 2)**2/2
Let f(y) = y**3 - 9*y**2 + 6*y - 4. Let i be f(8). Let l be 8 - 11 - i/6. Suppose -n**2 - l*n**3 - n - 1/3 = 0. What is n?
-1
Suppose -24*y - 10*y = 0. Factor -1/7*x**3 + 0*x + 0*x**2 + y - 2/7*x**4 - 1/7*x**5.
-x**3*(x + 1)**2/7
Let c(l) = -3*l**2 + 3*l. Let o(z) = 1. Let f(r) = -c(r) - 6*o(r). Factor f(p).
3*(p - 2)*(p + 1)
Let u be (12/8 + 0)/((-3)/(-6)). Factor 3/4*d**4 + 0 - 1/4*d**5 - 1/2*d**u + 0*d + 0*d**2.
-d**3*(d - 2)*(d - 1)/4
Let l(d) be the first derivative of 2*d**5/65 + d**4/26 - 2*d**3/13 - d**2/13 + 4*d/13 - 22. Solve l(p) = 0.
-2, -1, 1
Determine v so that 1/8*v**2 - 5/4 + 3/8*v = 0.
-5, 2
Let q(f) be the second derivative of f**7/840 - f**6/240 + f**4/48 - f**3/24 - 5*f**2/2 + 4*f. Let t(m) be the first derivative of q(m). Solve t(o) = 0 for o.
-1, 1
Suppose 82*f - 75*f - 21 = 0. Let q = 12555/11 - 1139. Find m, given that 10/11*m**4 + q*m**f - 2/11*m + 18/11*m**2 - 4/11 = 0.
-1, 2/5
Factor -1/2 + 1/4*l**3 - 1/4*l + 1/2*l**2.
(l - 1)*(l + 1)*(l + 2)/4
Suppose z - 1240 = -1234. Factor -z*i - 3/2*i**4 - 6*i**3 - 9*i**2 - 3/2.
-3*(i + 1)**4/2
Let l = -81/20 - 1291/180. Let g = -11 - l. Factor -8/9*f + g*f**2 + 2/3.
2*(f - 3)*(f - 1)/9
Let t = 28 - 22. Let b be t/(-8) + 3/4. Factor 5/3*l**2 + 4/3*l**4 + b + 1/3*l + 8/3*l**3.
l*(l + 1)*(2*l + 1)**2/3
Factor 4*c**3 - 9*c**3 - 4*c**2 + c**2 + 2*c.
-c*(c + 1)*(5*c - 2)
Let n(s) = -7*s**4 - 60*s**3 - 83*s**2 - 38*s. Let t(b) = -2*b**4 - 20*b**3 - 28*b**2 - 13*b. Let w(i) = 3*n(i) - 8*t(i). Factor w(h).
-5*h*(h + 1)**2*(h + 2)
Factor 12 - 8*t - 7*t**2 + 16*t + 3*t**2.
-4*(t - 3)*(t + 1)
Let u be 36/54*12/2. Suppose 4*n - 3*c = 3*n + 6, -4*n - 8 = u*c. Solve 0*o**2 + 0 + n*o - 1/3*o**3 = 0 for o.
0
Let s = 3761282/45 + -83588. Let q = s - -50/9. Factor 12/5*o**3 - q*o**4 + 2/5*o - 8/5*o**2 + 0 + 2/5*o**5.
2*o*(o - 1)**4/5
Let o(l) be the second derivative of l**5/20 + l**4/12 - l**3/6 - l**2/2 - 7*l. Let o(g) = 0. Calculate g.
-1, 1
Let x be 6/10 - 54/90. Let f(o) be the second derivative of 3*o + 0 - 1/6*o**4 - 1/3*o**3 + x*o**2. Determine j so that f(j) = 0.
-1, 0
Suppose -5*m + 0 = -10. Determine v, given that 4*v - v**4 + 0*v**2 - 6*v + 2*v**3 + v**m = 0.
-1, 0, 1, 2
Suppose -5*z + 7 = -l - 2*z, -3*l + z = -3. Factor -4*j**3 + 26*j + 4*j**3 - 2*j**5 + 4*j**4 - 4*j**l - 24*j.
-2*j*(j - 1)**3*(j + 1)
Let n(s) = 7*s - 112. Let g be n(16). Factor -b + 4/3*b**2 - 1/3*b**3 + g.
-b*(b - 3)*(b - 1)/3
Let p(a) be the first derivative of -a**7/1260 + a**6/540 + a**5/180 - a**4/36 - 7*a**3/3 - 6. Let j(v) be the third derivative of p(v). Factor j(d).
-2*(d - 1)**2*(d + 1)/3
Suppose -x = 2*o + 1, -2*o + 2 = -2*x + 12. Let t be o + 4 + 2/1. Factor -2*s**2 - t - 5 + 0 + 1 + 8*s.
-2*(s - 2)**2
Let j(k) be the third derivative of k**4/24 - 2*k**3/3 - 2*k**2. Let d be j(6). Factor -2/5*p**d + 2/5 + 0*p.
-2*(p - 1)*(p + 1)/5
Let b = 587/12936 - 2/539. Let i(f) be the second derivative of -4*f - b*f**4 + 0 + 1/6*f**3 + 0*f**2. Let i(y) = 0. Calculate y.
0, 2
Suppose 0*k = -5*k + 20. Let d(i) = 153*i**2 + 9*i. Let l(u) = -19*u**2 - u. Let w(f) = k*d(f) + 33*l(f). Factor w(y).
-3*y*(5*y - 1)
Let d(t) be the third derivative of t**5/120 - t**4/24 + t**3/12 - 2*t**2. Determine u, given that d(u) = 0.
1
Let p be 2*2/2 + 0 + 3. Let y(q) be the third derivative of 0*q**3 - 3*q**2 + 0 + 1/150*q**p - 1/30*q**4 + 0*q. Determine w, given that y(w) = 0.
0, 2
Solve -4*y**3 + 7*y**3 + 0*y**4 + 3*y**4 + 3*y**3 = 0 for y.
-2, 0
Let r be 0 - (-4 - 2/1). Let w(k) = k**4 + 3*k**3 - k**2 - 5*k - 4. Let h(g) = -6*g**4 - 18*g**3 + 7*g**2 + 31*g + 25. Let s(v) = r*h(v) + 39*w(v). Factor s(o).
3*(o - 1)*(o + 1)**2*(o + 2)
Suppose 2*n - 1 = -j - 0*j, 3*n + 6 = -3*j. Suppose n*w**2 + 6*w + 4 + 0*w**2 - w**2 = 0. Calculate w.
-2, -1
Let t(w) be the third derivative of -w**5/30 - w**4/3 - w**3 + 11*w**2. Factor t(o).
-2*(o + 1)*(o + 3)
Suppose 401 - 416 = -5*o. Solve -o*j**3 - 16/3*j**2 - 5/3*j + 2/3 = 0 for j.
-1, 2/9
Let h(z) be the third derivative of -z**5/420 + z**4/84 - z**3/42 + 24*z**2. Factor h(a).
-(a - 1)**2/7
Let v(s) = s**5 + s**4 + 5*s**3 - 5*s**2 - 4*s + 2. Let t(x) = -x**5 + 1. Let f(q) = -6*t(q) - 3*v(q). Solve f(o) = 0 for o.
-2, -1, 1, 2
Let a(x) be the first derivative of x**6/40 - 3*x**5/20 + x**4/4 - x**2 + 4. Let t(r) be the second derivative of a(r). Find m, given that t(m) = 0.
0, 1, 2
Determine l so that 1/5*l + 1/5*l**3 + 2/5*l**2 + 0 = 0.
-1, 0
Let j(a) = a**2 - 4*a - 5. Let h be j(6). Suppose -3*t = 1 - h. Factor 3*s**2 + s**4 + s**3 - t*s**2 + s**3.
s**2*(s + 1)**2
Factor -2/3*i**2 + 2/3 + 0*i.
-2*(i - 1)*(i + 1)/3
Find a, given that 4 + 0*a**2 - 8*a**4 - 8*a**5 + 24*a**3 - 14*a - 2*a**3 - 7*a**2 + 11*a**2 = 0.
-2, -1, 1/2, 1
Let s be (-160)/(-42) - 4/(-14). Let z = -24/7 + s. What is j in -2/3*j + 0 + 2/3*j**3 + 2/3*j**2 - z*j**4 = 0?
-1, 0, 1
Let j(q) = -q. Let y(g) = 4*g**2 - 28*g. Let k(v) = 4*j(v) - y(v). Find o such that k(o) = 0.
0, 6
Let u(q) be the first derivative of 1/12*q**4 - 1/40*q**5 + 0*q - 1 + q**2 - 1/12*q**3. Let v(d) be the second derivative of u(d). Factor v(z).
-(z - 1)*(3*z - 1)/2
Let l(o) be the second derivative of 0 + 5/9*o**3 + 2/3*o**2 + 2/9*o**4 - o + 1/30*o**5. Factor l(g).
2*(g + 1)**2*(g + 2)/3
Let t = 3 + 4. Let y(m) be the second derivative of 1/30*m**5 - 1/18*m**4 + 1/45*m**6 + 0*m**3 - 1/63*m**t + 0*m**2 + m + 0. Suppose y(h) = 0. What is h?
-1, 0, 1
Let k(a) be the third derivative of a**8/6720 + a**4/24 - 8*a**2. Let p(f) be the second derivative of k(f). Factor p(h).
h**3
Let w(c) be the first derivative of -c**5/165 - c**4/132 + 3*c**2/2 + 5. Let t(z) be the second derivative of w(z). Factor t(m).
-2*m*(2*m + 1)/11
Let p(y) be the third derivative of -y**2 + 5/6*y**4 + 0*y + 0 + 8/15*y**6 - 1/3*y**3 - 16/15*y**5. Find i, given that p(i) = 0.
1/4, 1/2
Let w(c) be the first derivative of 2*c**5/55 - c**4/22 - 2*c**3/33 + c**2/11 + 1. Solve w(j) = 0.
-1, 0, 1
Let p = -99 + 893/9. Suppose -p*i**3 + 2/9*i**4 + 0 - 2/9*i**2 + 2/9*i = 0. Calculate i.
-1, 0, 1
Let n = 38 + -38. Solve -1/5*s**2 + n - 1/5*s = 0 for s.
-1, 0
Let i(u) be the second derivative of -u**4/30 + 4*u**2/5 + 22*u. Let i(a) = 0. What is a?
-2, 2
Let f = 13 + -14. Let x(p) = p**3 + p**2 - p - 1. Let n(l) = -4*l**2 - 8*l - 4. Let k(s) = f*n(s) + 2*x(s). What is z in k(z) = 0?
-1
Let z = 1828/5 + -365. Factor -6/5*r**2 - 9/5*r + 0 + z*r**3.
3*r*(r - 3)*(r + 1)/5
Let b(c) be the second derivative of c**7/7560 + c**6/1080 - c**4/3 + 2*c. Let s(r) be the third derivative of b(r). Factor s(l).
l*(l + 2)/3
Suppose 0 = -2*i + 4*s - 2*s + 14, 16 = i - 4*s. Factor 0*a + 0*a**3 + 0 + 1/4*a**2 - 1/2*a**5 - 3/4*a**i.
-a**2*(a + 1)**2*(2*a - 1)/4
Let m be 4/((-7)/((-98)/4)). Let b = -11 + m. Factor 6/7*h**b - 2/7*h**4 - 6/7*h**2 + 2/7*h + 0.
-2*h*(h - 1)**3/7
Solve 14/3*w**2 - 8/3 - 8*w = 0.
-2/7, 2
Let m(z) be the third derivative of z**8/1008 + z**7/210 + z