. Let r(b) = 5*a(b) + 4*l(b). Find s such that r(s) = 0.
0, 1
Suppose 4*z - 3*m = 0, -3*z - 4*m + 7 = -6*z. Determine d, given that 2*d**2 - 2*d + 3*d**z - d**3 + 92*d**4 - 94*d**4 = 0.
-1, 0, 1
Let j(a) be the first derivative of 0*a + 9/16*a**4 + 3/4*a**3 + 3/8*a**2 + 1 + 3/20*a**5. Factor j(u).
3*u*(u + 1)**3/4
Let s = 633901/300 + -2113. Let w(o) be the third derivative of -s*o**6 + 0*o**4 + 0 + 0*o**3 + o**2 + 0*o - 1/150*o**5. Factor w(x).
-2*x**2*(x + 1)/5
Let p(t) be the first derivative of -60*t**5 + 6*t**2 + 0*t + 4 - 165/4*t**4 + 4*t**3. Factor p(c).
-3*c*(4*c - 1)*(5*c + 2)**2
Determine r so that -9/2 + 9/2*r**4 - 3*r + 24*r**2 - 21*r**3 = 0.
-1/3, 1, 3
Let n(w) be the first derivative of -2*w**6/15 + 4*w**5/25 + 5. Find p, given that n(p) = 0.
0, 1
Let x(v) be the third derivative of -v**6/60 - 3*v**5/20 + 7*v**3/6 + 3*v**2. Let n(k) = 2*k**3 + 8*k**2 - 6. Let a(t) = 7*n(t) + 6*x(t). Factor a(q).
2*q**2*(q + 1)
Suppose 59*q**2 - 17*q**3 - 75*q**2 - 92*q**4 - 28*q**5 - 63*q**3 = 0. Calculate q.
-2, -1, -2/7, 0
Let q(h) be the first derivative of 7 + 0*h - 2/27*h**3 + 2/9*h**2 - 1/18*h**4. Factor q(o).
-2*o*(o - 1)*(o + 2)/9
Let c(f) = 6*f + 1. Let d be c(-4). Let t = d + 70/3. Solve 0 - 4/3*p**2 - t*p**4 - 4/3*p**3 + 0*p = 0.
-2, 0
Let x(c) be the first derivative of 8*c**4/21 - 8*c**3/21 + c**2/7 - 4*c - 3. Let i(r) be the first derivative of x(r). Determine b, given that i(b) = 0.
1/4
Let d = 6 + -5. Let t = -1 + 3. Find c, given that 24*c - 18*c - t - 1 - 2*c**2 - d = 0.
1, 2
Let t(f) be the third derivative of f**8/1680 + 11*f**7/1050 - 9*f**6/100 + 43*f**5/150 - 59*f**4/120 + f**3/2 + 36*f**2. Solve t(k) = 0 for k.
-15, 1
Suppose 4*q = 3*d - 5, -2*d + 2 + 1 = -3*q. Let w = 1 + d. Let 4*z**3 - 3 - z**2 - z**4 + 2 - 5*z**2 + w*z = 0. What is z?
1
Let h(q) = q**5 - q**2 + q + 1. Let i(s) = -2*s**5 + 15*s**4 - 5*s**3 - 18*s**2 + 13*s + 3. Let v(l) = -3*h(l) + i(l). Let v(t) = 0. Calculate t.
-1, 0, 1, 2
Let k(z) = 2*z + 4. Let a be k(-2). Let d(v) be the second derivative of 11/20*v**5 + 2/3*v**3 - 1/10*v**6 - v**4 + a*v**2 - 3*v + 0. Factor d(r).
-r*(r - 2)*(r - 1)*(3*r - 2)
Let -3/4*a + 3/4*a**3 + 3/2*a**2 - 3/2 = 0. Calculate a.
-2, -1, 1
Let t be (-6)/(-15) - (4 - (-51)/(-10)). Factor -3*l**3 - 3/2*l**4 + 0*l**2 + t + 3*l.
-3*(l - 1)*(l + 1)**3/2
Suppose 6 = 5*l - 9. Solve 3*c**3 + 5*c**2 - 4*c**2 - 4*c - 4*c**2 + c + l*c**4 = 0.
-1, 0, 1
Let y(z) = 3*z**2 - 5*z + 4. Let d(j) = 10*j**2 - 16*j + 13. Let b(u) = 4*d(u) - 14*y(u). Solve b(f) = 0 for f.
1, 2
Suppose a - 3*x = -4*a + 4, a + 2*x = 6. Suppose 0 = -a*p + 5*z + 21, p - 2*z = -5*z - 6. Factor 2*b**p + 4 + 0*b**2 - 2*b + 0*b**2 - 4*b**2.
2*(b - 2)*(b - 1)*(b + 1)
Let k be 1/(-4) - (-17)/4. Let t be (k/(-10))/((-9)/30). Factor 0*b**4 + 0*b + 0 - 3*b**5 + t*b**3 + 0*b**2.
-b**3*(3*b - 2)*(3*b + 2)/3
Let z(y) be the second derivative of 3*y**5/50 + 2*y**4/9 + 13*y**3/45 + 2*y**2/15 + 3*y. Factor z(l).
2*(l + 1)**2*(9*l + 2)/15
Let c = 8441/755 - -3/151. Solve -8/5*h**2 + 0 - c*h**3 - 98/5*h**4 + 0*h = 0.
-2/7, 0
Suppose v + t + 1 = 0, 3*v = t - 0*t - 23. Let c be ((32/v)/(-4))/1. Solve -1/3*r**5 + 2/3*r**3 + 2/3*r**4 - c*r**2 + 2/3 - 1/3*r = 0 for r.
-1, 1, 2
Let u = -12 + 18. Let l(c) be the first derivative of -4*c**5/5 + 2*c**3/3 + 3*c**2/2 - c - 1. Let a(g) = g**4 - g. Let d(h) = u*a(h) + 2*l(h). Factor d(s).
-2*(s - 1)**2*(s + 1)**2
Let 2*c**3 - 1 + 2 + c**5 + 16*c**2 - 3*c - 14*c**2 - 3*c**4 = 0. What is c?
-1, 1
Let u(n) be the second derivative of 0 - 2*n - 21/5*n**5 - 8*n**3 - 1/2*n**6 - 12*n**4 + 24*n**2. Factor u(k).
-3*(k + 2)**3*(5*k - 2)
Let i(q) be the first derivative of -1 - 5/18*q**3 + 1/3*q + 1/10*q**5 + 5/24*q**4 - 5/12*q**2. What is h in i(h) = 0?
-2, -1, 1/3, 1
Let -12*b + 0*b**2 - 2*b - 48 - 10*b - 3*b**2 = 0. Calculate b.
-4
Solve 2/5*i - 2/5*i**3 + 0*i**2 + 0 = 0 for i.
-1, 0, 1
Suppose 27*w - 27 = 81. Factor 4/3 - 4/3*h - h**2 + 2/3*h**3 + 1/3*h**w.
(h - 1)**2*(h + 2)**2/3
Factor -4/3*k**5 - 4/3 + 4*k**4 - 8/3*k**2 - 8/3*k**3 + 4*k.
-4*(k - 1)**4*(k + 1)/3
Let c(p) be the first derivative of p**8/1120 - p**6/120 + p**4/16 + 4*p**3/3 - 4. Let t(o) be the third derivative of c(o). Factor t(l).
3*(l - 1)**2*(l + 1)**2/2
Let z be 2/(-6) + 91/(-63)*-3. Let t(l) be the first derivative of 1 - 4/3*l**3 + 0*l + 0*l**2 + 56/5*l**5 + 1/2*l**z. Let t(h) = 0. Calculate h.
-2/7, 0, 1/4
Let r(l) = l. Let n(i) = 2*i**2 - 26*i + 2. Let h(u) = 2*n(u) + 44*r(u). Factor h(o).
4*(o - 1)**2
Let u(r) = -2*r**5 + 6*r**4 - 2*r**3 + 2*r**2 - 4*r + 4. Let s(i) = -2*i**5 + 7*i**4 - 3*i**3 + 3*i**2 - 5*i + 5. Let j(h) = -4*s(h) + 5*u(h). Solve j(q) = 0.
-1, 0, 1
Suppose 0 = 4*a - 4*t + 20, 5*a - 4*t = 2*a - 20. Suppose 0 = 2*l - 4. Determine b, given that 2*b**3 - l*b + a*b**2 + 2*b**2 - 2*b**4 + 0*b**3 = 0.
-1, 0, 1
Let m = -54 + 54. Let g(b) be the second derivative of 1/48*b**4 + m*b**3 + 0 - 3*b - 1/8*b**2. Factor g(c).
(c - 1)*(c + 1)/4
Suppose -4*m - 22 = -3*l - 4, 0 = -3*l - 2*m. Let 0*f - 2/5*f**l - 2/5*f**3 + 0 = 0. What is f?
-1, 0
Let c(i) be the third derivative of -i**7/168 - i**6/24 + i**5/16 + 15*i**4/16 - i**2 + 17*i. Suppose c(g) = 0. Calculate g.
-3, 0, 2
Let p(y) be the first derivative of -y**5/330 - y**4/44 - 2*y**3/33 + y**2/2 - 2. Let m(z) be the second derivative of p(z). Determine i, given that m(i) = 0.
-2, -1
Let c(s) be the second derivative of -s**7/28 + 11*s**6/60 - 9*s**5/40 - 7*s**4/24 + s**3 - s**2 + 16*s. Suppose c(z) = 0. What is z?
-1, 2/3, 1, 2
Determine f so that -2/19*f**2 + 0 + 0*f = 0.
0
Suppose 6/13*m + 2/13*m**2 + 4/13 = 0. What is m?
-2, -1
Let q(a) be the second derivative of -a**7/560 - a**6/60 - a**5/20 - a**3/2 + 2*a. Let l(b) be the second derivative of q(b). Factor l(m).
-3*m*(m + 2)**2/2
Suppose 3*f = -2*r + 2 + 7, 6 = 2*f. Factor r + 0*d**2 + 0*d - 4/5*d**4 - 2/5*d**3 - 2/5*d**5.
-2*d**3*(d + 1)**2/5
Let c(g) = -g**5 - g**4 + g**3 - g**2 - g. Let z(l) = 7*l**5 + 2*l**4 - 22*l**3 + 12*l**2 + 17*l - 10. Let j(q) = 2*c(q) + z(q). Factor j(a).
5*(a - 1)**3*(a + 1)*(a + 2)
Suppose -24*s = 8 - 56. Let f(h) be the second derivative of 0 + 0*h**3 - 3*h + 3/2*h**s - 1/4*h**4. Factor f(q).
-3*(q - 1)*(q + 1)
Let r(j) be the second derivative of j**7/1050 + 7*j**6/450 + j**5/10 + 3*j**4/10 + 11*j**3/6 + 3*j. Let h(d) be the second derivative of r(d). Factor h(g).
4*(g + 1)*(g + 3)**2/5
What is c in 0*c + 2/5*c**3 - 4/5 - 3/5*c**4 + 9/5*c**2 = 0?
-1, 2/3, 2
Let g = 703/6 + -350/3. Factor g*l**4 + 0 - l**3 - 1/2*l**2 + l.
l*(l - 2)*(l - 1)*(l + 1)/2
Let s be 1/(-5) - 5/(-5). Factor s + 2/5*a**2 - 6/5*a.
2*(a - 2)*(a - 1)/5
Let z(o) be the first derivative of -o**5/60 + o**4/12 - o**3/6 + o**2 + 2. Let v(f) be the second derivative of z(f). Factor v(x).
-(x - 1)**2
Suppose 85 = 5*x + 15. Let g = x + -14. Find z, given that g + 0*z**2 - 2/5*z**3 + 0*z = 0.
0
Let m(r) = 9*r**3 - 9*r**2 + 12*r. Let y(g) = -19*g**3 + 18*g**2 - 25*g. Let i(v) = -13*m(v) - 6*y(v). Suppose i(x) = 0. Calculate x.
0, 1, 2
Let n(h) be the first derivative of 0*h + 3 - 4/3*h**3 + 2*h**2. Let n(y) = 0. What is y?
0, 1
Let r(d) = -5*d**3 + 9*d**2 - 4. Let j = -25 + 46. Suppose 5*t + 9 = -j. Let y(p) = -p**3 + p**2. Let l(s) = t*y(s) + r(s). Let l(h) = 0. Calculate h.
-2, 1
Let k(s) be the second derivative of s**7/840 - s**6/240 - s**5/20 - s**4/6 + 2*s. Let h(b) be the third derivative of k(b). Suppose h(l) = 0. Calculate l.
-1, 2
Let a = 237/2 + -118. Let m(k) be the first derivative of -1/6*k**3 - 4 - a*k - 1/2*k**2. Find b such that m(b) = 0.
-1
Suppose -2*n - 5*i = -10*i - 21, 4*i = -n - 9. Let h be 1 + -1 + 1/4. Factor 0*q + 1/4*q**2 + 0 + h*q**4 - 1/2*q**n.
q**2*(q - 1)**2/4
Suppose 0*h - 2*h + 30 = 0. Let i = -29/2 + h. Factor -5/4*p**5 + i*p + 0 - 13/4*p**4 - 9/4*p**3 + 1/4*p**2.
-p*(p + 1)**3*(5*p - 2)/4
Suppose -3*s = w - 6, -s = 2*w + w - 2. Factor 6/7*b**3 + w*b + 4/7*b**2 + 0 - 10/7*b**4.
-2*b**2*(b - 1)*(5*b + 2)/7
Let c = -4589/30 - -153. Let p(r) be the second derivative of -3/20*r**5 + r + 0 - 1/4*r**4 - 1/6*r**3 + 0*r**2 - c*r**6. Factor p(x).
-x*(x + 1)**3
Let k(o) be the third derivative of -1/6*o**4 + 0*o + 0*o**3 + 2*o**2 + 0 + 1/30*o**5. Suppose k(d) = 0. What is d?
0, 2
Let p = 4 - 2. Suppose 2*g**5 - p*g**4 - 2*g**4 + 4*g**4 - 2*g**3 = 0.