*r.
-5*r*(r + 1)*(6*r - 1)/2
Suppose -4*v = -7*v + 30. Suppose -p = 5*w - 20, -4*p = 3*w - w + v. Solve -1/3*k - 1/3*k**w - 1/3*k**4 + 2/3*k**3 + 2/3*k**2 - 1/3 = 0 for k.
-1, 1
Suppose -10 = -3*j + 5*f, 4*j = -5*f - 0 - 10. Let m(n) be the first derivative of 0*n + j*n**4 - 1/20*n**5 + 2 + 0*n**2 + 1/12*n**3. Let m(v) = 0. Calculate v.
-1, 0, 1
Suppose -2*b + 3*o + 141 = b, 5*b - 195 = -3*o. Let i be (-2)/(-4) + b/12. Find c, given that -10*c + 0 - 3*c**2 + i*c + 0 = 0.
-2, 0
Let o(f) = -8*f**3 + 8*f**2 + 6. Let d(p) = -9*p**3 + 8*p**2 + 5. Let j(l) = 6*d(l) - 5*o(l). Determine b so that j(b) = 0.
0, 4/7
Factor 2 - 29/5*h - 3/5*h**2.
-(h + 10)*(3*h - 1)/5
Let z(q) = q**2 + q - 1. Let h(d) = -7*d**2 + 58*d - 178. Let m(k) = h(k) + 2*z(k). What is c in m(c) = 0?
6
Suppose 0 = -3*v - v + 80. Let x be 8/v*1/1. Find u, given that x*u**4 - 1/5*u**5 + 1/5*u - 2/5*u**2 + 0*u**3 + 0 = 0.
-1, 0, 1
Let z = -15 - -21. Suppose z + 3*l**4 - 4 - 2 - 3*l**2 = 0. Calculate l.
-1, 0, 1
Let b(v) = 3*v - 6. Let s be b(8). Suppose -u - 2*r + 2 = -11, s = u + 3*r. Factor 2*y**4 + 3*y**2 - 2*y**5 - u*y**2.
-2*y**4*(y - 1)
What is g in 0*g + 0 + 0*g**2 + 0*g**3 + 2/3*g**5 - 4/3*g**4 = 0?
0, 2
Factor -27/4 - 3/4*h**2 + 9/2*h.
-3*(h - 3)**2/4
Solve 18/13 - 48/13*r + 32/13*r**2 = 0.
3/4
Factor 4*c + 4*c**2 - 7*c**2 - c**2 + 8.
-4*(c - 2)*(c + 1)
Let s(z) = -z**4 + 12*z**3 - 10*z**2 + 2. Let c(u) = -u**4 + 24*u**3 - 19*u**2 + 5. Let y(d) = -2*c(d) + 5*s(d). Let y(a) = 0. Calculate a.
0, 2
Let b(p) be the second derivative of p**8/6720 + p**4/12 - 2*p. Let m(q) be the third derivative of b(q). Let m(t) = 0. What is t?
0
Let u(j) be the first derivative of 2*j**6/9 - 4*j**5/9 - 2*j**4/9 + 8*j**3/9 - 2*j**2/9 - 4*j/9 + 21. Let u(d) = 0. Calculate d.
-1, -1/3, 1
Let k(g) be the second derivative of 1/40*g**5 - 1/8*g**3 + 1/168*g**7 + 0 + 1/8*g**2 - 4*g - 1/40*g**6 + 1/24*g**4. Solve k(v) = 0.
-1, 1
Suppose 5*w + 13 - 2 = -p, -p - 3*w - 7 = 0. Let i be (-10)/75*5*p. Suppose i*f**4 - 2/3*f**2 - 2/3*f**3 + 2/3*f + 0 = 0. What is f?
-1, 0, 1
Let t(h) = 3*h**4 - h**3 - 2*h**2 - h + 1. Let i(k) = k**5 - k**4 + k**3 - 1. Let j(p) = 2*i(p) + 2*t(p). Factor j(w).
2*w*(w - 1)*(w + 1)**3
Suppose b - 15 = -2*b. Factor h**3 + 4*h**5 + 4*h**4 - 4*h**5 - 2*h**4 + h**b.
h**3*(h + 1)**2
Factor -9*i**2 + 6*i**2 - 12 - i**2 + 16*i.
-4*(i - 3)*(i - 1)
Suppose 0 = -7*c + c. Let m(f) be the third derivative of -1/3*f**3 + 2*f**2 + 0*f**4 + 1/30*f**5 + c*f + 0. Suppose m(a) = 0. Calculate a.
-1, 1
Suppose 4*s + 12*l - 11*l + 2 = 0, -3*l = -3*s + 6. Factor s*f + 1/5*f**5 - 1/5*f**2 - 3/5*f**4 + 3/5*f**3 + 0.
f**2*(f - 1)**3/5
Let i(l) be the first derivative of 5*l**3/3 - 40*l**2 + 320*l - 24. Find s, given that i(s) = 0.
8
Let i(r) = -r**2 - 9*r - 9. Let c(y) = 4*y**2 + 17*y + 16. Let d(h) = h**2 - 1. Let n(u) = -c(u) + 2*d(u). Let o(k) = -5*i(k) + 3*n(k). Factor o(b).
-(b + 3)**2
Let 2/11*x**2 - 2/11 + 2/11*x - 2/11*x**3 = 0. What is x?
-1, 1
Let d(r) be the second derivative of -r**5/170 + r**4/102 - 4*r. Factor d(z).
-2*z**2*(z - 1)/17
Let a(q) be the first derivative of -4*q**6/21 - 2*q**5/5 - q**4/7 + 2*q**3/21 - 1. Determine v so that a(v) = 0.
-1, 0, 1/4
Suppose 5*d = 2*w + 17, -5*d = -4 - 21. Let s(v) be the second derivative of 1/18*v**w + 1/30*v**5 - 1/45*v**6 - 2*v + 0 - 1/9*v**3 + 0*v**2. Factor s(i).
-2*i*(i - 1)**2*(i + 1)/3
Suppose 0 = -n - 3*g + 6*g - 7, n + 13 = 5*g. Let w(m) = -m**2 + 3*m + 1. Let f be w(n). Factor -v**f + 6*v - 2*v**2 + 2*v**3 - 5*v.
v*(v - 1)**2
Let u(s) = -7*s**3 + s**2 - 1. Let z be u(1). Let k(n) = -n**2 - 8*n - 3. Let m be k(z). Solve 4*v**4 - 3*v + 3*v - 2*v**3 + v**5 - 3*v**m = 0.
-2, 0, 1
Let c(o) be the third derivative of o**7/4200 + o**6/1800 - o**3 - o**2. Let r(b) be the first derivative of c(b). Factor r(u).
u**2*(u + 1)/5
Let b(q) be the second derivative of q**8/17920 + q**7/20160 - q**6/1920 - q**5/960 + q**4/4 + 3*q. Let j(i) be the third derivative of b(i). Factor j(w).
(w - 1)*(w + 1)*(3*w + 1)/8
Suppose -2*z + 10 - 4 = 0. Let k be (z/(-4))/((-6)/4). Factor -1/2*t**2 - t - k.
-(t + 1)**2/2
Let b(w) be the second derivative of -w**5/60 + w**3/6 - w**2/3 + w. Suppose b(n) = 0. Calculate n.
-2, 1
Let w(p) be the second derivative of 8/21*p**7 + 0*p**2 + 2/15*p**6 - 4/5*p**5 + p + 0 + 0*p**3 - 1/3*p**4. Determine j, given that w(j) = 0.
-1, -1/4, 0, 1
Let s = 184 - 181. Let 10/11*a**2 - 16/11*a + 8/11 - 2/11*a**s = 0. Calculate a.
1, 2
Let f be (-1 + (-1 - 13))/(-1). Factor 2 + 36*b**3 - f*b**2 + 4*b + 1 - 24*b**2 + 1.
(3*b - 2)**2*(4*b + 1)
Let w be (-3)/(-2) - (-81 + 72). Let 9/4*p**5 + 3/2*p**2 - 9/4*p + 12*p**3 + w*p**4 + 0 = 0. Calculate p.
-3, -1, 0, 1/3
Let p(r) be the first derivative of r**4/10 - 8*r**3/15 - r**2 - 17. Determine u, given that p(u) = 0.
-1, 0, 5
Let n(j) be the first derivative of -1/12*j**4 - 9 + 0*j**3 + 1/6*j**2 + 0*j. Suppose n(s) = 0. What is s?
-1, 0, 1
Factor 8/3 + 1/3*w**2 - 2*w.
(w - 4)*(w - 2)/3
Let k(u) = -10*u - 2. Let l be k(-3). Determine n so that -l*n**2 - 25*n**5 - 6*n - 69*n**3 - 20*n**4 - 50*n**4 + 2*n = 0.
-1, -2/5, 0
Let p = 7 - 7. Determine g so that 4*g**2 - 18*g - 1 + p*g**2 - g**2 + 28 = 0.
3
Let h be (8*(-5)/(-15))/3. Factor 0 - h*n**4 - 2/9*n - 8/9*n**2 - 4/3*n**3 - 2/9*n**5.
-2*n*(n + 1)**4/9
Let n = 462 - 462. Factor 1/2*b**2 + 0 - 1/4*b**5 + n*b**3 + 1/4*b - 1/2*b**4.
-b*(b - 1)*(b + 1)**3/4
Suppose 0 = -4*f + i + 10, 0 = 2*f - 3*i - 1 - 9. Factor -m**3 - m**3 + f - m**3 + 4 + 9*m.
-3*(m - 2)*(m + 1)**2
Suppose 3*o = -2*y + 6*y - 8, -3*y + o = -6. Solve -3/5*h**y + 3/5 + 0*h = 0.
-1, 1
Determine f, given that 3*f**3 + 1 + 3*f**2 + 9*f - 5 - f**4 - 13*f - f**3 = 0.
-1, 2
Let x = -15 + 15. Suppose -3*r + 2*o - 9 = -o, 4*r + o - 13 = x. Determine u, given that -4/5*u + 0 + 2/5*u**r = 0.
0, 2
Find s, given that -7*s + 5*s**2 - 10 - s + 5*s - 2*s = 0.
-1, 2
Let c(n) = -n**2 + 2*n + 3. Let z be c(3). Let -5*y + 14*y**2 - 1 - 5*y - 3 + z*y**2 = 0. Calculate y.
-2/7, 1
Let k(w) be the second derivative of w**5/10 - w**4/3 + 20*w. Factor k(y).
2*y**2*(y - 2)
Let w(u) be the second derivative of -1/10*u**5 + 0*u**3 + 3*u + 1/6*u**4 + 0*u**2 + 0 - 2/15*u**6. Let w(v) = 0. Calculate v.
-1, 0, 1/2
Suppose y + 5*s + 7 + 2 = 0, -23 = 5*y + 3*s. Let n be y/(-14)*91/39. Factor -n*i**2 - 8/3 + 8/3*i.
-2*(i - 2)**2/3
Let -1/7*n**3 + 4/7 + 0*n - 3/7*n**2 = 0. What is n?
-2, 1
Let r(c) be the third derivative of 7*c**6/540 - c**5/30 - c**4/9 + 4*c**3/27 - 8*c**2. Find h such that r(h) = 0.
-1, 2/7, 2
Let j(b) = b**3 - 7*b**2 + 7*b - 1. Let a be j(6). Suppose 4*s = 5*d - 22, 0 = -2*d + a*s + 12 + 7. Factor d*h - 2*h + 2*h**2.
2*h**2
Suppose 3*g - 8 = -5*m - 3, -5*g - 5*m + 5 = 0. Let g*j + 2/9 - 2/9*j**2 = 0. What is j?
-1, 1
Let f(k) = 4*k**3 - k**2 + 6*k + 1. Let b(o) = -5*o**3 + o**2 - 7*o - 1. Let r(a) = -5*b(a) - 6*f(a). Factor r(q).
(q - 1)*(q + 1)**2
Let r(l) be the second derivative of l**6/180 - l**5/15 + l**4/4 - l**3/3 + 4*l. Let d(i) be the second derivative of r(i). Factor d(n).
2*(n - 3)*(n - 1)
Let h(s) = 16*s + 6. Let t be h(-3). Let c be (-86)/(-20) - t/(-28). Solve 22/5*u + c*u**3 - 32/5*u**2 - 4/5 = 0 for u.
2/7, 1
Let l(x) be the first derivative of -x**6/360 + x**5/90 - x**4/72 + x**2 + 3. Let s(k) be the second derivative of l(k). Factor s(y).
-y*(y - 1)**2/3
Let m(a) be the second derivative of -a**5/110 + a**4/33 + a**3/33 - 2*a**2/11 - 3*a. Suppose m(c) = 0. What is c?
-1, 1, 2
Let b be (-3)/((-9)/21) - 2. Factor 2*i**5 + 7*i**b + 2*i + 8*i**5 - 4*i**3 - 15*i**5.
2*i*(i - 1)**2*(i + 1)**2
Solve -4/9 + 44/9*o - 23/3*o**2 - 286/9*o**3 - 169/9*o**4 = 0 for o.
-1, 2/13
Solve 1/2 + 5/4*x + 1/4*x**3 + x**2 = 0 for x.
-2, -1
Let p(i) be the second derivative of i**5/270 - i**4/54 + i**3/27 - 3*i**2/2 + 2*i. Let l(h) be the first derivative of p(h). Find n, given that l(n) = 0.
1
Let y(g) be the first derivative of -10 - 15/4*g**2 - 3*g + 12*g**3 + 189/8*g**4. Factor y(t).
3*(3*t + 1)**2*(7*t - 2)/2
Suppose 0 = 6*l + 7 - 7. Suppose -1/2*i**2 + l*i + 1/2 = 0. Calculate i.
-1, 1
Let p(l) be the third derivative of 0*l + 2*l**2 + 0 + 0*l**5 + 1/504*l**8 - 1/315*l**7 + 0*l**4 + 0*l**3 - 1/90*l**6. What is n in p(n) = 0?
-1, 0, 2
Suppose 0 = 3*r - 4 - 2. Let q be r/(-1) - (-4)/1. Solve -x - 3*x**