
2*r*(r - 2)*(r + 1)*(r + 2)
Let o be (-46)/(-7) - (-3)/7. Let l = -5 + o. Let j(s) = 2*s. Let t(r) = r**2 + 7*r. Let d(m) = l*t(m) - 7*j(m). Factor d(i).
2*i**2
Let y(s) be the third derivative of 8/105*s**7 + 1/6*s**4 - 6*s**2 + 1/5*s**6 + 0 + 1/84*s**8 + 4/15*s**5 + 0*s**3 + 0*s. Factor y(q).
4*q*(q + 1)**4
Let c(j) be the first derivative of j**6/20 + 2*j**5/15 + j**4/9 + 3*j**2 - 9. Let p(k) be the second derivative of c(k). Find n, given that p(n) = 0.
-2/3, 0
Let r(m) be the third derivative of m**11/1330560 - m**10/100800 + m**9/26880 - 13*m**5/30 + 5*m**2. Let n(a) be the third derivative of r(a). Factor n(w).
w**3*(w - 3)**2/4
Let m(y) be the first derivative of 2*y**3/21 + 26*y**2/7 - 58. Factor m(x).
2*x*(x + 26)/7
Solve 3*r**5 + 196*r**2 - 7*r**5 + 24*r**4 - 101*r**2 - 24*r**3 - 8*r**3 - 119*r**2 + 36*r = 0 for r.
-1, 0, 1, 3
Let r(q) be the first derivative of q**2/2 + 7*q + 23. Let c be r(-4). Suppose -2/15*f**4 + 2/3*f**c - 8/15*f - 4/5*f**2 + 16/15 = 0. What is f?
-1, 2
Let i(y) be the first derivative of y**6/6 + 17*y**5/4 + 100*y**4/3 + 160*y**3/3 + 46*y + 7. Let k(c) be the first derivative of i(c). Factor k(n).
5*n*(n + 1)*(n + 8)**2
Solve 12*h - 15*h**2 - 5 - 4 + 9*h + 3*h**3 = 0 for h.
1, 3
Let s = 122354/15 - 8160. Let b = 18/5 - s. Let -2/3 - 20/3*m**2 + b*m**3 - 10/3*m**4 + 10/3*m + 2/3*m**5 = 0. Calculate m.
1
Let i(f) = f - 15. Let h be i(17). Suppose h*j + 16 = 3*z - 3*j, 5*z = j + 12. Factor -1/4*k + 0 + 1/2*k**3 - 1/4*k**z.
k*(k - 1)*(2*k + 1)/4
Let r(a) be the third derivative of -1/510*a**5 - 12*a**2 + 1/51*a**4 + 0 + 0*a - 1/17*a**3. Solve r(j) = 0 for j.
1, 3
Let f(m) be the first derivative of -2*m - 5/2*m**2 + m**3 - 10. Find b, given that f(b) = 0.
-1/3, 2
Let q be ((-22)/(-6) + -3)*9. Let z(h) = -228*h - 169*h**2 - 90*h + 122 - 29*h**2. Let s(b) = 18*b**2 + 29*b - 11. Let d(t) = q*z(t) + 68*s(t). Solve d(c) = 0.
-2, 2/9
Let 0*b**2 - 2/9*b**5 + 0*b + 10/9*b**4 + 0 + 4/3*b**3 = 0. What is b?
-1, 0, 6
Suppose -x + 14 = 3*n, -14 = -4*n + 5*n + 5*x. Let -5 + n + 8*o**3 + 16*o + 3 + 20*o**2 = 0. What is o?
-1, -1/2
Suppose 4*t - 3 = 2*u - 27, -5*t - 25 = 0. Let r(g) be the third derivative of 1/40*g**6 + 0*g + 0 + 1/16*g**4 + 0*g**3 - 3/40*g**5 - 5*g**u. Factor r(b).
3*b*(b - 1)*(2*b - 1)/2
Suppose 423*v - 4 + 5*v**3 - 45*v**2 - 423*v + 4 = 0. What is v?
0, 9
Let y(j) = -j**3 - 7*j + 13. Let w(a) = -4*a - 75 + 8*a + 69. Let p(g) = -5*w(g) - 2*y(g). Determine q so that p(q) = 0.
-2, 1
Suppose -216/11 - 88*o + 18/11*o**2 = 0. Calculate o.
-2/9, 54
Let w(l) be the first derivative of l**6/36 - l**4/8 - l**3/9 + 17. Factor w(d).
d**2*(d - 2)*(d + 1)**2/6
Let j(s) = 5*s + 27. Let l be j(-5). Factor -3*n**3 + n**l - 565 + 565 + 9*n**4 - 3*n**3.
n**2*(3*n - 1)**2
Let x(h) be the first derivative of 3/4*h**4 + 3/5*h**5 + 0*h**2 + 0*h - h**3 + 12 - 1/2*h**6. Factor x(n).
-3*n**2*(n - 1)**2*(n + 1)
Let r = -144 + 114. Let b be 2 - (6/r)/((-3)/30). Determine i, given that -i**4 + 1/2*i**3 + b*i + 0 + 1/2*i**5 + 0*i**2 = 0.
0, 1
Let f(z) be the second derivative of z**4/54 + 6*z**3 + 729*z**2 - 167*z. Factor f(v).
2*(v + 81)**2/9
Let k(z) be the first derivative of -5/9*z**2 - 2/27*z**3 + 4/3*z - 29. Factor k(q).
-2*(q - 1)*(q + 6)/9
Let f(b) be the first derivative of b**6/200 - b**5/100 - 17*b**2/2 + 11. Let j(u) be the second derivative of f(u). Factor j(h).
3*h**2*(h - 1)/5
Let t(x) be the third derivative of x**8/280 + 2*x**7/105 + 7*x**6/180 + x**5/30 + x**3/2 + 11*x**2. Let q(w) be the first derivative of t(w). Factor q(k).
2*k*(k + 1)**2*(3*k + 2)
Suppose 2*i + 0*i = 6. Suppose 8 = 5*y + i*r - 10, 0 = 3*y - 4*r - 5. Solve 3*w**4 - 6*w + 3*w - 3*w**2 + 0*w**2 + y*w**3 = 0.
-1, 0, 1
Let c(p) be the first derivative of -p**9/3024 - p**8/840 - p**7/840 + 28*p**3/3 + 27. Let u(o) be the third derivative of c(o). Factor u(l).
-l**3*(l + 1)**2
Let f be 0*(10/10)/(-3). Factor 0*h**2 - 1/8*h**3 + 0*h - 1/8*h**4 + f.
-h**3*(h + 1)/8
Factor 4*q**4 - 12*q**3 - 7*q**4 - 16*q**2 + 3*q**5 + 28*q**2.
3*q**2*(q - 2)*(q - 1)*(q + 2)
Let x(n) be the first derivative of 0*n**4 + 2/5*n**5 + 0*n**2 + 3*n - 8 + 2/15*n**6 - 2*n**7 + 0*n**3. Let p(f) be the first derivative of x(f). Factor p(v).
-4*v**3*(3*v - 1)*(7*v + 2)
Let t(y) = 6*y**3 - 44*y**2 - 37*y + 40. Let c be t(8). Factor -1/2*u**2 + c + 11/2*u.
-u*(u - 11)/2
Suppose 3*u - 24 = -21. Let q(o) = 4*o**3 - 11*o**2 - 14*o - 1. Let p(y) = -y**3 - y**2 + y - 1. Let x(f) = u*p(f) - q(f). Suppose x(n) = 0. What is n?
-1, 0, 3
Let c = -2/35 + 39/70. Let v(r) be the first derivative of c*r**4 + 0*r**2 + 2/3*r**3 + 0*r + 2. Factor v(d).
2*d**2*(d + 1)
Let y(z) be the first derivative of -z**3/9 - 2*z**2/3 - z + 160. Suppose y(p) = 0. Calculate p.
-3, -1
Let s(p) be the third derivative of p**8/8400 + p**7/2100 - p**5/300 - p**4/4 + 21*p**2. Let w(t) be the second derivative of s(t). Solve w(n) = 0 for n.
-1, 1/2
Find u such that -14*u + 0 - 2/7*u**3 - 4*u**2 = 0.
-7, 0
Factor 85/4*w + 0 - 3/4*w**3 + 127/2*w**2.
-w*(w - 85)*(3*w + 1)/4
Suppose -9 = -3*f - 2*f - 3*v, -f - 3 = 3*v. Suppose -4*n = -5 - f. Suppose -5*l**n + 2*l**2 + 6 - l - 2*l = 0. What is l?
-2, 1
Factor -8/9*j - 2/9*j**4 + 8/9*j**2 + 0 + 2/9*j**3.
-2*j*(j - 2)*(j - 1)*(j + 2)/9
Let 0*s**2 + 0 + 0*s**4 + 2/11*s**5 - 10/11*s**3 + 8/11*s = 0. What is s?
-2, -1, 0, 1, 2
Let h(l) be the first derivative of 2*l**5/5 + 3*l**4 + 22*l**3/3 + 6*l**2 + 54. Solve h(x) = 0.
-3, -2, -1, 0
Let c be 1*(-120)/350*(0 + (-28)/12). Factor 24/5*j + c*j**2 + 4.
4*(j + 1)*(j + 5)/5
Let c be 4/26 - (-378)/(-91). Let i(o) = -o**3 - 4*o**2 - 2*o - 6. Let r be i(c). Let 4*m + 2*m**4 + r*m**4 - 4*m - 4*m**3 = 0. What is m?
0, 1
Let p(v) = -89*v - 712. Let g be p(-8). Find x such that 1/3 - 2/3*x**3 + g*x**4 + 1/2*x + 1/6*x**5 - 1/3*x**2 = 0.
-1, 1, 2
Suppose 0 = 2*m - 3*x + 3, 3*x + 2*x = -2*m + 21. Let 15*q + 2*q**2 - 10*q**2 - m*q**4 + 18 - 7*q**2 - 15*q**3 = 0. What is q?
-3, -2, -1, 1
Suppose -4 - 8 = -4*f. Solve -2 - 2 - 4*y**2 + f*y + 6*y - y = 0 for y.
1
Let b = 788 + -788. What is i in -2/3*i**3 + 2/9*i**5 - 10/9*i**2 + 2/9*i**4 + b - 4/9*i = 0?
-1, 0, 2
Let k(a) = 7*a + 7. Let y be k(-4). Let n = 28 + y. Factor -3 + 8 + n*c**2 - 10*c - 2*c**2.
5*(c - 1)**2
Let p be 29/29 - -3 - -23. Find x, given that 243/8*x**2 + 6 + p*x = 0.
-4/9
Let g(v) be the first derivative of v**7/1680 - v**6/240 + 2*v**3/3 - 5. Let b(x) be the third derivative of g(x). Factor b(q).
q**2*(q - 3)/2
Let h(x) = 2*x**3 - 28*x**2 + 2*x - 19. Let k be h(14). Suppose k*l - 69 = -14*l. Let 2/3*r**l - 2/3 + 2/3*r**2 - 2/3*r = 0. Calculate r.
-1, 1
Let k be (330/(-20))/(-11)*6*1. Suppose 11*j = 13 + k. Factor 0 - 4/7*x - 4/7*x**j.
-4*x*(x + 1)/7
Let v(z) = 1. Suppose 0 = -2*p - 3 + 11. Let j(c) = 4*c**2 + 32*c + 60. Let y(q) = p*v(q) + j(q). What is o in y(o) = 0?
-4
Let r(v) be the second derivative of v**4/4 + 19*v**3 + 8*v - 6. Let r(d) = 0. Calculate d.
-38, 0
Determine y, given that -18/11*y**4 - 5712*y**2 + 1840/11*y**3 + 721344/11*y - 157216/11 = 0.
2/9, 34
Let c(h) be the second derivative of 1/6*h**6 + 5/3*h**3 + 0 + 0*h**2 + 25/12*h**4 + h**5 + 15*h. Factor c(v).
5*v*(v + 1)**2*(v + 2)
Let n(p) be the second derivative of -1/240*p**5 - 4*p**2 - 8*p + 0*p**4 + 0 + 1/24*p**3. Let a(c) be the first derivative of n(c). Find m, given that a(m) = 0.
-1, 1
Let a(z) = -2*z - 5. Let j be a(-5). Let n = 506 + -503. Solve -n*u**4 + 3*u**4 - 2*u**2 - 7*u**4 - 2*u**5 + 7*u**3 + 4*u**j = 0 for u.
0, 1/2, 1, 2
Let y(c) be the second derivative of c**4/3 + c**3/9 - 5*c**2/3 - 18*c - 2. Factor y(d).
2*(d + 1)*(6*d - 5)/3
Find m such that 0 + 64/3*m + 4/3*m**4 - 28/3*m**3 + 32/3*m**2 = 0.
-1, 0, 4
Let p = -14 - -27. Factor -p*o**3 - 8*o + 21*o**3 - 5*o**4 - 23*o**4 + 28*o**2.
-4*o*(o - 1)*(o + 1)*(7*o - 2)
Let -664/15*d + 2/15*d**2 + 55112/15 = 0. What is d?
166
Let c(b) be the third derivative of b**5/150 - 31*b**4/60 - 32*b**3/15 + 5*b**2. Factor c(q).
2*(q - 32)*(q + 1)/5
Suppose -18*f + 25*f + 21 = 0. Let j be ((-16)/(-60))/(-2)*(f + 2). Factor -32/15 - j*d**2 - 16/15*d.
-2*(d + 4)**2/15
Let w be (-1)/6*((-1)/2 + -1). Let w*s - 1/4*s**2 + 3/2 = 0. Calculate s.
-2, 3
Let r(n) be the first derivative of -585*n**4/28 + 388*n**3/7 - 573*n**2/14 - 6*n/7 - 90. Suppose r(m) = 0. Calc