
Let 1/4*r**2 + 3 - 13/4*r = 0. What is r?
1, 12
Let m(b) = 2*b - 8. Let t be m(6). Suppose t*d + 4 = 20. Factor d - v + 4*v + v**2 + v.
(v + 2)**2
Let d(l) be the second derivative of -l**2 + 8/3*l**4 - 14/5*l**6 - 5*l + 0 - 59/20*l**5 + 5/6*l**3. Determine v, given that d(v) = 0.
-1, -2/7, 1/4, 1/3
Factor 4/5 - 14/5*w**2 + 2*w.
-2*(w - 1)*(7*w + 2)/5
Let r(k) be the first derivative of 0*k**2 + 1/27*k**3 - 1/27*k**4 + 1/90*k**5 - 4*k + 2. Let s(l) be the first derivative of r(l). Factor s(m).
2*m*(m - 1)**2/9
Let q(w) = -4*w - 8. Let j be q(-3). Determine o so that 2*o**4 + j*o**2 - 2/5*o**5 - 2*o + 2/5 - 4*o**3 = 0.
1
Let q be (-1)/(-3) + (-20)/(-12). Suppose -3*y = q*y. Factor -2/5*h**2 + 0 + 2/5*h**4 + y*h + 0*h**3.
2*h**2*(h - 1)*(h + 1)/5
Suppose -c - 3*x = -8*x + 15, 5*c - x = -3. Suppose -4*g - 5*q + 12 = c, -g + 6 = g - q. Factor t + 2*t**g - 4*t**4 + t**2 + 3*t**4 - 2*t - t**3.
-t*(t - 1)**2*(t + 1)
Let y(r) = -r**2 + 24*r + 149. Let a be y(-5). Solve 1/2*w - 1/2*w**a + 0 - 3/2*w**2 + 3/2*w**3 = 0 for w.
0, 1
Let d(k) = -k**3 + 10*k**2 - 8*k - 9. Let i be d(9). Let t(a) be the second derivative of -2*a + 0*a**2 + i + 0*a**3 + 1/30*a**4. Solve t(r) = 0 for r.
0
Let z(j) be the first derivative of 7*j**4/16 + 13*j**3/6 + 13*j**2/8 - 3*j/2 - 9. What is u in z(u) = 0?
-3, -1, 2/7
Let o(v) be the first derivative of 2*v**3/33 - 2*v**2/11 + 2*v/11 - 4. Factor o(f).
2*(f - 1)**2/11
Let i(u) be the second derivative of 0*u**2 - 3/80*u**5 + 0 - 1/8*u**3 - 1/8*u**4 + u. Factor i(n).
-3*n*(n + 1)**2/4
Let j(d) be the first derivative of -d**6/1080 + d**5/120 - d**4/36 + d**3/3 + 2. Let w(p) be the third derivative of j(p). Factor w(x).
-(x - 2)*(x - 1)/3
What is c in 0 + 0*c - 1/2*c**2 = 0?
0
Let m(c) = 1. Let a(x) = -x - x - 5 - x**2 - 3*x + 3*x. Let v(u) = -3*a(u) - 15*m(u). Find p, given that v(p) = 0.
-2, 0
Let o(t) = 4*t**2 + 7*t + 22. Let m(r) = -11*r**2 - 22*r - 67. Let n(i) = -3*m(i) - 8*o(i). Determine u, given that n(u) = 0.
-5
Let 6*f**2 - 190 + 186 + 2*f - 4*f**3 + 4*f = 0. What is f?
-1, 1/2, 2
Factor -6/11*q - 4/11 - 2/11*q**2.
-2*(q + 1)*(q + 2)/11
Let y(z) = z**4 - z**2 - z. Let t(c) = -7*c**3 + 11*c**3 - c**2 + 2*c**2 - 5*c**4 + 4. Let w(s) = -3*t(s) - 12*y(s). Factor w(p).
3*(p - 2)**2*(p - 1)*(p + 1)
Let i(r) be the second derivative of -r**5/150 - r**4/90 + r**3/9 - r**2/5 + 17*r. Factor i(l).
-2*(l - 1)**2*(l + 3)/15
Suppose -5*l - 3*t = -52, 0 = 3*l - 4*t + 8*t - 40. Let x = l - 4. Factor 2 + 6*g - g**2 + 2*g**3 + 3*g**2 + x*g**2.
2*(g + 1)**3
Let m(r) = 15*r**4 + 48*r**3 + 64*r**2 + 40*r - 16. Let i(x) = -x**4 - x**3 + x**2 - x. Let c(o) = 24*i(o) + 3*m(o). Factor c(s).
3*(s + 2)**3*(7*s - 2)
Factor 0*w**2 + 0*w - 1/4*w**5 + 1/4*w**3 + 0 + 0*w**4.
-w**3*(w - 1)*(w + 1)/4
Let q(x) be the third derivative of x**8/10080 + x**7/2520 - x**5/10 - 5*x**2. Let m(r) be the third derivative of q(r). Factor m(b).
2*b*(b + 1)
Let v(k) be the second derivative of k**7/168 + k**6/60 + k**5/80 - 10*k. Factor v(p).
p**3*(p + 1)**2/4
Let u(h) be the second derivative of -h**6/3 - 3*h**5/5 + 3*h**4/2 + 2*h**3/3 - 3*h. Factor u(p).
-2*p*(p - 1)*(p + 2)*(5*p + 1)
Let o(r) = r**3 - r**2 - 2*r. Let z be o(0). Let l(c) be the second derivative of -1/24*c**4 + c + z - 1/2*c**2 + 1/4*c**3. Factor l(h).
-(h - 2)*(h - 1)/2
Suppose -18 + 66 = 24*c. Find z, given that -129/2*z**c + 63/2*z**4 + 6 - 6*z + 33*z**3 = 0.
-2, -1/3, 2/7, 1
Let x(c) be the first derivative of 2/3*c**2 + 2 + 2/3*c**3 + 1/6*c**4 + 0*c. Determine d, given that x(d) = 0.
-2, -1, 0
Suppose 6*m = -7 + 19. Let y(w) be the first derivative of 2/35*w**5 + 0*w - 3 + 2/7*w**3 + 3/14*w**4 + 1/7*w**m. Solve y(l) = 0 for l.
-1, 0
Let l(w) be the second derivative of w**6/75 - w**5/50 - w**4/30 + w**3/15 - 4*w. Factor l(g).
2*g*(g - 1)**2*(g + 1)/5
Let y(x) = 6*x**2 - 9*x - 8. Let h = 5 - 5. Suppose h = -k - 5*s + 6, -2*k + s + 0 = -12. Let q(p) = -5*p**2 + 8*p + 7. Let f(w) = k*y(w) + 7*q(w). Factor f(c).
(c + 1)**2
Suppose -2*i + 0 + 4 = 0. Factor -8/5 + 8/5*f - 2/5*f**i.
-2*(f - 2)**2/5
Let w(h) be the first derivative of 0*h**2 - 3/20*h**5 + 0*h + 2 + 3/16*h**4 - 1/12*h**3 + 1/24*h**6. Factor w(q).
q**2*(q - 1)**3/4
What is p in -3/5*p**2 - 3/5*p**4 + 0 + 18/5*p - 12/5*p**3 = 0?
-3, -2, 0, 1
Suppose -5*b + 9 = -3*i, 4*b - 3 = 2*i + 5. Find y, given that 4/3*y - 1/3*y**i - 4/3 = 0.
2
Suppose 0*w + 5*w + 3*t = 3, -w - 2*t = 5. Let p(y) be the first derivative of -4 + 0*y + 0*y**2 + 2/3*y**w. Suppose p(a) = 0. What is a?
0
Let w(y) be the third derivative of 7*y**5/150 - y**4/5 - 4*y**3/15 - 8*y**2. Let w(i) = 0. Calculate i.
-2/7, 2
Let c(s) be the second derivative of s**7/210 + s**6/30 + s**5/15 - 7*s**3/6 - 3*s. Let z(x) be the second derivative of c(x). Find q such that z(q) = 0.
-2, -1, 0
Factor 17*t - 64 + 18*t - 4*t**2 - 3*t.
-4*(t - 4)**2
Let x(h) = -4*h**2 - 2*h - 3. Let k(n) = -7*n**2 - 3*n - 5. Let p(v) = -3*k(v) + 5*x(v). Factor p(d).
d*(d - 1)
Let t(z) be the first derivative of z**4/26 + 2*z**3/13 - 8*z/13 + 1. Factor t(n).
2*(n - 1)*(n + 2)**2/13
Let y(w) be the third derivative of -w**8/10080 + w**7/2520 + w**5/15 - w**2. Let k(s) be the third derivative of y(s). Let k(d) = 0. Calculate d.
0, 1
Let z(x) be the second derivative of -x**5/120 + x**4/16 - x**3/6 - 5*x**2/2 - x. Let t(h) be the first derivative of z(h). Factor t(u).
-(u - 2)*(u - 1)/2
Let m(c) = -4*c**4 - 8*c**3 - 2*c. Let r(q) = q**5 + q**4 - q**3 + q**2 - q. Let i(w) = -m(w) + 2*r(w). Factor i(v).
2*v**2*(v + 1)**3
Let z(b) be the first derivative of 0*b + 2/5*b**5 - 4 + 0*b**2 + 2/3*b**3 + b**4. Factor z(o).
2*o**2*(o + 1)**2
Let b(u) be the third derivative of u**5/60 - u**4/36 + 8*u**2. Factor b(c).
c*(3*c - 2)/3
Suppose -3 = -5*v - 0*m - 4*m, 0 = 5*v + 2*m - 9. Solve 3/5*i**5 + 6/5*i**2 - 3/5*i + 0 - 6/5*i**4 + 0*i**v = 0 for i.
-1, 0, 1
Factor -2/3*p + 0 + 1/3*p**2.
p*(p - 2)/3
Let p(t) be the first derivative of -t**3/3 + t**2 - t + 5. Factor p(z).
-(z - 1)**2
Let u(d) = d**2 + 2*d - 1. Let l be u(1). Let s = 1345/2 + -672. Suppose 0*m + s - 1/2*m**l = 0. What is m?
-1, 1
Let o(p) be the second derivative of p**5/130 + p**4/26 + 2*p. Factor o(m).
2*m**2*(m + 3)/13
Let t = 130 + -130. Find w such that w**3 + 0*w - 1/3*w**2 + t - w**4 + 1/3*w**5 = 0.
0, 1
Let v(a) be the third derivative of -a**10/50400 + a**9/20160 + a**8/6720 - a**7/1680 + a**5/20 - 4*a**2. Let l(j) be the third derivative of v(j). Factor l(m).
-3*m*(m - 1)**2*(m + 1)
Let g(m) = -10*m - 10. Let t be g(5). Let v be 2*3*(-4)/t. Factor 0 + 4/5*h - 4/5*h**3 + v*h**4 - 2/5*h**2.
2*h*(h - 2)*(h - 1)*(h + 1)/5
Suppose -2*b = q + 2*b - 19, -13 = -3*q - b. Let -2*t - 2*t**3 + 5*t**3 + 4*t**2 + 0*t**3 - t**q - 4 = 0. What is t?
-2, -1, 1
Find n, given that 0 - 2/3*n**3 - 4/3*n**2 - 2/3*n = 0.
-1, 0
Let z(k) be the first derivative of -k**8/112 - k**7/35 + k**5/10 + k**4/8 - 5*k**2/2 - 9. Let h(s) be the second derivative of z(s). Factor h(x).
-3*x*(x - 1)*(x + 1)**3
Let h = -116/3 - -583/15. Factor -h*m**3 + m**2 + 4/5 - 8/5*m.
-(m - 2)**2*(m - 1)/5
Let c(x) be the first derivative of x**6/36 - x**5/10 + x**4/12 + x**3/9 - x**2/4 + x/6 + 29. Suppose c(f) = 0. What is f?
-1, 1
Determine u, given that -7*u + 17 - 5*u**3 - u**4 - 26 + 7 - 9*u**2 = 0.
-2, -1
Suppose 3*p - 7*p - 12 = 0. Let f be (p + 4)/((-14)/(-4)). Solve 0 - f*n + 2/7*n**2 = 0 for n.
0, 1
Let h be (4/(-70))/((-1)/((-15)/(-9))). Let n(z) be the first derivative of -2/7*z**2 - h*z**3 - 2/7*z - 3. Factor n(c).
-2*(c + 1)**2/7
Let d(p) be the third derivative of p**5/30 - p**4/4 + 2*p**3/3 + 6*p**2. Factor d(k).
2*(k - 2)*(k - 1)
Let n(a) be the second derivative of 0*a**4 + 1/3*a**3 - 3*a + 0 - 1/10*a**5 - 1/2*a**2 + 1/30*a**6. Solve n(j) = 0 for j.
-1, 1
Let j(z) be the third derivative of -4/27*z**4 - 1/108*z**6 + 0 - 4*z**2 + 4/27*z**3 + 17/270*z**5 + 0*z. Factor j(c).
-2*(c - 2)*(c - 1)*(5*c - 2)/9
Let d be -2 + 2 + 1 + 117/78. Let 1 + d*c + 1/2*c**3 + 2*c**2 = 0. What is c?
-2, -1
Find g, given that -12*g - 3/2*g**3 - 15/2*g**2 - 6 = 0.
-2, -1
Let o = -3/50551 + -50652087/252755. Let v = -199 - o. Determine x, given that 9/5*x**2 + 1/5*x**4 - v*x + 2/5 - x**3 = 0.
1, 2
Let h(n) be the first derivative of -n**5/25 + 2*n**3/15 - n/5 - 5. Factor h(b).
-(b - 1)**2*(b + 1)**2/5