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Let d(g) be the second derivative of 2*g**6/15 - g**5/5 - g**4/3 + 2*g**3/3 + 6*g. Determine l so that d(l) = 0.
-1, 0, 1
Let k(o) = 2*o - 5. Let j be k(4). Let n(g) be the first derivative of -7/9*g**j + 2 - 2/3*g - 3/2*g**2. Factor n(x).
-(x + 1)*(7*x + 2)/3
Let j(i) = i + 4. Let f be j(0). Let -s**3 + 0*s**4 + 2*s**3 + 2*s**2 + 2*s**f - 3*s**4 = 0. What is s?
-1, 0, 2
Let d(y) be the first derivative of -4 - 1/9*y**3 + 0*y**2 + 1/3*y. Let d(l) = 0. Calculate l.
-1, 1
Let 5/9*y - 1/3*y**5 + 7/9*y**4 - 2/9*y**3 - 2/3*y**2 - 1/9 = 0. What is y?
-1, 1/3, 1
Let r = -1209 - -32647/27. Let l(w) be the second derivative of 3*w - 2/27*w**4 + 0 + 0*w**2 + 2/15*w**6 + 1/6*w**5 - r*w**3. Determine p so that l(p) = 0.
-2/3, 0, 1/2
Let m(y) be the first derivative of -9*y**4/4 + 8*y**3 - 9*y**2/2 - 6*y - 36. Determine v, given that m(v) = 0.
-1/3, 1, 2
Suppose 2*q - 3*q + 4*t - 14 = 0, -3*t + 18 = 3*q. Factor 10/3*z**3 - 22/9*z**4 + 4/9*z + 0 + 2/3*z**5 - 2*z**q.
2*z*(z - 1)**3*(3*z - 2)/9
Let t(n) be the first derivative of -2*n**3/39 - 5*n**2/13 - 8*n/13 - 9. Factor t(j).
-2*(j + 1)*(j + 4)/13
Let l(d) be the second derivative of -d**5/30 - d**4/18 - 10*d. Determine t so that l(t) = 0.
-1, 0
Let w(a) = 4*a**2 + 12*a + 13. Let x be (3 - 2)/((-1)/(-5)). Let o(v) = -4*v**2 - 12*v - 14. Let p(h) = x*o(h) + 6*w(h). Factor p(j).
4*(j + 1)*(j + 2)
Let p(w) = -6 - 2*w + 6*w**2 + 8*w + 0*w. Let h(l) = l**4 + l**3 - l**2 + l. Let t(k) = -3*h(k) + p(k). Factor t(m).
-3*(m - 1)**2*(m + 1)*(m + 2)
Let i(d) be the second derivative of -3*d + 0 - 1/30*d**4 + 2/5*d**2 + 1/15*d**3. Factor i(a).
-2*(a - 2)*(a + 1)/5
Suppose -4/11*w**3 + 0*w + 2/11*w**2 + 0 + 2/11*w**4 = 0. What is w?
0, 1
Let g(s) be the first derivative of s**7/210 + s**6/180 + 2*s**3 - 6. Let u(c) be the third derivative of g(c). Determine y so that u(y) = 0.
-1/2, 0
Suppose 0 = 3*v - 12 + 3. Factor -1/2*f**v + 3/2*f**2 + 1/2 - 3/2*f.
-(f - 1)**3/2
Let w(p) = 2*p**2 - 12*p + 10. Let g be w(4). Let h be ((-2)/g)/((-1)/(-6)). Factor 2/3*u - 2/3 - 10/3*u**3 + 2*u**h + 4/3*u**4.
2*(u - 1)**3*(2*u + 1)/3
Let b(w) be the third derivative of 6*w**2 + 0*w - 1/27*w**3 + 0 + 1/36*w**4 + 1/540*w**6 - 1/90*w**5. Factor b(k).
2*(k - 1)**3/9
Let u be -1 + 2 + 553/5. Let s = 112 - u. Factor s*l**4 - 2/5 + 0*l**2 - 4/5*l**3 + 4/5*l.
2*(l - 1)**3*(l + 1)/5
Let x(n) be the third derivative of n**4/24 + n**3/6 + 2*n**2. Let z be x(2). Suppose -z*w**2 + 3*w**2 + 2*w**5 = 0. What is w?
0
Let k(a) be the first derivative of -a**3/4 + 3*a**2/2 - 9*a/4 - 19. Factor k(w).
-3*(w - 3)*(w - 1)/4
Let w(v) be the third derivative of v**6/108 + v**5/135 - v**2. Determine c, given that w(c) = 0.
-2/5, 0
Let w be (-1)/2 - (-5)/2. Suppose -w*k = k. What is s in k*s**2 + 2 - 3 + s**2 = 0?
-1, 1
Let n = -59 - -59. Let d(s) be the third derivative of 7/60*s**4 - 3*s**2 + 0 + 1/30*s**5 + 2/15*s**3 + n*s. Factor d(r).
2*(r + 1)*(5*r + 2)/5
Suppose -2 = q - 5. Let t be (1/((-2)/(-8 - 0)))/14. Factor -2/7 + 2/7*y**q + 2/7*y**2 - t*y.
2*(y - 1)*(y + 1)**2/7
Let t(f) be the second derivative of 1/150*f**5 + 0*f**2 + 1/900*f**6 + 0 - f + 0*f**4 - 1/3*f**3. Let n(u) be the second derivative of t(u). Factor n(j).
2*j*(j + 2)/5
Let y(r) be the second derivative of r**7/210 - r**6/40 + r**5/20 - r**4/24 + 3*r**2/2 - 2*r. Let g(a) be the first derivative of y(a). Factor g(c).
c*(c - 1)**3
Let k(d) = -6*d - 5*d**2 + 2*d + 4*d + 2*d + 7. Let n(r) = 3*r**2 - r - 4. Suppose v + 7 = 2*v. Let y(f) = v*n(f) + 4*k(f). Factor y(g).
g*(g + 1)
Factor -2/7*p**3 + 0 - 2/7*p**5 + 0*p**2 + 0*p + 4/7*p**4.
-2*p**3*(p - 1)**2/7
Let p(j) be the third derivative of 7*j**7/30 + 7*j**6/20 - 47*j**5/60 - j**4 + 8*j**3/3 - 7*j**2. What is l in p(l) = 0?
-1, 4/7
Find g such that 14/13*g**3 - 24/13*g - 18/13*g**2 + 8/13 = 0.
-1, 2/7, 2
Factor -d**3 - 2*d + 120 + 125 - 3*d**2 - 245.
-d*(d + 1)*(d + 2)
Let b(f) be the third derivative of -6*f**2 + 1/105*f**7 + 0*f**3 - 1/15*f**6 + 0*f + 2/15*f**5 + 0 + 0*f**4. Factor b(i).
2*i**2*(i - 2)**2
Solve -2*o**3 - 3/2*o**4 + 0 + 1/2*o**2 + o = 0.
-1, 0, 2/3
Let k(u) = -3*u**3 + 7*u**2 - 7*u - 2. Let f = 3 - 2. Let q(a) = -a**3 + a**2 - a. Let m be 1/((-3)/15 - 0). Let p(v) = f*k(v) + m*q(v). Factor p(x).
2*(x - 1)*(x + 1)**2
Let 4*o**4 + 1850*o - 1850*o + 2*o**3 + 2*o**5 = 0. Calculate o.
-1, 0
Let q be (8/14)/((6/(-7))/(-2)). Determine u, given that q*u - 2/3*u**2 + 0 = 0.
0, 2
Let y(b) = -2*b - 14. Let d be y(-8). Let a(i) be the first derivative of -1/15*i**3 + 1/5*i - 1 + 1/10*i**d - 1/20*i**4. Factor a(s).
-(s - 1)*(s + 1)**2/5
Let y(g) be the second derivative of -g**4/27 + 2*g**3/9 + 20*g**2/9 - 5*g + 3. Factor y(o).
-4*(o - 5)*(o + 2)/9
Let t(i) be the second derivative of -i**4/12 + i**3/6 + 11*i. Factor t(o).
-o*(o - 1)
Let n(v) be the first derivative of v**6/30 - v**4/6 + v**2/2 - 9*v + 6. Let w(a) be the first derivative of n(a). Factor w(j).
(j - 1)**2*(j + 1)**2
Let q(c) = -c + 1. Let m(z) = -4*z**2 - 8*z + 12. Let r(o) = -m(o) + 16*q(o). Factor r(w).
4*(w - 1)**2
Let g = -17/10 + 33/10. What is k in -2*k + 4/5 - 2/5*k**3 + g*k**2 = 0?
1, 2
Let k(i) be the second derivative of i**5/120 + i**4/18 + 5*i**3/36 + i**2/6 - 51*i. Factor k(s).
(s + 1)**2*(s + 2)/6
Let v(u) = -3*u**4 + 31*u**3 - 87*u**2 + 108*u - 27. Let x(o) = o**3 + o**2. Let t(r) = v(r) - 3*x(r). Suppose t(m) = 0. What is m?
1/3, 3
Let m(d) = 4*d. Let j be m(1). Let x = 130/357 - 4/51. Find r such that 0*r**2 + 0 + 4/7*r**3 + 0*r**j - 2/7*r**5 - x*r = 0.
-1, 0, 1
Suppose -2*k - 5*c = -32 - 25, -2*k + 4*c + 12 = 0. Let q be (-2)/k - 15/(-24). Factor -h + 3/2*h**2 + 0 - q*h**3.
-h*(h - 2)*(h - 1)/2
Suppose -8*c + 0 + 32 = 0. Let p(h) be the first derivative of 0*h**2 + 1/12*h**3 + 0*h - 1 - 1/16*h**c. Factor p(z).
-z**2*(z - 1)/4
Let g = 21 + -22. Let c be 3*g + 2 + 1. Solve 1/3 - 1/3*p**2 + c*p = 0.
-1, 1
Let j(k) = -10*k**3 + 12*k**2 + 9*k. Let g(r) = -r**3 + r**2 + r. Let p(v) = 44*g(v) - 4*j(v). Factor p(h).
-4*h*(h - 1)*(h + 2)
Let h be (-6 + 5)*5*(-1)/3. Solve 1/3*u**2 + 4/3 - 1/3*u**4 - h*u**3 + 8/3*u + 1/3*u**5 = 0.
-1, 2
Suppose 4*a - 15 + 5 = -2*r, 0 = -2*a - 4*r + 8. Let -8*u - 8 - 2*u**2 - u**a + u**2 = 0. What is u?
-2
Let j be 0/(4/3 + (-1)/3). Let q(f) be the first derivative of 4 + 0*f + 1/27*f**6 + 4/27*f**3 + 0*f**5 - 1/6*f**4 + j*f**2. Solve q(d) = 0.
-2, 0, 1
Let w(y) be the second derivative of -y + 3/80*y**5 + 0*y**3 + 0*y**2 + 1/48*y**4 + 0 + 1/168*y**7 + 1/40*y**6. Find g, given that w(g) = 0.
-1, 0
Let u(o) = -o**3 - 7*o**2 + 2*o. Let g(y) = 6*y**2 - 2*y. Let v(l) = -3*g(l) - 2*u(l). Find j, given that v(j) = 0.
0, 1
Factor -8*b**2 - 6*b**3 + 4*b - 6*b + 3*b + 28*b**3 + 9*b**5 - 24*b**4.
b*(b - 1)**2*(3*b - 1)**2
Let j(l) be the first derivative of -l**4/18 + l**2/3 + 2*l - 4. Let o(i) be the first derivative of j(i). Determine v, given that o(v) = 0.
-1, 1
Let d(u) = u**2 - 2*u - 7. Let a be d(7). Suppose -6 - 24*p**2 + 18*p**3 + 2 + 6*p - a*p = 0. What is p?
-1/3, 2
Let c(j) be the first derivative of j**4/20 - j**3/15 + 29. Suppose c(b) = 0. Calculate b.
0, 1
Let z(q) be the second derivative of -7/18*q**3 + 1/18*q**4 - 4*q + 7/60*q**5 + 0 - 1/3*q**2. Factor z(d).
(d - 1)*(d + 1)*(7*d + 2)/3
Let y(u) be the third derivative of u**7/630 + u**6/360 - u**5/30 - u**4/18 + 4*u**3/9 - 7*u**2. Solve y(m) = 0 for m.
-2, 1, 2
Let g(o) be the second derivative of o**2 + 0 + 3/20*o**5 + 2*o - 1/3*o**4 - 5/6*o**3. Factor g(q).
(q - 2)*(q + 1)*(3*q - 1)
Let h = -24 + 26. Suppose 3*o = -4*b - h, -10 = -2*o - 2*o + b. What is z in -1/4 + 0*z + 1/4*z**o = 0?
-1, 1
Let s = 0 - -5. Let t(w) = 9*w**2 + 2 - 5*w**2 - 4*w + 2*w. Let p(k) = -9*k**2 + 4*k - 5. Let y(r) = s*t(r) + 2*p(r). Factor y(z).
2*z*(z - 1)
Let h be (8 - 8) + (-1)/(-45). Let n(t) be the second derivative of 1/18*t**4 + 0*t**2 + 0*t**3 + 0 - 2*t + 0*t**5 - h*t**6. Determine f so that n(f) = 0.
-1, 0, 1
What is q in 0*q**3 + 0*q**2 + 0 + 4/3*q**4 - 14/3*q**5 + 0*q = 0?
0, 2/7
Let m(k) = -k**2 - 1. Let a(i) = 8*i**2 + 8*i + 8. Let t(r) = a(r) + 12*m(r). Factor t(z).
-4*(z - 1)**2
Suppose 0 = 5*x - 25, -4*g = -3*g + 2*x - 10. Let f be (g/(-3) - 0) + 0. Suppose -1/2*p**2 + p + f - 1/2*p**3 = 0. Calculate p.
-2, 0, 1
Let 57/2*v**2 - 6 - 12*v - 21/2*v**3 = 0. Calculate v.
-2/7, 1, 2
