b - h*b**3 + 1 + 4*b**2 = 0.
2/3, 1
Suppose -3*i - 3 = -12. Let s(n) be the second derivative of 1/6*n**i + 1/20*n**5 - 1/6*n**4 + 0 + n + 0*n**2. Factor s(l).
l*(l - 1)**2
Let c(z) be the first derivative of 0*z**2 - 1/360*z**6 + 1/12*z**4 + 1/3*z**3 - 1/120*z**5 - 1 + 0*z. Let o(a) be the third derivative of c(a). Factor o(s).
-(s - 1)*(s + 2)
Let a(l) be the first derivative of -2*l**5/5 + 2*l**3/3 + 6. Factor a(q).
-2*q**2*(q - 1)*(q + 1)
Let f be 0 + (-17)/9 - -1. Let n = f - -14/9. Factor 0 + 0*t + 2/3*t**4 + 0*t**2 - n*t**5 + 0*t**3.
-2*t**4*(t - 1)/3
Determine t so that -34/7*t**2 + 2/7*t**3 + 18*t + 162/7 = 0.
-1, 9
Let i(w) = w**5 - w**4 - 2*w**3 + 3. Let v(z) = -4*z**5 + 6*z**4 + 10*z**3 - 14. Let m(y) = -28*i(y) - 6*v(y). Factor m(l).
-4*l**3*(l + 1)**2
Let d = -3/341 - -727/5115. Let v(c) be the first derivative of -d*c**3 - 1 + 0*c + 3/10*c**4 - 4/25*c**5 + 0*c**2. Factor v(n).
-2*n**2*(n - 1)*(2*n - 1)/5
Let 0 + 1/4*k + 0*k**2 - 1/4*k**3 = 0. Calculate k.
-1, 0, 1
Let l(r) be the first derivative of -1/22*r**4 - 2 + 0*r - 2/55*r**5 + 1/33*r**6 + 2/33*r**3 + 0*r**2. Suppose l(b) = 0. Calculate b.
-1, 0, 1
Let w(s) be the third derivative of -s**5/420 + 9*s**2. Let w(o) = 0. Calculate o.
0
Let z be ((-4)/18)/((-16)/24). Find o such that -1/3 + 1/3*o**2 + z*o - 1/3*o**3 = 0.
-1, 1
Let p be 4/10 - 884/(-40). Let g = p + -22. Find y, given that 1/2 - g*y**2 + 0*y = 0.
-1, 1
Let p(y) = 21*y**2 - 15*y - 42. Let i(k) = 11*k**2 - 7*k - 20. Let l(c) = 9*i(c) - 4*p(c). Factor l(u).
3*(u - 1)*(5*u + 4)
Let u(y) be the third derivative of -2*y**2 + 0 + 1/90*y**5 - 1/360*y**6 + 0*y + 0*y**3 - 1/72*y**4. Solve u(v) = 0.
0, 1
Let l(d) = d**2 - 10*d + 2. Let t be l(10). Let n(f) = f**2 - 2*f + 3. Let w(m) = 3*m**2 - 5*m + 7. Let k(s) = t*w(s) - 5*n(s). Factor k(p).
(p - 1)*(p + 1)
Suppose -5*k + 10*k - 35 = 0. Let m(p) be the third derivative of -3*p**2 + 0*p**5 + 0*p**4 + 1/1680*p**8 + 0*p + 0*p**k - 1/600*p**6 + 0 + 0*p**3. Factor m(u).
u**3*(u - 1)*(u + 1)/5
Suppose -5*k - 25 = -2*j - 3*j, -3*k + 5*j - 25 = 0. Suppose 24 = 4*g - k*g. Factor -2*a + 7 - 3*a**2 + 4*a**2 - g.
(a - 1)**2
Let r(z) be the first derivative of -z**3/2 - 11*z**2/4 - 3*z - 22. Factor r(x).
-(x + 3)*(3*x + 2)/2
Factor 3 + 3/2*y**2 - 9/2*y.
3*(y - 2)*(y - 1)/2
Let i(w) be the first derivative of 2*w**5/65 + 2*w**4/13 + 10*w**3/39 + 2*w**2/13 + 3. What is q in i(q) = 0?
-2, -1, 0
Let h(y) be the second derivative of -27*y**5/40 + 21*y**4/8 - 4*y**3 + 3*y**2 + 16*y. Determine s, given that h(s) = 0.
2/3, 1
Suppose 3*i - 35 = -2*i - 3*h, -20 = -4*h. Let z(w) be the first derivative of 2*w**3 + w**2 - 1 + 3/2*w**i + 2/5*w**5 + 0*w. Factor z(n).
2*n*(n + 1)**3
Suppose 0 = -2*p + 8 - 0. Find v such that 3*v + 27/2*v**p + 36*v**3 + 39/2*v**2 + 0 = 0.
-2, -1/3, 0
Solve -68*q**4 - q + 69*q**4 + q**3 + 0*q**2 - q**2 + 0*q**2 = 0 for q.
-1, 0, 1
Let g = 17 - 11. Let i(q) be the second derivative of 1/12*q**4 - 1/30*q**g + 0*q**5 + 0*q**3 + 0 + 0*q**2 - 2*q. Factor i(t).
-t**2*(t - 1)*(t + 1)
Let a(g) be the third derivative of -g**7/105 + g**6/12 - 3*g**5/10 + 7*g**4/12 - 2*g**3/3 + 3*g**2 + 3. Factor a(n).
-2*(n - 2)*(n - 1)**3
Suppose 3*g - 15 = -l, 0 = -9*l + 6*l + 5*g - 25. Factor 1/5*k**2 + 0*k + l + 1/5*k**3.
k**2*(k + 1)/5
Suppose 0 = 4*r + 5*b - 37, -3*b = -3*r - 0*b - 6. Suppose -f - r = -5. Suppose t**5 + f*t - 4*t**4 + 4*t**2 + 6*t**5 - t**5 - 8*t**3 = 0. What is t?
-1, -1/3, 0, 1
Let o(z) be the first derivative of z**6/2 - 9*z**5/5 + 3*z**4/2 + 3. Factor o(l).
3*l**3*(l - 2)*(l - 1)
Let b(l) be the first derivative of 4*l**5/25 - 6*l**4/5 + 16*l**3/5 - 16*l**2/5 + 14. What is t in b(t) = 0?
0, 2
Let r(c) be the second derivative of -1/168*c**7 + 0*c**6 + 0 - 1/24*c**3 + 0*c**4 + 0*c**2 + 1/40*c**5 + 3*c. What is g in r(g) = 0?
-1, 0, 1
Let l(k) = -k**2. Let p(j) = 16*j**3 - 6*j**2. Let n(o) = 2*l(o) - p(o). Factor n(i).
-4*i**2*(4*i - 1)
Let h(s) be the first derivative of 2 + 0*s**2 - 3/22*s**4 + 0*s + 4/33*s**3 + 2/55*s**5. Factor h(i).
2*i**2*(i - 2)*(i - 1)/11
Let g(d) = -d**3 - 10*d**2 + 2. Let o be g(-10). Suppose z + 2 = 2*z - 2*a, 0 = z - 5*a - o. Solve 4/3*k - 4/3 - 1/3*k**z = 0.
2
Let a = -2 - -8. Let b(d) be the first derivative of 2 - 1/6*d**3 + 1/10*d**5 + 1/24*d**a + 0*d + 0*d**4 - 1/8*d**2. Factor b(h).
h*(h - 1)*(h + 1)**3/4
Let q(o) = o + 6. Suppose -2*w + 0 = 8. Let g be q(w). Factor 0 + 0*h + 1/3*h**4 + 1/3*h**g + 2/3*h**3.
h**2*(h + 1)**2/3
Let d(u) be the first derivative of u**6/60 - u**4/8 - u**3/6 + 4*u + 3. Let r(v) be the first derivative of d(v). Factor r(i).
i*(i - 2)*(i + 1)**2/2
Let u(b) be the second derivative of -b**5/50 + 7*b**4/15 - 49*b**3/15 + 14*b. Factor u(k).
-2*k*(k - 7)**2/5
Let l(i) be the third derivative of 0 + 1/180*i**5 + i**2 + 1/18*i**3 + 0*i - 1/36*i**4. Find y such that l(y) = 0.
1
Suppose 15 = 11*n - 6*n. Find i, given that 5*i**2 + 0*i**n - 2*i**2 + 3*i**3 + i + i**4 = 0.
-1, 0
Let s(w) be the third derivative of 1/1080*w**6 + 0 + 1/180*w**5 + 0*w - 1/3*w**3 + 2*w**2 + 0*w**4. Let h(n) be the first derivative of s(n). Factor h(q).
q*(q + 2)/3
Let j(w) be the second derivative of 4*w**2 + 1/10*w**5 + 0 - 3*w + 8/3*w**3 + 5/6*w**4. Factor j(h).
2*(h + 1)*(h + 2)**2
Let z(x) be the third derivative of -x**8/23520 + x**6/840 + x**5/210 + x**4/8 + 3*x**2. Let b(l) be the second derivative of z(l). Factor b(q).
-2*(q - 2)*(q + 1)**2/7
Let o be (5/(-3))/(3/9). Let y(z) = -2*z - 5. Let k be y(o). Solve i**5 + i**5 - 2*i**4 - 3*i**k - i**3 = 0.
-1, 0
Factor 6/7*i + 2/7*i**2 + 0.
2*i*(i + 3)/7
Factor 4/3*q**3 - 2/9*q**4 + 16/9*q - 8/3*q**2 + 0.
-2*q*(q - 2)**3/9
Let l(b) = 4*b**3 + 12*b**2 + 18*b - 28. Let z(h) = -11*h**3 - 35*h**2 - 53*h + 83. Let g(c) = 8*l(c) + 3*z(c). Solve g(y) = 0 for y.
-5, 1
Let w be (-338)/(-91) - 4/(-14). Suppose j - w*r - 22 = 0, -5*j + 3 + 2 = r. Factor 3/2*k**3 + 3/2*k + 3*k**j + 0.
3*k*(k + 1)**2/2
Suppose 97/6*n**2 + 24*n + 32/3 + 1/6*n**4 + 3*n**3 = 0. Calculate n.
-8, -1
Suppose 5 = 5*b - 5. Factor -h + 2 + h**3 - 3*h**2 - 3*h**2 + 4*h**b.
(h - 2)*(h - 1)*(h + 1)
Let m(s) be the second derivative of s**6/45 + 7*s**5/120 + s**4/36 - s**3/36 + 4*s. Suppose m(n) = 0. Calculate n.
-1, 0, 1/4
Let u(x) = x**3 + 5*x**2 - 7*x - 6. Let k be u(-6). Suppose k = -0*v - 5*v + 15. Factor -2/7*q**4 + 0*q + 0 - 2/7*q**v + 0*q**2.
-2*q**3*(q + 1)/7
Let t = -15 + 18. Factor 3/2*z**2 + 0 - t*z.
3*z*(z - 2)/2
Let w(m) be the second derivative of -1/8*m**2 + 1/80*m**5 + 0 - 1/24*m**3 + 1/48*m**4 - 3*m. Factor w(v).
(v - 1)*(v + 1)**2/4
Let y = 31 + -29. Let i(v) be the second derivative of 0 + 2/135*v**6 - 1/54*v**4 + 1/90*v**5 - 3*v + 0*v**3 + 0*v**y. Factor i(t).
2*t**2*(t + 1)*(2*t - 1)/9
Let p(h) be the third derivative of 2*h**3 + 2/3*h**4 + 1/15*h**5 + 8*h**2 + 0 + 0*h. Factor p(b).
4*(b + 1)*(b + 3)
Let h = 3/31 + -5/372. Let t(z) be the first derivative of -2 + 1/8*z**2 + h*z**3 - 1/2*z. Find o such that t(o) = 0.
-2, 1
Let z be (-6)/9 - 2/(-3). Suppose z = -0*t + 3*t. Factor t + 5/3*g**4 - 4/3*g**2 + 8/3*g**3 + 0*g.
g**2*(g + 2)*(5*g - 2)/3
Let l(w) = -7 - 4 + 12*w - 8*w**2 - w**2 - 2*w**2. Let i(x) = -5*x**2 + 6*x - 5. Let f(z) = 5*i(z) - 2*l(z). Factor f(p).
-3*(p - 1)**2
Let n(a) be the first derivative of 2/15*a**5 - 1/12*a**4 + 8 + 0*a**3 - 1/18*a**6 + 0*a**2 + 0*a. Determine c, given that n(c) = 0.
0, 1
Factor 4/7 + 6/7*v**2 + 2*v.
2*(v + 2)*(3*v + 1)/7
Let w(g) be the second derivative of g**5/20 + g**3/6 + g**2 - g. Let j be w(0). Solve -4*y**j + 3*y**3 + 6*y**2 - y**3 = 0 for y.
-1, 0
Let u(y) be the second derivative of -9*y + 0 + 1/9*y**3 + 1/18*y**4 - 2/3*y**2. Let u(d) = 0. What is d?
-2, 1
Let b(a) = -5*a**3 + 11*a**2 + 12*a - 36. Let j(h) = h**3 - 3*h**2 - 3*h + 9. Let v(w) = 2*b(w) + 9*j(w). Let v(f) = 0. Calculate f.
-3, 1
Let i be 5768/1440 + (-1 - 3). Let w(h) be the third derivative of -3*h**2 + 0*h - 1/36*h**4 + 0 + 0*h**3 + 0*h**5 + i*h**6. Find s, given that w(s) = 0.
-1, 0, 1
Let q be (22/5)/((-1)/(-5)). Suppose 2*o - 10 = -0*o. Factor 10*n**4 + n**2 + 3*n**2 + 14*n**o + 22*n**4 + q*n**3.
2*n**2*(n + 1)**2*(7*n + 2)
Let a(g) be the second derivative of -g**6/10 + 9*g**5/40 + g**4/4 - 11*g. Find p such that a(p) = 0.
-1/2, 0, 2
Let y(m) = -m. Let u(p) = -4*p**2 + 12*p - 16. Let 