*m*(m + 1)*(4*m + 1)**2/5
Solve -3*r**3 + 28*r**5 + 2*r**2 + 0*r**3 - 27*r**5 = 0 for r.
-2, 0, 1
Let t(p) = -7*p + 1. Let m be t(1). Let z(b) = 4*b**2 - 11*b - 3. Let i(s) = -12*s**2 + 33*s + 9. Let a(q) = m*i(q) - 21*z(q). Find o such that a(o) = 0.
-1/4, 3
Suppose 0 = 2*i - i + r + 5, -2*i = -4*r - 20. Suppose 2*p = -i*p + 6. What is v in 1/3*v - 8*v**4 + 0 - 8/3*v**2 + 22/3*v**p + 3*v**5 = 0?
0, 1/3, 1
Let z(r) be the first derivative of r**4/2 + 2*r**3/3 - 2*r**2 + 44. Let z(s) = 0. What is s?
-2, 0, 1
Let l(v) = -3*v**2 - 3*v - 2. Let w = 10 + -8. Let o(f) = 7*f**2 + 6*f + 4. Let s(r) = w*o(r) + 5*l(r). Factor s(z).
-(z + 1)*(z + 2)
Factor -2/7*l**4 - 8/7 + 26/7*l + 2*l**3 - 30/7*l**2.
-2*(l - 4)*(l - 1)**3/7
Let l = 56/3 + -785/42. Let k = 9/14 - l. Find s, given that -2/3*s**4 + 0 + k*s**3 - 2/3*s + 2/3*s**2 = 0.
-1, 0, 1
Let w(a) be the third derivative of a**8/168 - a**7/35 + a**6/30 + a**5/15 - a**4/4 + a**3/3 + 3*a**2. Factor w(z).
2*(z - 1)**4*(z + 1)
Let c(i) be the second derivative of i**6/180 + i**5/60 - i**4/6 - i**3/2 + 3*i. Let a(o) be the second derivative of c(o). Determine w, given that a(w) = 0.
-2, 1
Let l be 85/9 + (4 - 7). Let y = l - 52/9. Determine z so that z**4 + 2/3*z**3 - y*z - z**2 + 0 = 0.
-1, -2/3, 0, 1
Let l(o) be the second derivative of 0*o**2 - 3*o + 0 + 1/15*o**4 - 1/15*o**3. Factor l(u).
2*u*(2*u - 1)/5
Let s(z) = z + 10. Let t be s(-6). Factor f**3 - 4*f**4 + t*f - 10 + 4*f**2 - 5*f**3 + 10.
-4*f*(f - 1)*(f + 1)**2
Suppose 5*z + 0*m - 4*m = 23, 0 = -3*m - 6. Suppose -2*q + z = -3. Let 0*y**2 + 0*y + 2/7*y**4 + 0 - 2/7*y**q = 0. Calculate y.
0, 1
Suppose 80 = -6*h + 2*h. Let d be (-32)/h + (-4)/(-10). Find i, given that 18/7*i - 20/7*i**d - 4/7 = 0.
2/5, 1/2
Factor -11*v - 3*v**2 - 10 - 2 + 3*v - 4*v.
-3*(v + 2)**2
Let s(y) = y**3 + 7*y**2 + 4*y + 8. Let n be s(-7). Let x be (1/(-5))/(12/n). What is j in x*j**2 + 0*j - 1/3 = 0?
-1, 1
Let h(i) be the first derivative of i**5/50 + i**4/30 - 2*i**3/15 + 2*i - 3. Let d(u) be the first derivative of h(u). Solve d(o) = 0 for o.
-2, 0, 1
Let b(a) be the second derivative of 1/12*a**4 - 3*a + 0 + 1/3*a**3 - 1/20*a**5 + 0*a**2. Factor b(f).
-f*(f - 2)*(f + 1)
Let a**4 + 9/5*a**3 + 0 + 7/5*a**2 + 2/5*a + 1/5*a**5 = 0. What is a?
-2, -1, 0
Let g = 546/17 - 2322/85. What is z in 12/5*z**2 + 3/5*z**5 + 0 + 0*z + 3*z**4 + g*z**3 = 0?
-2, -1, 0
Let c(d) be the second derivative of d**4/60 - d**3/10 + d**2/5 - d. Suppose c(j) = 0. Calculate j.
1, 2
Let c = 16 + -17. Let a(t) = -t**5 + t**4 - t**3 - 1. Let m(b) = -81*b**5 + 141*b**4 - 78*b**3 + 12*b**2 - 6. Let o(z) = c*m(z) + 6*a(z). Factor o(w).
3*w**2*(w - 1)*(5*w - 2)**2
Let r(o) be the third derivative of 5/12*o**5 + 1/6*o**3 - o**2 + 0*o + 0 + 5/12*o**4. Suppose r(l) = 0. Calculate l.
-1/5
Let v(a) be the first derivative of -2 - 1/7*a**4 - 2/7*a + 1/7*a**2 + 4/21*a**3 + 1/21*a**6 - 2/35*a**5. Suppose v(n) = 0. Calculate n.
-1, 1
Let a(j) be the third derivative of j**6/120 + j**5/60 - j**4/12 - 10*j**2. Factor a(i).
i*(i - 1)*(i + 2)
Let -15*g**5 - 96*g**2 + 385*g**4 + 48 - 96*g - 733*g**4 + 369*g**4 + 84*g**3 = 0. Calculate g.
-2, -1, 2/5, 2
Factor 16 - 100*h**2 + 27*h - 147*h - 52.
-4*(5*h + 3)**2
Suppose -y - 3/4 - 1/4*y**2 = 0. Calculate y.
-3, -1
Let v = 147 - 141. Let u(x) be the third derivative of 1/270*x**5 - 1/540*x**v + 0 - 1/27*x**3 + 1/108*x**4 + 0*x + 4*x**2. Factor u(w).
-2*(w - 1)**2*(w + 1)/9
Let j(z) = -z**2 - 6*z + 10. Let g be j(-7). Determine x, given that -28/3*x**2 + 0 + 20*x**g + 4/3*x - 12*x**4 = 0.
0, 1/3, 1
Let a(g) = -6*g + 8 - g**2 + 3 + 2*g**2. Let b(s) = 1. Let k be ((-8)/6)/(-1 - 10/(-6)). Let f(r) = k*b(r) + a(r). Factor f(o).
(o - 3)**2
Let o(t) be the third derivative of 1/18*t**3 - 1/360*t**6 - 3*t**2 - 1/180*t**5 + 0*t + 0 + 1/72*t**4. What is z in o(z) = 0?
-1, 1
Let m(r) be the second derivative of 1/24*r**4 + r + 0 + 1/2*r**3 + 9/4*r**2. What is x in m(x) = 0?
-3
Factor q**2 - 4*q**4 + 7*q**2 - 4*q**3 - 14 + 14.
-4*q**2*(q - 1)*(q + 2)
Let m(o) be the third derivative of 1/96*o**4 - 6*o**2 - 1/24*o**3 + 0*o + 1/240*o**5 + 0 - 1/480*o**6. Let m(c) = 0. Calculate c.
-1, 1
What is p in -p**2 - 3*p - p + 2*p - 1 = 0?
-1
Let v(n) be the first derivative of -5*n**6/6 - 3*n**5 - 15*n**4/4 - 5*n**3/3 + 4. Determine t so that v(t) = 0.
-1, 0
Let u(j) be the first derivative of -2 + 2/11*j**2 + 6/11*j - 2/33*j**3. What is d in u(d) = 0?
-1, 3
Let u(q) be the third derivative of q**5/330 - q**4/22 + 3*q**3/11 - 2*q**2. Factor u(f).
2*(f - 3)**2/11
Let z(u) be the second derivative of u**10/40320 + u**9/20160 - u**4/3 + 4*u. Let a(d) be the third derivative of z(d). Factor a(o).
3*o**4*(o + 1)/4
Let y be (11/((-44)/8))/(6/(-9)). Factor -2/5*m - 2/5*m**y + 0 - 4/5*m**2.
-2*m*(m + 1)**2/5
Suppose -q - 18 = -5*i, -2*i + 3 = -2*q + 3*q. Let h(s) = -s**3 + 4*s**2 - 3*s + 2. Let x be h(i). Let 3/4*b + 1/2 + 1/4*b**x = 0. What is b?
-2, -1
Let r(z) = -4 - 5 - 2*z + 3 + 3*z. Let b be r(8). Factor 8 + s**3 - 2*s + s**b - 8.
s*(s - 1)*(s + 2)
Let r = -9 + 12. Factor 14*c**2 - 3*c**2 + 6*c**2 + 5*c**r + 4 + 16*c.
(c + 1)*(c + 2)*(5*c + 2)
Let v(k) be the second derivative of -k**4/6 - k**3 + 4*k. Let j(g) = -2*g**2 - 7*g + 1. Let q(w) = -2*j(w) + 3*v(w). Factor q(f).
-2*(f + 1)**2
Let k(o) = o**3 - o**2 - o + 1. Let m(v) = -12*v**3 + 216*v**2 - 528*v + 144. Let a(u) = 16*k(u) - m(u). Factor a(i).
4*(i - 4)**2*(7*i - 2)
Let d(q) = q**2 - 9*q + 3. Let f be d(7). Let o = f - -26. Let 0*c**3 + o*c**2 - 7*c**3 - 20*c**3 - c + 21*c**5 + 7*c - 15*c**4 = 0. Calculate c.
-1, -2/7, 0, 1
Suppose 4*x + x = 10. Suppose 0 = 5*n + 2*c - c - 19, 0 = x*n + 3*c - 18. Factor 2/3*h**4 - 2/3 - 4/3*h**n + 0*h**2 + 4/3*h.
2*(h - 1)**3*(h + 1)/3
Factor 1/5*n**3 + 0 - 1/5*n**2 - 2/5*n.
n*(n - 2)*(n + 1)/5
Let m(d) be the first derivative of -1/3*d**2 - 1/9*d**3 - 1/3*d + 3. Suppose m(f) = 0. What is f?
-1
Let u(j) be the third derivative of j**8/672 + 9*j**2. Solve u(r) = 0.
0
Let u = 88 - 82. Let y(m) be the third derivative of 0 - 1/105*m**5 + 0*m + 2/735*m**7 + 0*m**3 - 4*m**2 + 1/420*m**u - 1/84*m**4. What is t in y(t) = 0?
-1, -1/2, 0, 1
Let x = -4 + 8. Let b be (-8)/(-6)*2/x. Let -2/3*n**2 + 2/3*n**4 - 2/3*n + b*n**3 + 0 = 0. What is n?
-1, 0, 1
Let g = 27 + -13. Let r be ((-84)/(-98))/(8/g). Factor r*f**2 + 0 + 3*f.
3*f*(f + 2)/2
Let b(w) be the second derivative of w**4/30 - w**3/15 - 7*w. Factor b(k).
2*k*(k - 1)/5
Factor 6 - 345*l + 341*l + 0*l**2 - 2*l**2.
-2*(l - 1)*(l + 3)
Let p be (-39)/(4 - 25/10). Let c be ((-1)/(-4))/((-13)/p). Factor 1/2*a + 0 - 1/2*a**3 - c*a**4 + 1/2*a**2.
-a*(a - 1)*(a + 1)**2/2
Suppose -4/3*f - 26/3*f**3 + 7/3*f**4 - 4/3 + 9*f**2 = 0. What is f?
-2/7, 1, 2
Factor -18/11*i**3 - 10/11*i**4 - 2/11*i**5 + 0 - 4/11*i - 14/11*i**2.
-2*i*(i + 1)**3*(i + 2)/11
Suppose 3*c = 2*c. Let n(g) be the second derivative of 1/20*g**5 + 1/16*g**4 + 0*g**2 + c - 1/24*g**3 - g. Find y, given that n(y) = 0.
-1, 0, 1/4
Factor -6*y - 46 + 30*y + 2*y**2 + 68 + 50.
2*(y + 6)**2
Suppose -3*a = -g, g = -2*g - 5*a + 42. Factor 12 - 12*z + 3*z**4 - 5*z**4 - g*z**2 - z**4 + 12*z**3.
-3*(z - 2)**2*(z - 1)*(z + 1)
Let r(p) be the first derivative of p**5/60 - p**4/18 - p**3/18 + p**2/3 + 5*p - 6. Let d(n) be the first derivative of r(n). Factor d(a).
(a - 2)*(a - 1)*(a + 1)/3
Suppose -4*k = -3*k + 3*k. Let -1/5*b**3 + 3/5*b - 2/5 + k*b**2 = 0. Calculate b.
-2, 1
Factor -3/2*g**2 + 12*g - 24.
-3*(g - 4)**2/2
Let k(h) = -18*h**4 - 37*h**3 + 31*h**2 + 31*h - 7. Let v(o) = 6*o**4 + 12*o**3 - 10*o**2 - 10*o + 2. Let g(b) = 2*k(b) + 7*v(b). Solve g(i) = 0.
-2, -2/3, 0, 1
Let x be (-426)/(-28) + 4/14. Let c = 16 - x. Factor 1/4*i**2 + 3/4*i + c.
(i + 1)*(i + 2)/4
Suppose -12 = 4*y, 0*t - 5 = -t + y. Determine u, given that 4*u**3 - 5*u**3 - u**4 - 3*u**3 + 0*u**3 - 5*u**2 - t*u = 0.
-2, -1, 0
Factor 1/5*h**4 - 3/5*h**2 + 2/5*h + 0*h**3 + 0.
h*(h - 1)**2*(h + 2)/5
Let t(q) be the second derivative of -25*q**7/7 + 13*q**6/4 + 129*q**5/20 - 8*q**4 + 7*q**3/2 - 3*q**2/4 + 5*q. Solve t(s) = 0 for s.
-1, 1/5, 1/4, 1
Let p(t) = -t + 6. Let q be p(3). Factor -2*f + f + 3*f - 2*f**3 + 0*f**q.
-2*f*(f - 1)*(f + 1)
Let b(c) be the second derivative of -7*c**5/20 + 4*c**4/3 - 11*c**3/6 + c**2 + 3*c. Factor b(t).
-(t - 1)**2*(7