, 6
Suppose 22 = 4*h - 2. Let p be 16/h + (-2)/3. Let p*l**3 - l**3 + l**3 = 0. Calculate l.
0
Suppose 2*p - 2 = -4*s + 3*s, 8 = 4*s - 4*p. Factor -n + 0*n - n**2 + n**2 + s*n**2.
n*(2*n - 1)
Let r(z) be the third derivative of 0 + 7*z**2 - 1/36*z**4 + 0*z + 0*z**3 + 2/45*z**5. Find s, given that r(s) = 0.
0, 1/4
Let t(j) be the first derivative of 3*j**2 - 5 + 2 - 2 + 9*j**3. Factor t(l).
3*l*(9*l + 2)
Let h = -4647/7 - -665. Let b(u) be the first derivative of h*u - 3 + 2/21*u**3 - 4/7*u**2. Factor b(g).
2*(g - 2)**2/7
Let c be ((-2)/4)/(3/(-60)). Let g = 12 - c. Suppose -1 - 1 - 3*j + g - 15*j**2 + 15*j**4 + 3*j**3 = 0. What is j?
-1, -1/5, 0, 1
Let l(u) be the third derivative of 0*u + 1/60*u**5 + 1/24*u**4 - 1/3*u**3 + 0 + 3*u**2. Determine o so that l(o) = 0.
-2, 1
Let d(p) be the third derivative of p**5/60 + p**4/8 - p**3/3 + p**2. Let w be d(3). Factor 12*y**3 - 8*y**4 - 14*y + w*y + 5*y**5 - 8*y**2 - 3*y**5.
2*y*(y - 1)**4
Let c(q) be the second derivative of 3/5*q**5 + 0*q**2 + 2/3*q**4 + 4*q - 2/21*q**7 + 0 + 0*q**6 + 0*q**3. What is g in c(g) = 0?
-1, 0, 2
Let v = 12 - 7. Suppose 0 = s + 3 - v. Factor -2*x + 2/3 - 2/3*x**3 + s*x**2.
-2*(x - 1)**3/3
Let w(v) = -v**3 + 7*v**2 + 2*v + 10. Let l be w(7). Suppose -l*b**2 + 3*b**2 - b + 7*b = 0. What is b?
0, 2/7
Let h(i) be the first derivative of 1 + 1/7*i**2 + 0*i + 4/21*i**3 - 1/21*i**6 - 4/35*i**5 + 0*i**4. Factor h(l).
-2*l*(l - 1)*(l + 1)**3/7
Find g such that -130*g**2 + 5*g**2 + 35*g**2 + 39*g**2 + 3*g**3 - 192 + 240*g = 0.
1, 8
Suppose 26 = 18*a - 28. Factor 4/5*v**2 - 6/5*v**4 - 2/5*v**5 + 2/5 - 4/5*v**a + 6/5*v.
-2*(v - 1)*(v + 1)**4/5
Suppose -5*t - 5 = -6*t. Let g(l) be the third derivative of 1/90*l**t - 1/9*l**3 - 4*l**2 + 0*l**4 + 0*l + 0. Factor g(b).
2*(b - 1)*(b + 1)/3
Let s(l) be the first derivative of -2*l - 1 - 1/4*l**4 + 0*l**2 + 0*l**3 + 3/20*l**5. Let z(r) be the first derivative of s(r). Factor z(m).
3*m**2*(m - 1)
Let h be (5 + -2)/(-3)*18. Let t be 3/(-5) + h/(-30). What is o in t + 0*o + 1/2*o**2 = 0?
0
Let t(s) be the first derivative of -s**3 + s**2/2 - 6*s + 9. Suppose 5*i - i = -4. Let a(l) = l**2 + 1. Let q(k) = i*t(k) - 4*a(k). Solve q(y) = 0 for y.
-2, 1
Let w = 62413 + -3744863/60. Let j = -1/20 - w. Factor 1/3*o**3 + 8/3*o - 5/3*o**2 - j.
(o - 2)**2*(o - 1)/3
Let h(r) be the first derivative of 3*r**5/10 - 7*r**4/8 + 5*r**3/6 - r**2/4 + 11. Find f such that h(f) = 0.
0, 1/3, 1
Let p = -7 - -9. Suppose -2*h = p*h - 12. Factor 4*y - h + 0 + 2*y + 0*y - 3*y**2.
-3*(y - 1)**2
Suppose 4*a - 6 - 10 = 0. Determine p, given that 8*p**3 - a*p + 2 + 1 - 6 - 2*p**4 - 4*p**5 + 4*p**2 + 1 = 0.
-1, -1/2, 1
Let r = 2 - 0. Factor -221 - 4*g + 2*g**r + 2*g**3 + 221 - 4*g**2.
2*g*(g - 2)*(g + 1)
Let v(w) be the first derivative of -14/5*w**3 + 3 - 4/5*w - 2/5*w**5 + 17/10*w**4 + 11/5*w**2. Find m, given that v(m) = 0.
2/5, 1
Suppose 2*i - 11 = q, -q - 12 = -i - 2*i. Let h(x) = x + 12. Let f be h(q). Let 1/3*y + 0 + 2/3*y**2 + 1/3*y**f = 0. Calculate y.
-1, 0
Let d(h) = h**4 + h**2 - h. Let p(k) = k**4 + 2*k**2 - 2*k. Let n(t) = -2*d(t) + p(t). Let n(y) = 0. What is y?
0
Let j(q) be the first derivative of -q**3/9 + 2*q**2/3 + 5*q/3 + 17. Let j(k) = 0. Calculate k.
-1, 5
Let w(q) be the first derivative of q**9/6048 + q**8/1680 + q**7/1680 - q**3 - 2. Let g(a) be the third derivative of w(a). Factor g(s).
s**3*(s + 1)**2/2
Factor -1/2*x**3 + 0*x**2 - 1 + 3/2*x.
-(x - 1)**2*(x + 2)/2
Let o(v) = -v**3 + 7*v**2 - 5*v - 3. Let h be o(6). Factor -5*f**2 - 3*f + 0*f**3 + 3 + h*f**4 - f**2 - 3*f**5 + 6*f**3.
-3*(f - 1)**3*(f + 1)**2
Suppose 10 = 3*s - 2*i + i, 5*s = -i + 30. Let a(m) be the first derivative of 2 + 1/6*m**3 + 1/10*m**s + 1/4*m**4 + 0*m + 0*m**2. Solve a(h) = 0 for h.
-1, 0
Let f be 2/8 - 685/20. Let g(l) = 4*l**2 + l + 3. Let k(o) = 23*o**2 + 5*o + 17. Let m(t) = f*g(t) + 6*k(t). Factor m(a).
2*a*(a - 2)
Let a(i) be the second derivative of i**7/210 - 2*i**5/25 + 8*i**3/15 - 18*i. Determine v so that a(v) = 0.
-2, 0, 2
Let n(i) = -3*i**4 - 24*i**3 - 18*i**2 + 9*i. Let y(d) = d**3 - d. Let v(r) = -n(r) - 9*y(r). Factor v(f).
3*f**2*(f + 2)*(f + 3)
Let n be 6/51*995/120. Let q = n + 14/51. Factor -13/4*a - 3/2 + q*a**2.
(a - 3)*(5*a + 2)/4
Let j be 5/((-15)/9) - 1. Let i be (-1 - j)/(-1)*-1. Factor 0*g - 1/2*g**i + 3/4*g**2 - 1/4.
-(g - 1)**2*(2*g + 1)/4
Let g = 47 + -35. Suppose 5*r = 2*r + g. Solve 4/13*p**3 - 2/13 - 4/13*p + 2/13*p**r + 0*p**2 = 0 for p.
-1, 1
Let t be (235/(-165) + 1)*(-6)/7. Suppose 0 + 6/11*d**2 - t*d = 0. What is d?
0, 2/3
Let b be (-4)/(-30)*(4 - -1). Find j such that b*j**3 + 1/3*j**4 - 2/3*j - 1/3 + 0*j**2 = 0.
-1, 1
Let b(p) = p - 1. Let t(a) = 3*a**2 - 5*a + 3. Let u(f) = 15*b(f) + 5*t(f). Factor u(m).
5*m*(3*m - 2)
Let n(l) = 5*l**3 - 6*l**2 - 3*l - 4. Let o(u) = u**3 - u**2 - u - 1. Let j(a) = n(a) - 4*o(a). Find x, given that j(x) = 0.
0, 1
Suppose 2*v = 6, -3*u + 4*v - 2 - 1 = 0. Let 4*q**3 + q**4 + 3*q**5 - 7*q**u - 4*q**4 + 3*q**2 = 0. What is q?
-1, 0, 1
Let q(o) = -6*o**3 + 11*o**3 - o**3. Let a(v) = v**3. Let p(y) = 7*a(y) - 2*q(y). Let p(u) = 0. Calculate u.
0
Let u be (-5*4/(-20))/((-10)/(-4)). Determine n so that u*n + 2/5*n**2 + 0 = 0.
-1, 0
Let n(p) be the third derivative of p**8/3360 - p**7/1260 - p**6/360 + p**5/60 + 5*p**4/24 + 2*p**2. Let a(v) be the second derivative of n(v). Factor a(t).
2*(t - 1)**2*(t + 1)
Let u(p) be the second derivative of p**5/300 - p**4/120 + 2*p**2 - 2*p. Let t(d) be the first derivative of u(d). Determine s so that t(s) = 0.
0, 1
Suppose 2*d - 4 = 0, -w + 1 - 7 = -4*d. Let y = -7/18 + 8/9. Factor y - 1/4*l**w + 1/4*l.
-(l - 2)*(l + 1)/4
Let f = -47515/48 - -990. Let n(h) be the third derivative of 0 - 1/40*h**5 - f*h**4 - 1/6*h**3 + h**2 + 0*h. Factor n(o).
-(o + 1)*(3*o + 2)/2
Let b(g) = 32*g**2 + 5*g + 22. Let c(l) = -48*l**2 - 7*l - 33. Let y(i) = 8*b(i) + 5*c(i). Let k(f) = 3*f**2 + f + 2. Let d(w) = -11*k(w) + 2*y(w). Factor d(o).
-o*(o + 1)
Let q(x) = -2*x - 4. Let c be q(-3). Factor -3*g**2 + 3*g + 6*g**3 + g**4 + 10*g**c - g**3.
g*(g + 1)**2*(g + 3)
Let y be (-36)/(-504)*(1 + 0 - -3). Let v(i) be the first derivative of -3/14*i**2 + 4 - y*i - 1/21*i**3. Let v(r) = 0. What is r?
-2, -1
Factor -2/3*p**2 - 8/3 - 8/3*p.
-2*(p + 2)**2/3
Suppose 10 = 26*o + 10. Factor 0 + 0*x - 1/4*x**5 - 1/4*x**3 + o*x**2 - 1/2*x**4.
-x**3*(x + 1)**2/4
Find p, given that -1/2*p**3 - 1/2*p**4 + 1/2*p**5 + 1/2*p**2 + 0 + 0*p = 0.
-1, 0, 1
Let c(g) = g - 1. Let t be c(4). Suppose -2*v = -3*v + 3. Suppose -d**v - 3*d**t + 3*d**3 = 0. Calculate d.
0
Let j(h) = h**5 - 8*h**4 - 11*h**3 + 4*h**2 + 7*h + 4. Let f(n) = -2*n**5 + 8*n**4 + 12*n**3 - 4*n**2 - 6*n - 4. Let w(m) = -3*f(m) - 4*j(m). Solve w(q) = 0.
-2, -1, 1
Let b(m) be the second derivative of -3*m**6/55 + 3*m**5/55 - m**4/66 - 2*m + 58. Determine g, given that b(g) = 0.
0, 1/3
Solve 0 + 0*b + 5/6*b**4 + 1/6*b**5 + 0*b**2 + 2/3*b**3 = 0.
-4, -1, 0
Determine o so that 0*o**4 + 1/3*o + 1/3*o**5 + 0 - 2/3*o**3 + 0*o**2 = 0.
-1, 0, 1
Let r(h) = 5*h**3 - 5*h**2 - 5*h + 1. Let b(v) = -26*v**3 + 26*v**2 + 26*v - 4. Let g(z) = 2*b(z) + 11*r(z). Factor g(j).
3*(j - 1)**2*(j + 1)
Let r(o) be the first derivative of o**6/54 + o**5/15 + o**4/18 - 2*o**3/27 - o**2/6 - o/9 - 1. Factor r(p).
(p - 1)*(p + 1)**4/9
Let c(s) be the second derivative of s**5/16 + s**4/6 + s**3/8 - 10*s. Suppose c(f) = 0. What is f?
-1, -3/5, 0
Let v(g) be the first derivative of g**4/16 - g**3/4 + 5. Factor v(z).
z**2*(z - 3)/4
Let p(n) be the second derivative of -n**7/10080 - n**6/360 - n**5/30 - n**4/2 + 9*n. Let f(j) be the third derivative of p(j). Factor f(r).
-(r + 4)**2/4
Suppose 0*m**4 + 2/3*m - 4/3*m**3 + 0 + 2/3*m**5 + 0*m**2 = 0. Calculate m.
-1, 0, 1
Let m(z) = z - 6. Let n be m(11). Factor 0 - 6*o**3 + 3/2*o**2 + 15/2*o**4 - 3*o**n + 0*o.
-3*o**2*(o - 1)**2*(2*o - 1)/2
Factor -3/2*z**2 - 9*z - 15/2.
-3*(z + 1)*(z + 5)/2
Let g(v) = v**3 + v**2 + v + 1. Let k(x) = 6*x**3 + 74*x**2 + 434*x + 866. Let l(t) = 2*g(t) - k(t). Solve l(u) = 0 for u.
-6
Let l(v) be the second derivative of 3*v**5/25 + 9*v**4/20 + v**3/5 - 8*v. Find x such that l(x) = 0.
-2, -1/4, 0
Let s(k) be the second derivative of 2*k**7/21 - 13*k**6/45 - k**5/15 + 7*k**4/18 + 2*k**3/9 + 5*k. Suppose s(