h**2 - 10*h = 0. Calculate h.
-1, -2/9, 0, 1/4
Let v(u) = u**3 + 6*u**2 - 29*u - 16. Let z be v(-9). Solve -8/5*q + 8/5 + 6/5*q**3 - 2*q**z = 0.
-1, 2/3, 2
Let l(a) = a**5 - a**4 + a**3 + a**2 - 1. Let w(d) = d**5 - 3*d**4 + 4*d**3 + 2*d**2 - 2. Let t(i) = -6*l(i) + 3*w(i). Factor t(y).
-3*y**3*(y - 1)*(y + 2)
Let b(x) be the first derivative of -x**6/4 - 3*x**5/5 - 10. Factor b(d).
-3*d**4*(d + 2)/2
Let y be (-4)/(-10)*(0 - 5). Let p be (y/(-2))/(4/8). Factor 0*l**p + 4/9*l**3 - 2/9*l**4 + 2/9 - 4/9*l.
-2*(l - 1)**3*(l + 1)/9
Find f, given that -12*f**4 + 22*f**4 + 12*f**5 + 3*f**5 = 0.
-2/3, 0
Let b(x) be the first derivative of -7*x**6/3 - 36*x**5/5 - 109*x**4/14 - 24*x**3/7 - 4*x**2/7 - 5. Factor b(z).
-2*z*(z + 1)**2*(7*z + 2)**2/7
Let k(w) be the second derivative of -w**2/2 - w. Let p(r) = -r**2 + 2. Let q(a) = -6*k(a) - 3*p(a). Solve q(y) = 0 for y.
0
Let u = 10 + -8. Find d, given that 2*d**4 + u*d**2 - 1/2*d**5 - 3*d**3 + 0 - 1/2*d = 0.
0, 1
Let f = 109/165 + 1/165. Factor 2/3*n**2 - f*n + 0.
2*n*(n - 1)/3
Let i be 13 + (0 - (-2 + -2)). Suppose 14*j + 9 = i*j. Determine s, given that -2/5 + 2/5*s + 2/5*s**2 - 2/5*s**j = 0.
-1, 1
Suppose 3*a - 3*w - 5 = -8*w, 5*w - 40 = 4*a. Let j = a + 7. Let -30*d**2 - 24*d**3 + 7*d - 26*d**3 + 11*d - j = 0. What is d?
-1, 1/5
Let p(w) = -2*w**3 - 4*w**2 + 2*w. Let r(x) = 2*x - 4. Let o be r(4). Let s(q) = -q**3 - q**2 + q. Let f(z) = o*s(z) - p(z). Factor f(b).
-2*b*(b - 1)*(b + 1)
Let n(a) be the second derivative of a**7/1680 + a**6/180 - a**5/80 - a**4/12 + 6*a. Let y(o) be the third derivative of n(o). Suppose y(d) = 0. What is d?
-3, 1/3
Let a(p) = -p**3 + 4*p**2 + 2*p - 6. Let g be a(4). Suppose 4*c**2 - 12 + c**2 - c**3 + 12*c + 3*c**4 - 11*c**3 + 4*c**g = 0. Calculate c.
-1, 1, 2
Let q(m) = -4*m**5 - 16*m**4 - 12*m**3 + 2*m - 2. Let i(p) = -3*p**5 - 16*p**4 - 12*p**3 + 2*p - 3. Let r(u) = -2*i(u) + 3*q(u). Find y such that r(y) = 0.
-1, 0, 1/3
Let s(c) be the third derivative of 1/420*c**7 + 1/12*c**3 + 5*c**2 + 0 + 0*c**6 - 1/60*c**5 + 0*c**4 + 0*c. Factor s(q).
(q - 1)**2*(q + 1)**2/2
Let g = 13 - 8. Suppose 8 = 3*z - r, -8 = 3*z - r - 4*r. Factor -x**5 + 7*x**2 + 5*x**4 - g*x + z*x - 2*x - 9*x**3 + x.
-x*(x - 2)*(x - 1)**3
Let u = 21 + -17. Let k(f) be the second derivative of 0*f**2 - 1/10*f**5 - 1/15*f**6 - f + 1/21*f**7 + 0 + 1/6*f**u + 0*f**3. Determine s so that k(s) = 0.
-1, 0, 1
Let p(w) be the third derivative of 1/12*w**4 + 0*w + 1/15*w**5 + 0 + 1/60*w**6 - w**2 + 0*w**3. Factor p(m).
2*m*(m + 1)**2
Let o(n) = -3*n**2 + 13*n. Let y(u) = -u**2 + 4*u. Let r(h) = -2*o(h) + 7*y(h). Factor r(v).
-v*(v - 2)
Let f(l) be the first derivative of 1/10*l**5 + 0*l**3 + 1/16*l**4 + 5 + 0*l**2 + 0*l + 1/24*l**6. Factor f(r).
r**3*(r + 1)**2/4
Let g(y) be the second derivative of -y**7/7 - 7*y**6/15 - y**5/5 + 2*y. Factor g(p).
-2*p**3*(p + 2)*(3*p + 1)
Let n be (-64)/(-30) + 10/(-75). Find y such that -1/4*y + 0 - 3/4*y**n - 3/4*y**3 - 1/4*y**4 = 0.
-1, 0
Let u(q) = -9*q**2 - 9*q. Let i(x) = -3*x**2 - 3*x. Let s = 14 + -22. Let a(l) = s*i(l) + 3*u(l). Factor a(p).
-3*p*(p + 1)
Let h(u) be the third derivative of u**6/600 - u**5/100 + u**4/60 + 3*u**2. Factor h(w).
w*(w - 2)*(w - 1)/5
Let z(h) = -h**2 - 6*h + 10. Let v be z(-7). Let g(i) be the first derivative of 1/2*i + 3/8*i**2 - v + 1/12*i**3. Let g(x) = 0. Calculate x.
-2, -1
Suppose -4*b = -4, 3*b - 30 = -3*z - 0*z. Let x be (-12)/z - (-50)/24. Let 1/4*h**2 + 1/4*h**5 + 0 + 3/4*h**3 + 0*h + x*h**4 = 0. What is h?
-1, 0
Let s be (-1 - -2)/(1/4). Suppose 1 = s*f - 7. Determine k so that 2*k**2 + 8*k + 8 + k**2 - k**f = 0.
-2
Suppose -11*k + 7*k = -8. Factor b - k*b**3 + 1 + 0*b + b**3 - b**2 + 0*b**3.
-(b - 1)*(b + 1)**2
Let u(x) = -x**3 - x**2 + x. Let g(i) = 4*i**3 + 2*i**2 - 8*i + 4. Let j(v) = -g(v) - 2*u(v). Let j(n) = 0. What is n?
-2, 1
Suppose -4 + 8/3*u + 1/3*u**2 - 1/3*u**3 = 0. Calculate u.
-3, 2
Let l be (2/2)/(2/4). Find k such that 3*k**3 + 81*k + 23*k**2 + 81 - 6*k**2 + 10*k**l = 0.
-3
Suppose -5*b - 5 = -15. Let 1/4*p**3 + 0 + 0*p**b - 1/4*p = 0. What is p?
-1, 0, 1
Suppose -2 - 4 = -3*m. Solve 53 - 53 + 3*u**m = 0.
0
Determine x so that 2/13*x**2 + 6/13*x - 8/13 = 0.
-4, 1
Let p(z) be the first derivative of 2*z**3/15 - z**2 - 6. Let p(g) = 0. Calculate g.
0, 5
Let w = -3 - -2. Let i be 3 + (-2 - w - -1). Let 5*o**2 - 9*o**4 - 60*o**5 - 20*o**4 + 3*o**i - 3*o**2 = 0. What is o?
-2/5, -1/3, 0, 1/4
Let h(m) = m**2 + m + 1. Let y(q) = 20*q**2 - 165*q + 25. Let r(i) = 15*h(i) + y(i). Find f, given that r(f) = 0.
2/7, 4
Let p(i) be the second derivative of i**8/224 - i**6/40 + i**4/16 + 3*i**2/2 - i. Let f(n) be the first derivative of p(n). Factor f(o).
3*o*(o - 1)**2*(o + 1)**2/2
Let k(j) be the first derivative of j**3 - 3*j**2 + 3*j + 1. Factor k(h).
3*(h - 1)**2
Let x = 36 - 34. Let y(n) be the second derivative of 3*n - 1/3*n**3 - 1/24*n**4 - n**x + 0. Factor y(j).
-(j + 2)**2/2
Let x be (-2)/(-4)*0*(-3)/9. Factor x + 1/3*t**2 + 1/3*t**3 + 0*t.
t**2*(t + 1)/3
Let w(m) be the first derivative of m**2 - 1 + 8/3*m**3 + 0*m. Solve w(i) = 0.
-1/4, 0
Let p(r) = -r**5 - 3*r**4 - 2*r**3 - r**2 + r. Let t(q) = -q**4 - q**3 - q**2 + q. Let l(y) = -p(y) + t(y). Factor l(c).
c**3*(c + 1)**2
Let u(j) = 46*j**2 - 53*j + 19. Let x(n) = 45*n**2 - 52*n + 20. Suppose -3 = -5*g + 17. Let s(c) = g*u(c) - 3*x(c). Find t, given that s(t) = 0.
4/7
Find w such that -35*w**3 + 15*w**4 + 6*w**2 + 3*w**2 + w**2 = 0.
0, 1/3, 2
Let i = -24 - -26. Suppose i*j + 10 = 7*j. Factor 1/2*x**4 - x**j + 1/2*x + 1/2 - x**3 + 1/2*x**5.
(x - 1)**2*(x + 1)**3/2
Let g be 4*1/(-4)*(-2)/7. Suppose -g*k + 2/7 - 6/7*k**3 - 10/7*k**2 = 0. Calculate k.
-1, 1/3
Let w = 22 - 18. Let c(h) be the second derivative of 0 - 3*h - 1/100*h**5 - 1/30*h**3 + 1/30*h**w + 0*h**2. Factor c(u).
-u*(u - 1)**2/5
Let i(t) be the second derivative of t**9/15120 - t**8/1680 + t**7/630 + t**4/12 - 3*t. Let y(d) be the third derivative of i(d). Factor y(s).
s**2*(s - 2)**2
Let q(v) be the first derivative of 3*v**4 + 32*v**3/3 - 6*v**2 + 5. Factor q(t).
4*t*(t + 3)*(3*t - 1)
Let l(t) be the second derivative of 0 + 1/12*t**3 + 3/16*t**5 - 3/16*t**4 + 1/56*t**7 + 0*t**2 - 11/120*t**6 - 3*t. Solve l(q) = 0.
0, 2/3, 1
Let j(b) = 10*b**3 + 10*b**2 - 7*b + 7. Let h(a) = -2*a + 1 + 3*a**3 - 1 - 2 + 3*a**2 + 4. Let r(w) = 7*h(w) - 2*j(w). Suppose r(o) = 0. What is o?
-1, 0
Let o(q) = -q - 1. Suppose 4*y - y - 6 = 0. Let c(d) = -4*d - 5*d + 4 - 12 - d**y. Let m(r) = c(r) - 6*o(r). Factor m(b).
-(b + 1)*(b + 2)
Factor 0*d**4 + 25*d - d**3 + d**2 - 45*d - d**4 + 21*d.
-d*(d - 1)*(d + 1)**2
Let i(n) = n**3 + 4*n**2 - 20*n + 9. Let j be i(-7). Solve 18/5*f**j + 14/5*f**3 - 24/5*f - 8/5 = 0 for f.
-2, -2/7, 1
Suppose -12 + 36 = 3*z. Let h = z - 4. Factor 275/3*w**h + 0 + 68/3*w**2 + 125/3*w**5 + 70*w**3 + 8/3*w.
w*(w + 1)*(5*w + 2)**3/3
Suppose -2/17*s**5 - 2/17*s + 0 - 12/17*s**3 + 8/17*s**2 + 8/17*s**4 = 0. Calculate s.
0, 1
Factor 3/5*m**2 + 1/5*m**3 + 1/5 + 3/5*m.
(m + 1)**3/5
Find i such that 56/3*i - 4*i**2 + 20/3 = 0.
-1/3, 5
Let f(w) = 24*w**3 + 155*w**2 + 221*w + 85. Let u(g) = -156*g**3 - 1008*g**2 - 1436*g - 552. Let j(s) = -32*f(s) - 5*u(s). Factor j(y).
4*(y + 1)*(y + 5)*(3*y + 2)
Find a such that -3/5*a**2 + 0 + 33/5*a = 0.
0, 11
Let j(d) = 8*d**4 + 2*d**3 - 12*d**2 - 25*d - 10. Let u(s) = s**4 - s**3 + s**2. Let p(t) = j(t) - 3*u(t). Factor p(c).
5*(c - 2)*(c + 1)**3
Suppose 7*n = 4*n + 15. Factor n*r**2 - r**2 - 1 + 0*r**2 - 3*r**2.
(r - 1)*(r + 1)
Let z(s) be the third derivative of s**8/112 - s**7/210 - 7*s**6/180 + s**5/90 + 5*s**4/72 + s**3/18 + 7*s**2. Let z(b) = 0. Calculate b.
-1, -1/3, 1
Let t(v) be the first derivative of -v**5/45 - v**4/18 - v**3/27 + 27. Factor t(w).
-w**2*(w + 1)**2/9
Factor 21*o + o**3 - 2*o**2 - 4 - 13*o - 3*o**2.
(o - 2)**2*(o - 1)
Suppose 0 = 3*z - 2*c - 16, -z + 3*c = 2*c - 6. Suppose 7*l = z*l. Factor 0*b**2 + l + 0*b - 2/5*b**3.
-2*b**3/5
Let z(i) = -i**3 - 8*i**2 + 10*i + 12. Let k be z(-9). Let v(a) be the first derivative of -3/4*a**2 + 3/8*a**4 - 1 + 1/2*a - 1/6*a**k. Solve v(y) = 0 for y.
-1, 1/3, 1
Let u = 5/9 - -7/36. Suppose -u*i**2 + 0*i**3 + 0 + 0*i + 3/4*i**4 = 0. What is i?
-1, 0, 1
Let t(o) = 2*o - 2. Let g(q) = -q - 1. Let z be g(-4).