r = -25 + 30. Suppose j = 3*u - 3, -4*u - 2 + 8 = -2*j. Factor -2/7*y + 8/7*y**4 - 12/7*y**3 + u + 8/7*y**2 - 2/7*y**r.
-2*y*(y - 1)**4/7
Let v be (-4)/(-1) - (-3 - (-19)/3). Let v*z**2 + 2/9 - 2/9*z**3 - 2/3*z = 0. Calculate z.
1
Let c(k) = -k**2 - 5*k - 4. Let l be c(-4). Let z(s) be the third derivative of 1/150*s**5 + 0 + 0*s**3 - 1/60*s**4 + s**2 + l*s. Factor z(m).
2*m*(m - 1)/5
Let u(f) be the second derivative of 0*f**2 + 1/16*f**4 + 0*f**5 + 0 + 0*f**3 + 8*f - 1/40*f**6. Let u(z) = 0. Calculate z.
-1, 0, 1
Factor -9/4*h**2 + 3/4 - 33/8*h.
-3*(h + 2)*(6*h - 1)/8
Let -27*n**2 + 5*n**2 - 15*n + 4*n**5 - 18*n**2 - 30*n**3 + n**5 = 0. What is n?
-1, 0, 3
Let c(j) be the second derivative of j**6/10 + 9*j**5/10 + j**4/4 - 12*j**3 + 24*j**2 + 17*j. Factor c(t).
3*(t - 1)**2*(t + 4)**2
Let k be (6 + -7)/((-2)/6). Suppose -5*l**4 + 2*l - 4*l**2 - 4*l + k*l**4 - 6*l**3 - 2*l**2 = 0. What is l?
-1, 0
Solve 2/7*x + 0 - 2/21*x**2 = 0.
0, 3
Let y be 5 - (3 - (4 - 3)). Factor -2/5*x**2 + 4/5*x**y + 0*x - 2/5*x**4 + 0.
-2*x**2*(x - 1)**2/5
Let u(z) be the second derivative of -3*z**9/224 - 3*z**8/224 + 2*z**7/105 - z**6/180 + z**3/3 - 5*z. Let r(k) be the second derivative of u(k). Factor r(q).
-q**2*(q + 1)*(9*q - 2)**2/2
Let m(x) be the second derivative of -x**6/165 + x**5/55 + 41*x. Let m(j) = 0. What is j?
0, 2
Let u(o) be the first derivative of -o**6/48 - o**5/8 - 5*o**4/16 - 5*o**3/12 - 5*o**2/16 - o/8 + 4. Factor u(g).
-(g + 1)**5/8
Let a(u) = -u + 12. Let t be a(0). Suppose t = 4*p - p. Factor 3*v**4 - 4*v**p + v**5 - 2*v**4 + 0*v**4 - v**2 + 3*v**3.
v**2*(v - 1)**3
Let v = -2 + 3. Let u = 87 + -85. Factor b + v + 1/4*b**u.
(b + 2)**2/4
Let i = -1 - -3. Let v = i - -1. Factor v*z**4 + 5*z**5 + 2*z**2 - 3*z**5 - 5*z**4 - 2*z**3.
2*z**2*(z - 1)**2*(z + 1)
Let z(u) = u + 8. Let s be z(-6). Factor 0 - 10*a**s - 8 + a + 19*a + 4*a.
-2*(a - 2)*(5*a - 2)
Let y(f) = -6*f**2 + 6*f**2 + 1 - f + 0 - f**2. Let s(p) = 51*p**2 + 30*p + 2. Let v(z) = -s(z) - 2*y(z). Factor v(t).
-(7*t + 2)**2
Let m(w) be the second derivative of 0 + 2*w + 1/2*w**2 - 1/12*w**4 - 1/6*w**3 + 1/20*w**5. Factor m(v).
(v - 1)**2*(v + 1)
Suppose -4*w + 155 = 5*l, 3*l - 2*l - 2 = 5*w. Factor -50*m**2 + 24*m**2 + m**3 + l + 35*m**2 + 27*m.
(m + 3)**3
Factor 2/7*i - 2/7*i**3 + 4/7*i**2 - 4/7.
-2*(i - 2)*(i - 1)*(i + 1)/7
Suppose -20*t**3 + 647 + 19*t**3 - 15*t**2 - 300*t + 353 + 45*t**2 = 0. What is t?
10
Let c(t) be the second derivative of t**4/28 - 3*t**3/14 + 3*t**2/7 + 3*t. Factor c(z).
3*(z - 2)*(z - 1)/7
Let y(w) = 70*w**4 - 79*w**3 - 120*w**2 + 29*w - 11. Let i(f) = -35*f**4 + 39*f**3 + 60*f**2 - 14*f + 6. Let a(n) = 11*i(n) + 6*y(n). Factor a(c).
5*c*(c - 2)*(c + 1)*(7*c - 2)
Factor -3/4*k**3 - 1/8*k**5 + 1/2*k**2 - 1/8*k + 1/2*k**4 + 0.
-k*(k - 1)**4/8
Let p(n) = -3*n - 1. Let s be p(-1). Factor -2*o + o**2 - o**2 - o**s.
-o*(o + 2)
Let l(h) be the first derivative of 1 - 3/7*h**2 - 4/7*h - 2/21*h**3. Factor l(o).
-2*(o + 1)*(o + 2)/7
Let d(c) be the first derivative of -4*c**3/3 - 12*c**2 + 28*c - 31. Let d(a) = 0. Calculate a.
-7, 1
Find g such that -2/11*g**2 + 0 + 0*g**3 + 0*g + 2/11*g**4 = 0.
-1, 0, 1
Let a(z) = -2*z**5 - 2*z**4 - 5*z**3 - 2*z**2 + 4*z + 4. Let x(t) = t**5 + t**4 + t**3 - t - 1. Let o(y) = -5*a(y) - 15*x(y). Let o(j) = 0. Calculate j.
-1, 1
Let d be 1/4 - 0/(-1). Let i be (-49)/28 - (1 - 3). Let 0 - i*b - d*b**2 = 0. Calculate b.
-1, 0
Let j(f) = -1 - 3*f**2 + 1 + 1 + 1. Suppose -4*c + 2*r = -2*r + 24, -5*c = 2*r + 9. Let n(l) = -4*l**2 + 3. Let k(h) = c*j(h) + 2*n(h). Factor k(q).
q**2
Let j(t) = t**4 - t**2 - 3*t**3 + 6*t**3 - 4*t**3. Let p(g) = -8*g**4 + 10*g**3 + 12*g**2 - 8*g - 8. Let h(q) = -6*j(q) - p(q). Factor h(k).
2*(k - 2)**2*(k + 1)**2
Let l(w) be the second derivative of -w**4/12 - 4*w. Factor l(r).
-r**2
Suppose -9*y + 6*y = -6. Determine s, given that -13*s**y - 2*s + 10*s**2 + 0*s**3 - s**3 = 0.
-2, -1, 0
Let w(x) = -20*x**2 - 60*x - 40. Let g(t) = -5*t**2 - 15*t - 10. Let b(m) = 9*g(m) - 2*w(m). Suppose b(k) = 0. What is k?
-2, -1
Suppose -4*n + 0*n = -20. Suppose 25 = n*f - 5*z, -2*z = -f + 2*f + 4. Factor -5*k - 1/2 - 25/2*k**f.
-(5*k + 1)**2/2
Let z(s) be the second derivative of -s**4/66 + 5*s**3/33 + 14*s**2/11 + s - 12. Let z(x) = 0. Calculate x.
-2, 7
Let u(f) be the third derivative of f**5/138 - 13*f**4/276 - 2*f**3/23 - 36*f**2. Factor u(l).
2*(l - 3)*(5*l + 2)/23
Let j(f) = 112*f**4 - 92*f**3 - 100*f**2 + 92*f + 12. Let z(g) = -45*g**4 + 37*g**3 + 40*g**2 - 37*g - 5. Let x(l) = 5*j(l) + 12*z(l). Solve x(u) = 0.
-1, 0, 4/5, 1
Suppose -l + 5*h - 20 = 0, 5*h = -2*l + h + 16. Let r(v) be the second derivative of 0*v**3 + 1/36*v**4 - 1/20*v**5 + v + 1/45*v**6 + 0*v**2 + l. Factor r(o).
o**2*(o - 1)*(2*o - 1)/3
Let y(a) = a**3 + a - 1. Let z(i) = 12*i**3 + 4*i**2 + 14*i - 14. Let c(m) = 28*y(m) - 2*z(m). Factor c(w).
4*w**2*(w - 2)
Let p be 5 + 3 + (-8 - -2). Factor 2*z**4 + 3*z**5 + z**3 + 0*z**4 - p*z**5.
z**3*(z + 1)**2
Factor 1/4*b**4 + 5/4*b**3 + 2*b**2 + b + 0.
b*(b + 1)*(b + 2)**2/4
Let p(b) = b**2 - 5*b - 15. Let y(m) = m**2 - 5*m - 16. Let k(z) = 6*p(z) - 5*y(z). Let x be k(7). Factor -2*l + x*l**2 - 3*l**2 + l**2.
2*l*(l - 1)
Let j be 560/98 - (-2)/7. Let v(w) = 4*w**2 - w + 3. Let c(d) = -9*d**2 + d - 6. Let z(r) = j*c(r) + 14*v(r). What is h in z(h) = 0?
1, 3
Let l(s) = -3*s**4 - 5*s**3 - 3*s**2 - s. Let c(q) = -7*q**4 - 11*q**3 - 6*q**2 - 2*q. Let t(o) = -2*c(o) + 5*l(o). Solve t(k) = 0.
-1, 0
Let m(y) be the third derivative of -y**8/3360 - y**7/1512 - y**6/2160 - y**4/24 - 6*y**2. Let x(f) be the second derivative of m(f). Factor x(d).
-d*(2*d + 1)*(3*d + 1)/3
Let p(a) be the first derivative of -2*a**5/25 - 5. Factor p(v).
-2*v**4/5
Let t(r) be the first derivative of r**8/3920 - r**7/392 + 3*r**6/280 - r**5/40 + r**4/28 + 2*r**3/3 - 3. Let g(h) be the third derivative of t(h). Factor g(l).
3*(l - 2)*(l - 1)**3/7
Let a = -33/7 - -799/168. Let c(t) be the third derivative of 1/60*t**5 + 0 - a*t**4 + 3*t**2 + 0*t**3 + 0*t. Factor c(j).
j*(j - 1)
Let a be (-20)/(-2) + (14 - 17). Let q(d) be the third derivative of 0*d + 0 + 1/60*d**5 - 4*d**2 + 1/120*d**6 - 1/210*d**a + 0*d**3 - 1/24*d**4. Factor q(c).
-c*(c - 1)**2*(c + 1)
Let z = 3/16 - -119/48. What is x in 64/9*x - 2*x**3 + z + 10/3*x**2 = 0?
-2/3, 3
Let h(p) = p**3 - 4*p**2 + p - 1. Let y be h(4). Let f(r) = -r + 7. Let d be f(4). Suppose -x - 2*x**d - x**3 - x**4 + 0*x**y - 3*x**2 = 0. Calculate x.
-1, 0
Let u(a) = -2*a**2 + 8*a - 4. Let q(h) = 2*h + 2 - h**2 + 3*h**2 + 1 - 10*h. Suppose 1 = x - 4. Let f(c) = x*u(c) + 4*q(c). Factor f(o).
-2*(o - 2)**2
Let j(b) be the second derivative of b**5/90 + 2*b**4/9 + 7*b**3/9 + 10*b**2/9 + 2*b - 26. Determine p so that j(p) = 0.
-10, -1
Let m = 2/13 + 3/65. Factor -1/5*b**2 + 1/5 - 1/5*b + m*b**3.
(b - 1)**2*(b + 1)/5
Let m = 11 + -7. Let r be (4 - 3)/(1/m). Let -2*n**r + 0*n**3 + 4*n**4 - 2*n**3 = 0. What is n?
0, 1
Let z(l) = -l + 1. Let h(t) = -63*t**5 - 60*t**4 + 72*t**3 + 66*t**2 - 7*t - 8. Suppose 3 = -3*o + 6. Let v(p) = o*h(p) + 2*z(p). What is c in v(c) = 0?
-1, -2/7, 1/3, 1
Let g = 20 - 2. Solve -7*i + 4*i**5 + 20*i**4 + 10*i**2 + 36*i**3 + 15*i + g*i**2 = 0 for i.
-2, -1, 0
Let d be (-16)/8*(-2)/4 + 1. Let i(m) be the second derivative of 0 - 1/75*m**6 + 3/50*m**5 + 0*m**d - 2*m - 1/10*m**4 + 1/15*m**3. Solve i(s) = 0.
0, 1
Let w(p) be the third derivative of -3*p**2 + 0*p**3 + 1/24*p**4 + 0 + 0*p - 1/120*p**5 - 1/120*p**6 + 1/420*p**7. Determine r so that w(r) = 0.
-1, 0, 1, 2
Let g = -4/47 - -114/235. Determine i, given that -2/5*i**2 - 4/5*i + g*i**3 + 0 = 0.
-1, 0, 2
Let x(r) be the second derivative of -5*r - 1/4*r**3 - 1/8*r**2 + 0 - 3/16*r**4 - 1/20*r**5. Factor x(l).
-(l + 1)**2*(4*l + 1)/4
Let s(g) = -g**4 + g**3 - 5*g**2 - g. Let x(y) = -5*y**4 + 5*y**3 - 20*y**2 - 5*y. Let u(v) = 25*s(v) - 6*x(v). Let u(c) = 0. Calculate c.
-1, 0, 1
Suppose 0 = -2*n + 6, 3*n - 9 = 2*w - w. Let c(m) be the first derivative of -1 - 4/9*m**3 + w*m + 0*m**2 + 0*m**5 + 1/2*m**4 - 1/9*m**6. Factor c(o).
-2*o**2*(o - 1)**2*(o + 2)/3
Let p(a) = 8*a + 24. Let x be p(-3). Let y(g) be the third derivative of x*g + 0 - 1/20*g**5 + 1/120*g**6 - 1/6*g**3 - g**2 + 1/8*g**4. Factor y(j).
(j - 1)**3
Let w(i) = i**2 + 7*i + 