 - 1)**2/3
Let h(r) = -15*r**5 - r**4 + 9*r**3 + 16*r**2 - r - 8. Let u(b) = -7*b**5 - b**4 + 5*b**3 + 8*b**2 - b - 4. Let m(o) = -3*h(o) + 7*u(o). Factor m(v).
-4*(v - 1)**2*(v + 1)**3
Let 0*h**3 + 3/4 + 2*h + 3/2*h**2 - 1/4*h**4 = 0. Calculate h.
-1, 3
Let k(b) be the first derivative of -b**7/2520 + b**5/360 + b**3/3 - 2. Let a(c) be the third derivative of k(c). Factor a(u).
-u*(u - 1)*(u + 1)/3
Let f(s) be the third derivative of 0*s**4 + 1/240*s**6 + 0 + 0*s**3 - 3*s**2 - 1/360*s**5 + 0*s. Let f(q) = 0. Calculate q.
0, 1/3
Let i(w) be the third derivative of -w**5/60 + w**4/4 + 6*w**2. Let r be i(5). Suppose -4/7*u**4 - 2/7*u**3 + 4/7*u**2 + 2/7*u**r + 0 + 0*u = 0. What is u?
-1, 0, 1, 2
Let a(y) be the first derivative of 3*y**5/35 + 13*y**4/28 - y**3/21 - 33*y**2/14 + 18*y/7 - 27. Determine o, given that a(o) = 0.
-3, 2/3, 1
Let d(l) be the third derivative of 11*l**7/560 + l**6/160 - 29*l**2. Factor d(a).
3*a**3*(11*a + 2)/8
Let w(d) be the third derivative of d**5/15 - d**4/2 + 4*d**3/3 + 29*d**2. Factor w(u).
4*(u - 2)*(u - 1)
Let t = -13/17 + 73/51. Factor 0*q + 0 + 2/3*q**3 - 2/3*q**5 + 2/3*q**4 - t*q**2.
-2*q**2*(q - 1)**2*(q + 1)/3
Let t(m) be the first derivative of 0*m**5 + 0*m**2 + 0*m - 1/1260*m**6 - 2 + 0*m**4 + 1/3*m**3. Let p(h) be the third derivative of t(h). Factor p(n).
-2*n**2/7
Factor 4*t + 8*t - 12*t**2 + 3*t**3 + 0*t**3 + 0*t.
3*t*(t - 2)**2
Let d(s) be the first derivative of -s**5/24 + s**4/6 + s**3/3 - s**2 - 2. Let g(i) be the second derivative of d(i). Solve g(a) = 0 for a.
-2/5, 2
Let q = -107 + 322/3. Find g such that 1/3*g**5 - q*g**3 - 1/3*g**4 + 0*g + 1/3*g**2 + 0 = 0.
-1, 0, 1
Suppose 20*u**3 + 5*u**4 + 9*u**4 - 11*u**4 - 84*u + 4*u**2 + u**4 - 72 = 0. Calculate u.
-3, -1, 2
Let c(s) be the first derivative of 1/5*s**4 - 2/5*s**2 + 0*s**3 - 2/5*s + 2/25*s**5 + 2. Factor c(x).
2*(x - 1)*(x + 1)**3/5
Let i(s) = s**2 + 6*s - 4. Suppose -4*l - 5*b - 34 = -3*b, 0 = -3*l - 3*b - 30. Let n be i(l). Factor 2 - 3*h**3 - 5*h + 3*h**n + 2*h**3 - 2*h**2 + 3*h.
2*(h - 1)**2*(h + 1)
Factor 4/3*q + 10/9*q**2 + 0 - 4/9*q**3 - 2/9*q**4.
-2*q*(q - 2)*(q + 1)*(q + 3)/9
Let w = 95/248 + -1/124. Let y(f) be the first derivative of -3 - w*f**2 + 1/16*f**4 + 0*f**3 - 1/2*f. Factor y(b).
(b - 2)*(b + 1)**2/4
Let k(y) be the third derivative of -y**5/60 - y**4/2 - 3*y**2. Let v be k(-12). Factor 2/7*s + v*s**4 + 2/7*s**5 - 4/7*s**3 + 0*s**2 + 0.
2*s*(s - 1)**2*(s + 1)**2/7
Let b be -3 + (1 - (336/(-52) + 4)). Suppose 8/13*u - 2/13 - b*u**2 = 0. What is u?
1/3, 1
Let -28*t**4 + 4 - 8*t**2 + 0*t**2 + 32*t**4 = 0. What is t?
-1, 1
Let h(p) = p**3 + 2*p**2 - p + 2. Let n be h(-2). Let f be ((2 - 8) + 1)*-1. Suppose -2*y**4 - y**5 + 3*y**f - 2*y**n + 2*y**3 = 0. What is y?
0, 1
Let b = -2 - -6. Find p, given that p + 3*p + b*p**2 - 2*p**2 - 2*p**3 = 0.
-1, 0, 2
Let a(h) be the third derivative of -h**7/70 - h**6/8 - 7*h**5/20 - 3*h**4/8 - 6*h**2. Factor a(u).
-3*u*(u + 1)**2*(u + 3)
Suppose -7 = -3*o - 4. Factor 16*g**2 + 2 + o - 14*g**2 + 1 - 6*g.
2*(g - 2)*(g - 1)
Let t(h) = -h**3 + 7*h**2 + 8*h + 2. Let j be t(8). Let n be j/(-4)*(-4)/9. Factor 2/9 - n*i**5 - 4/9*i**2 + 2/9*i**4 + 4/9*i**3 - 2/9*i.
-2*(i - 1)**3*(i + 1)**2/9
Factor -4/5*t + 2/5*t**2 + 2/5.
2*(t - 1)**2/5
Let i(x) = -x**3 - 14*x**4 - 9*x**3 - x**2 + 10*x**2 - 5*x. Let w(n) = -n**2 + n. Let y(l) = i(l) + 5*w(l). What is s in y(s) = 0?
-1, 0, 2/7
Suppose -9/7 + 3/7*k**2 - 6/7*k = 0. Calculate k.
-1, 3
Let x(d) be the third derivative of d**9/241920 - d**7/20160 - d**5/30 + 3*d**2. Let f(l) be the third derivative of x(l). Let f(q) = 0. Calculate q.
-1, 0, 1
Let b(i) = -i**3 + 4*i**2 + 4. Let n be b(4). Suppose -y + 5*h = 2*h - 5, -n*h + 6 = 5*y. Factor -1/2*u**3 + 2 + 0*u - 3/2*u**y.
-(u - 1)*(u + 2)**2/2
Let b(v) = v**5 - v**3 + v**2. Let f(m) = -6*m**5 - m**4 + 5*m**3 - 5*m**2. Let s(o) = 5*b(o) + f(o). Factor s(p).
-p**4*(p + 1)
Factor -40*p**3 + 14*p**3 + 23*p**3 + 3*p**5.
3*p**3*(p - 1)*(p + 1)
Suppose -2*v + 12 = 4*q, -3*v + 2*v - 4*q = -12. Suppose -7/5*t**4 - 2/5*t**3 + v*t**2 + 0*t + 0 = 0. Calculate t.
-2/7, 0
Let i = 2575/2247 + -1/321. Suppose -2/7*w**2 - i*w - 8/7 = 0. Calculate w.
-2
Suppose -2/5*v + 2/5*v**3 - 4/5 + 4/5*v**2 = 0. What is v?
-2, -1, 1
Let n(b) be the second derivative of 0*b**2 - 5/12*b**4 - 3/20*b**5 - 3*b + 1/42*b**7 + 1/30*b**6 - 1/3*b**3 + 0. Solve n(g) = 0 for g.
-1, 0, 2
Solve -235*j**2 - 4*j**3 + 235*j**2 + 4*j = 0 for j.
-1, 0, 1
Let m = 2 - 0. Let b(y) = y**3 - 7*y**2 + 6*y + 2. Let d be b(6). Solve -2*a**3 + 0*a**5 + d*a + 2*a**5 - m*a**3 = 0.
-1, 0, 1
Let j(i) be the first derivative of -3*i**5/50 + i**4/40 + 3*i**3/10 - 9*i**2/20 + i/5 + 54. Find y, given that j(y) = 0.
-2, 1/3, 1
Let r be (28/(-315))/(2/(-12)). Let b = r + -2/15. What is y in 0 + b*y**2 + 2/5*y**3 - 2/5*y**4 - 2/5*y**5 + 0*y = 0?
-1, 0, 1
Solve 1 - 1/2*k**2 + 1/2*k = 0.
-1, 2
Let u(v) be the third derivative of -v**6/10 + v**5/6 + v**4/12 + v**2. Let l(k) = 13*k**3 - 11*k**2 - 2*k + 2 - 2. Let i(g) = -5*l(g) - 6*u(g). Factor i(s).
s*(s - 1)*(7*s + 2)
Let v(d) = d**2 + 3*d**2 + 5*d - 5*d**2. Let k be v(4). Suppose c**5 - 3 + k*c**2 + 2*c**4 + 4*c**3 - 3*c**5 - 4*c**4 - 2*c + 1 = 0. Calculate c.
-1, 1
Let z(o) = -o + 10. Let r be z(6). Let u(i) be the second derivative of i + 0 - 1/3*i**2 - 1/6*i**r + 1/3*i**3 + 1/30*i**5. Let u(b) = 0. What is b?
1
Let s(y) = 20*y**2 - 17*y - 8. Let i = 4 - 2. Let o(p) = 10*p**2 - 8*p - 4. Let g(n) = i*s(n) - 5*o(n). Factor g(c).
-2*(c - 1)*(5*c + 2)
Let i(s) be the third derivative of 0 - 1/30*s**6 + 1/30*s**5 + 3*s**2 + 0*s + 0*s**4 - 1/35*s**7 + 0*s**3. Determine h so that i(h) = 0.
-1, 0, 1/3
Let j(i) = -i**3 - i - 1. Let s(n) = -6*n**4 + n**3 + 6*n**2 + 5*n + 3. Let x(w) = 3*j(w) + s(w). Factor x(u).
-2*u*(u - 1)*(u + 1)*(3*u + 1)
Let l be ((-91)/14 - -5)/(18/(-64)). Factor -4/3*g**2 + l*g - 16/3.
-4*(g - 2)**2/3
Factor -11/3*l**2 + 0 - 3*l**3 - 2/3*l.
-l*(l + 1)*(9*l + 2)/3
Let c(m) be the second derivative of m**4/66 - 4*m**2/11 - 3*m - 3. Determine q so that c(q) = 0.
-2, 2
Let q(s) = s**4 + 17*s**3 - 8*s**2 + 5*s. Let y(h) = h**4 + h**3 + h. Let i(z) = q(z) - 5*y(z). Let i(j) = 0. Calculate j.
0, 1, 2
Let f(x) be the second derivative of -x**8/560 + x**7/140 - x**6/120 - 7*x**3/6 - 2*x. Let h(w) be the second derivative of f(w). Factor h(l).
-3*l**2*(l - 1)**2
Suppose 0 = 5*m - 3*m - 6. Find a such that -4*a**m - 6*a + 8*a - 8*a**3 - 6*a**5 - 16*a**4 = 0.
-1, 0, 1/3
Let u(r) = -9*r**2 + 6*r - 3. Let j(v) = 6*v + 16. Let i(l) = l + 3. Let x(h) = 11*i(h) - 2*j(h). Let k(s) = -u(s) - 3*x(s). What is o in k(o) = 0?
0, 1/3
Suppose -65*f - 3*f**2 + 9 - 9*f**3 + 74*f - 3*f**2 - 3 = 0. Calculate f.
-1, -2/3, 1
Let c(i) be the third derivative of i**7/105 - i**5/15 + i**3/3 + 11*i**2. Let c(q) = 0. What is q?
-1, 1
Let a = 160 + -157. Let i(z) be the first derivative of -4 - 2/3*z**a - 2*z**2 + 0*z. Let i(o) = 0. Calculate o.
-2, 0
What is m in 6/7*m**2 + 3/7*m - 3/7*m**3 - 6/7 = 0?
-1, 1, 2
Suppose 0 = 2*p - 0*p - 2*t - 16, 5*p - 4*t = 36. Suppose -i - p = -d, -23 = 4*i - 7. Factor d*l**4 + 0*l + 0 - 2/5*l**5 + 0*l**2 + 2/5*l**3.
-2*l**3*(l - 1)*(l + 1)/5
Factor -2*d + 8*d**2 - 7/2*d**3 + 0.
-d*(d - 2)*(7*d - 2)/2
Let l(t) = -t**2 + t + 4. Let s(i) = -12*i**2 + 12*i + 51. Suppose 2 = -2*k + 3*k. Let v(b) = k*s(b) - 27*l(b). Factor v(o).
3*(o - 2)*(o + 1)
Let g(k) be the first derivative of -k**5 - 5*k**4/2 + 5*k**3/3 + 5*k**2 + 14. Factor g(u).
-5*u*(u - 1)*(u + 1)*(u + 2)
Let r(u) be the second derivative of u**8/5880 - u**7/1470 + u**6/1260 - u**3/3 - 3*u. Let i(q) be the second derivative of r(q). What is z in i(z) = 0?
0, 1
Factor 16*m + 17*m + 20*m**2 + 12*m + 15*m**3 - 40*m.
5*m*(m + 1)*(3*m + 1)
Let a be (-2)/5 + 3/(-5). Let n = a - -3. Determine j, given that 4*j + 6*j**2 - 20*j**n + 0*j = 0.
0, 2/7
Let s(p) be the first derivative of 3*p**2 + 0*p**4 - 3/5*p**5 + 0*p + 2 + 3*p**3. Find t, given that s(t) = 0.
-1, 0, 2
Factor -4/3 - 8/9*u**3 - 34/9*u - 10/3*u**2.
-2*(u + 1)*(u + 2)*(4*u + 3)/9
Let d(k) = -4*k. Let h be d(-1). Let f(u) be the second derivative of -1/12*u**3 + 1/48*u**h - 2*u + 0 + 1/8*u**2. Solve f(n) = 0 for n.
1
Suppose 0 = -3*s + 2 + 4. Solve -s*j + 0*j**2 - j**3 + j + 2*j**2 = 0.
0, 1
Factor