2/7*g**2.
2*g**2*(g - 1)**3/7
Let p(o) = 0*o**2 + 5*o**2 + o - 2*o**2. Let q be p(1). Determine c, given that -4*c + q + c**2 + 5 - 5 = 0.
2
Suppose 0*p - 4*p + 24 = 0. Factor 2*i**2 + i + 2 + 3 - p + 0*i.
(i + 1)*(2*i - 1)
Let w(m) be the first derivative of -3*m**6/4 + 3*m**5/5 + 9*m**4/4 - 2*m**3 - 9*m**2/4 + 3*m - 9. Solve w(r) = 0 for r.
-1, 2/3, 1
Let b(p) be the second derivative of 0 + 1/20*p**5 - 1/2*p**2 + 1/120*p**6 + 1/8*p**4 + 2*p + 1/6*p**3. Let r(y) be the first derivative of b(y). Factor r(s).
(s + 1)**3
Let 2*c + 2/9*c**3 + 0 - 4/3*c**2 = 0. What is c?
0, 3
Suppose 0 = -q + 5 - 3. Solve q*j - 2*j**2 + 2 - 2*j = 0.
-1, 1
Solve -24*r**2 + 52*r**2 + 676 - 104*r - 24*r**2 = 0 for r.
13
Let m(i) be the first derivative of i**2 + 1/60*i**5 + 1 + 0*i - 1/24*i**4 + 0*i**3. Let p(s) be the second derivative of m(s). Factor p(h).
h*(h - 1)
Let q be (6/12)/(1/(-2)). Let b(s) = s + 1. Let t(f) = -f**2 - f - 1. Let c(v) = q*b(v) - t(v). Let c(a) = 0. Calculate a.
0
Factor -3/8*t**2 - 1/8*t**4 + 0 - 1/2*t**3 + 0*t.
-t**2*(t + 1)*(t + 3)/8
Let m(z) be the second derivative of 9/20*z**5 + 0 - 4*z**2 - 5/2*z**4 - z + 14/3*z**3. Factor m(j).
(j - 2)*(3*j - 2)**2
Determine x so that 6*x**3 + 9*x**4 + 131*x - 131*x + 3*x**5 = 0.
-2, -1, 0
Suppose -17 = -2*z - 13. Factor -1/2*y + 1 - 1/2*y**z.
-(y - 1)*(y + 2)/2
Factor 5*w**3 + 0*w**3 - 7*w**3 - 3*w**3 - 35*w**2.
-5*w**2*(w + 7)
Let l(v) be the second derivative of -1/30*v**5 + 0 - 6*v + 0*v**4 + 0*v**3 + 0*v**2 - 1/45*v**6. Solve l(w) = 0 for w.
-1, 0
Let g(h) be the second derivative of 0*h**4 + 0 - 1/3*h**3 + 1/720*h**6 - 1/240*h**5 - h + 0*h**2. Let y(o) be the second derivative of g(o). Factor y(p).
p*(p - 1)/2
Let r(z) = z**2 + 1. Let h(q) = -2*q**3 - 4*q**2 - 2*q + 16. Let l(t) = h(t) - 4*r(t). What is c in l(c) = 0?
-3, -2, 1
Let s = 12596/8827 + 2/1261. Factor -4/7 - 8/7*u**2 - s*u - 2/7*u**3.
-2*(u + 1)**2*(u + 2)/7
Let y be (-2)/4*(-8 + -2). Let f be -7 + 9 + (-8)/y. Find w such that 2/5*w**4 + 0 - f*w**3 + 2/5*w - 2/5*w**2 = 0.
-1, 0, 1
Factor -2/5*c**4 + 16/5*c**2 - 8/5*c**3 - 32/5 + 1/5*c**5 + 16/5*c.
(c - 2)**3*(c + 2)**2/5
Let f(t) be the second derivative of -t**7/42 - t**6/10 - 3*t**5/20 - t**4/12 - 8*t. Factor f(a).
-a**2*(a + 1)**3
Let j(u) be the second derivative of u**7/10080 - u**6/2880 - u**4/6 - 3*u. Let a(z) be the third derivative of j(z). Let a(c) = 0. Calculate c.
0, 1
Suppose 2*h - 4*l - 15 - 5 = 0, 3*l + 15 = -4*h. Factor h*x**3 - 1/4*x**5 + 1/4*x + 0 - 1/2*x**2 + 1/2*x**4.
-x*(x - 1)**3*(x + 1)/4
Let k be (-33)/(-11) - (0 + -2). Let o(z) be the second derivative of 0*z**2 + 2*z + 4/21*z**3 + 0 - 2/21*z**4 + 1/70*z**k. Factor o(l).
2*l*(l - 2)**2/7
Let y(r) be the first derivative of r**6/30 - r**5/10 - r**4/4 + 2*r**3/3 + 2*r**2 - 3. Let l(t) be the second derivative of y(t). Factor l(m).
2*(m - 2)*(m + 1)*(2*m - 1)
Suppose 4*k + 12 = 8*k. Let o(g) be the first derivative of 1/8*g**6 + 0*g - 1/4*g**k + 3/20*g**5 + 2 + 0*g**2 - 3/16*g**4. Factor o(s).
3*s**2*(s - 1)*(s + 1)**2/4
Suppose 2*q + 3 = 3*f, -2*f = -4*q - 6*f + 24. Let z(s) be the first derivative of s**6 + 0*s**q + 0*s**2 - 16/5*s**5 + 0*s - 1 + 2*s**4. Solve z(j) = 0.
0, 2/3, 2
Let b(y) be the first derivative of 4*y**3/27 - 16*y**2/9 + 64*y/9 + 21. Solve b(f) = 0.
4
Let q(z) be the second derivative of -1/8*z**2 + 3*z + 1/12*z**3 + 0 - 1/48*z**4. Factor q(i).
-(i - 1)**2/4
Let v(h) = -h**4 + 4*h**3 + 10*h**2 - 6*h - 9. Let w(t) = 3*t**4 - 7*t**3 - 21*t**2 + 12*t + 18. Let o(i) = 5*v(i) + 2*w(i). Factor o(c).
(c - 1)*(c + 1)*(c + 3)**2
Suppose -l = 4*l - 15. Factor 8*z**l + 2*z**3 - 9*z**3 - z**4.
-z**3*(z - 1)
Let p(o) be the second derivative of -o**7/14 + 7*o**6/10 - 57*o**5/20 + 25*o**4/4 - 8*o**3 + 6*o**2 - 2*o. Determine a, given that p(a) = 0.
1, 2
Let c(x) be the second derivative of x**2 + 5/18*x**4 + 1/30*x**5 + 0 + 4*x + 7/9*x**3. Factor c(q).
2*(q + 1)**2*(q + 3)/3
Let f(w) be the second derivative of 5*w**7/42 - w**5/2 + 5*w**3/6 - 18*w. Factor f(r).
5*r*(r - 1)**2*(r + 1)**2
Let g(h) be the third derivative of h**6/540 + h**5/90 + h**4/54 + 8*h**2. Factor g(u).
2*u*(u + 1)*(u + 2)/9
Let t(s) = -3*s**2 - 6*s - 27. Let d(a) = -4*a**2 - 7*a - 27. Let i(l) = -6*d(l) + 7*t(l). Solve i(h) = 0.
-3, 3
Let y be 1/(((-3)/(-1))/15). Let 19*n**3 - y*n**4 - 2*n - 2*n - 2*n**4 - 8*n**2 = 0. What is n?
-2/7, 0, 1, 2
Let u(x) = -x**3 + x**2 - x - 1. Let o(c) = -c**3 - 5*c**2 - c - 3. Let k be o(-5). Let j(v) = v. Let l(s) = k*j(s) + u(s). Factor l(g).
-(g - 1)**2*(g + 1)
Let n(l) = -15*l**3 - 5*l**2 - 2*l - 11. Let t(x) = 8*x**3 + 3*x**2 + x + 6. Let b(k) = 6*n(k) + 11*t(k). What is o in b(o) = 0?
0, 1/2, 1
Let h(d) be the second derivative of d**6/75 + d**5/25 - 2*d**3/15 - d**2/5 - 7*d. Factor h(n).
2*(n - 1)*(n + 1)**3/5
Let d be 4 + ((-5)/(-1))/5. Let l be ((-1)/d)/(6/(-10)). Determine n so that -l*n**2 + 0 - 2/3*n + 2/3*n**3 + 1/3*n**4 = 0.
-2, -1, 0, 1
Let q(f) be the third derivative of 1/1092*f**8 + 0*f - 5*f**2 + 0 - 1/195*f**7 - 1/78*f**4 + 2/195*f**6 - 1/195*f**5 + 1/39*f**3. Factor q(b).
2*(b - 1)**4*(2*b + 1)/13
Let b(c) be the first derivative of c**4/4 + 4*c**3/3 + 3*c**2/2 - 39. Solve b(u) = 0 for u.
-3, -1, 0
Determine w, given that 0 - 1/6*w**3 - 1/3*w**2 + 0*w + 1/6*w**4 = 0.
-1, 0, 2
Let s = 695 - 693. Solve 8/7*x + 6/7 + 2/7*x**s = 0 for x.
-3, -1
Let o(y) = 2*y**2 + 2*y + 11. Let x(j) be the first derivative of -6*j - 1 - 1/2*j**2 - 1/3*j**3. Let g(d) = 6*o(d) + 11*x(d). Suppose g(a) = 0. What is a?
-1, 0
Suppose -29*v + 35*v = 24. Let i(y) be the second derivative of -y**2 + 7/6*y**3 + 0 - 7/12*y**v + 4*y + 1/10*y**5. Solve i(u) = 0.
1/2, 1, 2
Suppose -15 = 5*l + 5*n, n - 1 - 2 = -4*l. Factor 1/2 - b + 1/2*b**l.
(b - 1)**2/2
Suppose 0 - 1/2*w**3 + 0*w**2 + 1/2*w = 0. What is w?
-1, 0, 1
Let v = 10 + -3. Let i(u) = -u**3 + 7*u**2 + u - 7. Let k be i(v). Factor -4/5*x + 2/5*x**2 + k.
2*x*(x - 2)/5
Suppose -8 = -2*l + 2*i - 0, 2*l = -5*i - 6. Solve 6*f**3 - 8*f**l + 8*f + f**3 - 5*f**3 = 0.
0, 2
Let i(w) be the first derivative of -w**4/6 + 2*w**3/3 + 4*w**2/3 - 20. Factor i(f).
-2*f*(f - 4)*(f + 1)/3
Let s be 206/6*(-9)/(-12). Let z = 26 - s. Determine u so that -z*u**5 - 1/2*u**3 - 3/4*u**4 + 3/4*u + 1/4 + 1/2*u**2 = 0.
-1, 1
Let o(b) = 4*b**4 + 8*b**3 + 5*b**2 + 5. Let z(q) = -12*q**4 - 24*q**3 - 16*q**2 - 16. Let w(u) = -16*o(u) - 5*z(u). Factor w(g).
-4*g**3*(g + 2)
Let t(o) be the first derivative of 4*o**3/3 + 3*o**2 + 2*o - 18. Factor t(z).
2*(z + 1)*(2*z + 1)
Suppose 6*m - 5 = m. Let t = m - -3. Find c such that -c**3 + 2*c**t - 5*c**4 + 2*c**4 = 0.
-1, 0
Let y = -13 + 18. Factor -l**5 + 5*l**y + 0*l**2 + 2*l**3 - l**2 + 7*l**4.
l**2*(l + 1)**2*(4*l - 1)
What is y in -6 + 3*y + 5*y**2 - 6*y**2 + y**2 + 3*y**2 = 0?
-2, 1
Factor 8*u + 13*u - 33*u + 80 + 5*u**2 - 28*u.
5*(u - 4)**2
Let m(i) = -i**3 + 11*i**2 + 10*i - 11. Let c(x) = -x**3 + 6*x**2 + 5*x - 6. Let f(a) = -9*c(a) + 4*m(a). Factor f(t).
5*(t - 2)*(t - 1)*(t + 1)
Let l(i) be the first derivative of -1 - i**2 + 0*i**3 + 1/6*i**4 + 2*i. Let p(c) be the first derivative of l(c). Solve p(k) = 0.
-1, 1
Let -20 + 22*q - 10*q**3 + 16*q - q**2 + 5*q**4 - 14*q**2 + 2*q = 0. What is q?
-2, 1, 2
Let u(t) be the second derivative of -t**5/4 + 5*t**4/2 + 21*t. What is j in u(j) = 0?
0, 6
Let x(d) be the first derivative of 2/3*d**6 - 4*d - 4/5*d**5 - 2 + 2*d**2 + 8/3*d**3 - 2*d**4. Factor x(l).
4*(l - 1)**3*(l + 1)**2
Suppose -6*p**2 - 3*p + 3*p**3 + 6 + 6*p - 6*p = 0. Calculate p.
-1, 1, 2
Let y(u) be the third derivative of -u**7/525 + u**6/300 + u**5/75 + 6*u**2. Solve y(k) = 0.
-1, 0, 2
Suppose -5*c**2 - 92*c - 12*c**3 + 2*c**2 + 92*c = 0. What is c?
-1/4, 0
Let n(q) be the first derivative of q**5 + 1 + q - 1/2*q**4 - 1/2*q**2 + 1/2*q**6 - 2*q**3. Factor n(d).
(d - 1)*(d + 1)**3*(3*d - 1)
Let u(a) be the first derivative of 4*a**6/15 - 2*a**5/5 - 3*a**4/10 + 2*a**3/3 - a**2/5 + 6. Solve u(j) = 0 for j.
-1, 0, 1/4, 1
Let s = -979/5497 + 1/239. Let g = s + 31/46. Factor 1/2*r**2 + g*r + 0.
r*(r + 1)/2
Let a(i) be the second derivative of 1/84*i**7 + 0*i**2 + 4*i - 1/40*i**5 + 0 - 1/60*i**6 + 0*i**3 + 1/24*i**4. Factor a(d).
d**2*(d - 1)**2*(d + 1)/2
Let c = -6 - -8. Suppose -v + l = -7, -c*v + 2*l + 18 = v. Solve 0 - q**5 + 