for y.
1/2, 1
Let p = -82/5 - -18. Factor 0 + p*r**2 + 6/5*r**3 + 2/5*r.
2*r*(r + 1)*(3*r + 1)/5
Let x be -4 + -3 + 9/3. Let w be x - -3 - (-6)/5. Solve w*y**3 + 0 + 0*y**2 - 1/5*y = 0 for y.
-1, 0, 1
Let w(r) be the first derivative of 1 + 0*r - r**3 + 0*r**2 + 0*r**4 - 1/180*r**6 + 0*r**5. Let b(h) be the third derivative of w(h). Factor b(o).
-2*o**2
Factor -2/3*p - 4/3*p**2 + 1/6*p**5 - 1/2*p**3 + 0 + 1/3*p**4.
p*(p - 2)*(p + 1)**2*(p + 2)/6
Let u be (-8)/6*6/(-4). Suppose -n = -2*n + u. Factor n + 4*b + 2*b**2 + 2*b**2 - 2*b**2.
2*(b + 1)**2
Suppose 0 = -j - j + 4. Solve 0*r + r + 0*r**j - 4*r**2 + 3*r**2 = 0 for r.
0, 1
Let r(n) be the first derivative of 16*n**4/7 - 48*n**3/7 + 54*n**2/7 - 27*n/7 + 34. Factor r(d).
(4*d - 3)**3/7
Let u = 10/21 - 4/21. Let n = 2729/1596 - -1/228. Factor -48/7*z**3 - u - 32/7*z**4 + n*z - 2/7*z**2.
-2*(z + 1)**2*(4*z - 1)**2/7
Let b(u) be the third derivative of -u**6/60 + 2*u**5/15 - u**4/3 + 23*u**2. Factor b(x).
-2*x*(x - 2)**2
Let r be ((-5)/30)/(-1*10). Let u(b) be the third derivative of -r*b**6 + 0*b**3 + 0 + b**2 - 1/30*b**5 + 0*b + 1/168*b**8 + 0*b**4 + 1/105*b**7. Factor u(h).
2*h**2*(h - 1)*(h + 1)**2
Suppose 4*o - 2*a - 18 = 0, 4*a = -3*o - 2*o - 10. Factor -8/5*p**4 + 22/5*p**3 - 18/5*p**o + 2/5 + 2/5*p.
-2*(p - 1)**3*(4*p + 1)/5
Let n(s) = s**3 + 2*s**2 - s - 2. Let a(z) = -3*z**3 - 9*z**2 + 3*z + 9. Let o be 3/((-6)/4*-1). Let h(x) = o*a(x) + 9*n(x). Factor h(w).
3*w*(w - 1)*(w + 1)
Let a(r) be the second derivative of -6*r**2 - r + 3/5*r**5 + 1/10*r**6 - 2*r**3 + 0 + 3/4*r**4. Factor a(j).
3*(j - 1)*(j + 1)*(j + 2)**2
Suppose -5*t + u = 5*u + 23, 0 = 2*u + 4. Let i = 1 - t. Let 2/9 + 4/3*z**2 + 8/9*z**3 + 2/9*z**i + 8/9*z = 0. What is z?
-1
Suppose -2*u = 4*x, u + x - 7 = 6*x. Suppose b + b - 10 = u*r, 5*b + 4*r = -2. Let 2*i - 7*i**3 + 0*i**2 + i**b + 5*i**4 - i**3 = 0. What is i?
-2/5, 0, 1
Let z(t) = t**3 - 5*t**2 + 4*t + 3. Let p be z(4). Determine q, given that -q**3 + 6*q + p*q**3 - 2 + 4 + 6*q**2 + 0*q**3 = 0.
-1
Let z(k) be the second derivative of -k**7/105 + 3*k**6/40 - k**5/5 + k**4/6 + 2*k**2 - 8*k. Let g(s) be the first derivative of z(s). Factor g(n).
-n*(n - 2)**2*(2*n - 1)
Suppose -19 - 5 = -6*w. Let s(i) be the first derivative of -i**w + 11/2*i**2 - 1 + 2*i + 14/3*i**3 - 7/6*i**6 - 16/5*i**5. Factor s(z).
-(z - 1)*(z + 1)**3*(7*z + 2)
Suppose 0 = a - 0*a. Let s = 9 - a. Solve -11*h**3 - h**5 + s*h**3 + 3*h**5 = 0 for h.
-1, 0, 1
Factor 5*n**2 + 23*n**4 - 5*n**2 - 8*n - 12*n**2 - 19*n**4.
4*n*(n - 2)*(n + 1)**2
Let s(w) = 7*w**2 + 4*w + 7. Let g(h) = 2 + 11*h**2 - 1 + 19 + 9*h**2 + 11*h. Let o(r) = -6*g(r) + 17*s(r). Factor o(a).
-(a - 1)**2
Let j(c) = -c**4 + 4*c**3 + 4*c**2 + 4*c. Let g(v) = 10*v**4 - 35*v**3 - 35*v**2 - 35*v. Let x(z) = 4*g(z) + 35*j(z). Suppose x(f) = 0. Calculate f.
0
Let b(q) be the third derivative of -3*q**2 + 0 - 1/240*q**5 - 1/48*q**4 + 1/8*q**3 + 0*q. Factor b(t).
-(t - 1)*(t + 3)/4
Let b(o) be the third derivative of o**5/180 + o**4/36 - 8*o**2. Factor b(c).
c*(c + 2)/3
Let l(o) = -10*o - 88. Let s be l(-9). Find w such that 0*w + w**3 - 1/3*w**s + 0 = 0.
0, 1/3
Let c be (2/4)/((-60)/(-48)). Let z = 14/15 - 8/15. Determine t so that c*t**2 + 0 - z*t = 0.
0, 1
Suppose -4*q + 15 = 3. Let s(u) be the first derivative of 4/3*u - u**2 + 2/9*u**q + 3. Solve s(n) = 0.
1, 2
Let l(b) be the first derivative of 0*b + 1/7*b**2 - 3 + 8/21*b**3. Factor l(o).
2*o*(4*o + 1)/7
Let f(k) be the third derivative of -k**5/20 + 7*k**2. Factor f(t).
-3*t**2
Let m be 2/(-7) + 86/7. Let j be (m/(-7))/((-4)/14). Factor -j*a**2 - 8 - 1 + 1 + 16*a.
-2*(a - 2)*(3*a - 2)
Let n = -4 - -7. Let r be n/(1 + -2) - -7. Determine h so that 0*h - 2/5*h**2 + 1/5 + 1/5*h**r + 0*h**3 = 0.
-1, 1
Let x(a) be the first derivative of 1/70*a**5 - 1 - 1/420*a**6 + 1/21*a**3 + 0*a - 1/2*a**2 - 1/28*a**4. Let w(h) be the second derivative of x(h). Factor w(m).
-2*(m - 1)**3/7
Factor -1 - 5 - 63*y**2 - 51*y**3 - 33*y + 0 - 15*y**4.
-3*(y + 1)**3*(5*y + 2)
Let u(d) = d**2 + 6*d + 2. Let f be u(-6). Let h(p) be the second derivative of 4/9*p**2 + 0 + 1/3*p**5 + 5/27*p**6 - 11/54*p**4 + f*p - 4/9*p**3. Factor h(r).
2*(r + 1)**2*(5*r - 2)**2/9
Let z be -1*(-51)/12 - 3. Determine y, given that 1/2*y**2 - 3/4 - z*y = 0.
-1/2, 3
Let g(f) be the second derivative of f**6/18 + f**5/12 - 5*f**4/12 - 5*f**3/18 + 5*f**2/3 - 5*f. Factor g(s).
5*(s - 1)**2*(s + 1)*(s + 2)/3
Let c(n) be the first derivative of 4*n**5/65 + 9*n**4/26 + 8*n**3/13 + 4*n**2/13 + 14. Find b, given that c(b) = 0.
-2, -1/2, 0
Let w(l) be the second derivative of 7*l**6/120 + l**5/40 - 7*l**4/48 - l**3/12 - 3*l. Factor w(m).
m*(m - 1)*(m + 1)*(7*m + 2)/4
Let c be 4/6 - (-620)/(-15). Let u = 41 + c. Factor u*q - 2/3 + 1/3*q**2.
(q - 1)*(q + 2)/3
Let u(j) be the second derivative of -5*j + 0 - 3/40*j**5 + 0*j**2 + 1/4*j**3 + 1/20*j**6 - 1/8*j**4. Determine n, given that u(n) = 0.
-1, 0, 1
Solve -2*i + 5 - 2 - 2 + i**2 = 0 for i.
1
Suppose 0*m + 9 = m. Factor m*w**2 + 2*w**3 - 2*w**3 - 7*w + 3 - 3*w**3 - 2*w.
-3*(w - 1)**3
Let v(f) be the second derivative of -f**7/336 + f**5/80 - f**3/48 - 9*f. Let v(s) = 0. Calculate s.
-1, 0, 1
Let u(d) = -d**3 - 6*d**2 + 3*d + 1. Let i(v) = v**3 + v - 1. Let c(j) = 6*i(j) + 2*u(j). Determine b so that c(b) = 0.
1
Let c be (2/6)/((-78)/(-36) + -2). Factor 0 + 3/5*a + 3/5*a**c.
3*a*(a + 1)/5
Let u(j) be the third derivative of -2/9*j**3 + 0*j + 3*j**2 + 1/18*j**5 + 0 - 1/12*j**4. Factor u(x).
2*(x - 1)*(5*x + 2)/3
Let k be (-3)/(-1 + (-1)/2). Factor 3*m**4 + 0*m**3 - m**4 + k*m - 4*m**3 - 2*m**2 + 2*m**3.
2*m*(m - 1)**2*(m + 1)
Let d(j) = -j**3 + 10*j**2 + j - 7. Let r be d(10). Let h be 1/r + 4/24. Factor 1/2*p**3 + 1/2*p**2 - h*p - 1/2.
(p - 1)*(p + 1)**2/2
Let g(d) be the first derivative of -4/3*d**2 + 2 + 8/3*d + 2/9*d**3. Determine t so that g(t) = 0.
2
Let k = -115 - -119. Let -2/5*h**k + 0 + 2/5*h**2 + 2/5*h**5 + 0*h - 2/5*h**3 = 0. Calculate h.
-1, 0, 1
Let r(n) be the second derivative of -n**6/1260 + n**4/84 - n**3/6 + n. Let d(g) be the second derivative of r(g). Factor d(l).
-2*(l - 1)*(l + 1)/7
Let g(k) be the first derivative of k**7/140 + 2*k**6/45 + 7*k**5/60 + k**4/6 + k**3 - 1. Let z(m) be the third derivative of g(m). Factor z(f).
2*(f + 1)**2*(3*f + 2)
Suppose d + 5*g = -8, 0 = d - 5*d - 5*g - 2. Factor 10/3*r - 2/3*r**2 - 2/3*r**3 - d.
-2*(r - 1)**2*(r + 3)/3
Suppose 3*q - 15 = 0, d = -0*d - 2*q + 25. Suppose -17 = -v - 4*s, -4*s + d = s. Find j, given that 0*j**3 - 2/9*j**v + 0 - 4/9*j**4 + 2/9*j + 4/9*j**2 = 0.
-1, 0, 1
Let g(h) be the first derivative of h**3/4 + 3*h**2/4 + 3*h/4 - 12. Solve g(a) = 0.
-1
Let v(z) be the third derivative of 0 + 3*z**2 + 0*z + 1/70*z**7 + 24/5*z**5 + 128*z**3 + 32*z**4 + 2/5*z**6. Determine w so that v(w) = 0.
-4
Suppose -6*h + 10 = -h. What is v in 3*v**h + 2*v - v**2 + 0*v - 2*v**4 - 2*v**3 = 0?
-1, 0, 1
Let n(l) = l**2 - 5*l. Let o(w) = -w**2 + 6*w. Let y(k) = k**2 + k + 7. Let h be y(0). Let z(j) = h*n(j) + 6*o(j). Suppose z(g) = 0. What is g?
-1, 0
Let b(p) = p**3 + 4*p**2 + p. Let j(t) = -2*t**3 - 5*t**2 - t - 1. Let l(q) = 3*q - 1. Let s be l(2). Let x = s - 9. Let w(g) = x*j(g) - 6*b(g). Factor w(k).
2*(k - 2)*(k - 1)*(k + 1)
Let f(l) be the second derivative of -2*l**6/5 - l**5 - l**4/3 + 2*l**3/3 - 9*l. Find p such that f(p) = 0.
-1, 0, 1/3
Let l(t) be the first derivative of t**3/21 - 3*t**2/7 + 8*t/7 + 2. Solve l(a) = 0 for a.
2, 4
Suppose 3*n + 4*v + 0 = 10, 0 = -3*v + 3. Suppose 5*r - 12 = 5*g + 2*r, 3*g - 8 = -n*r. Let 2/3*j**3 + 1/3*j**4 - 1/3 - 2/3*j + g*j**2 = 0. What is j?
-1, 1
Determine k so that k**5 + 6*k**4 + 0*k**4 + 2*k**5 = 0.
-2, 0
Factor -2/3*i + 0 + 20/3*i**2 + 80/3*i**4 - 32/3*i**5 - 22*i**3.
-2*i*(i - 1)**2*(4*i - 1)**2/3
Let b(z) be the first derivative of -z**8/4200 + z**7/350 - 13*z**6/900 + z**5/25 - z**4/15 + z**3/3 - 6. Let j(h) be the third derivative of b(h). Factor j(x).
-2*(x - 2)**2*(x - 1)**2/5
Let f(k) = 48*k + 1. Let w be f(-2). Let g = w - -141. What is l in -56/3*l - 140/3*l**3 - 50/3*l**4 - g*l**2 - 8/3 = 0?
-1, -2/5
Let n = -72 + 798/11. What is r in -8/11*r**5 + 0 - n*r**4 + 10/11*r**3 + 6/11*r**2 - 2/11*r = 0?
-1, 0, 1/4, 1
Let a(u) be the third derivative of u**8/784 - u**7/490 - u**6/14