Let y be 117/24 + 4/32. Factor -45*s**5 + 44*s**y + 0 + 0.
-s**5
Let w(t) be the second derivative of -t**6/780 + t**5/130 - 4*t**3/39 - t**2/2 - 2*t. Let p(b) be the first derivative of w(b). Factor p(h).
-2*(h - 2)**2*(h + 1)/13
Let h(b) = -b + 10. Let t be h(5). Suppose -t = g, -5*d + 85 = -5*g + 20. Factor 12*n**2 - 7*n**2 + 0*n**2 - d*n**3 + 9*n**2 - 2 - 4*n.
-2*(n - 1)**2*(4*n + 1)
Let c = -31/100 + 9/25. Let u(i) be the second derivative of -1/4*i**4 + c*i**5 + 0*i**3 + 0 + 2*i**2 - 2*i. Determine o so that u(o) = 0.
-1, 2
Let m(i) be the third derivative of 0*i**3 + 1/24*i**4 + 0*i + 1/30*i**6 + 0 + i**2 - 1/12*i**5. What is t in m(t) = 0?
0, 1/4, 1
Let y(g) = -g**4 + g**3 + g**2 + 1. Let q(f) = f**4 + 5*f**3 - 13*f**2 + 3*f - 4. Let a(s) = -q(s) - 4*y(s). Factor a(l).
3*l*(l - 1)**3
Let p(v) be the second derivative of v**8/112 + v**7/105 - v**6/40 - v**5/30 + 3*v**2/2 - 2*v. Let z(x) be the first derivative of p(x). Factor z(t).
t**2*(t - 1)*(t + 1)*(3*t + 2)
Let l(a) be the third derivative of a**6/660 - a**4/132 - 16*a**2. Solve l(y) = 0.
-1, 0, 1
Let f(l) = 7*l**3 + 5*l**2 + 3*l. Let x(z) = -3*z**3 - 2*z**2 - z. Let b = -8 - -5. Let a be 1 + (0 - b)/3. Let q(t) = a*f(t) + 5*x(t). What is o in q(o) = 0?
-1, 0, 1
Let n(d) = -d**3 - d**2 + 5*d + 2. Let x be n(-3). Suppose -3 - 5 = -4*q, x*q = -4*j + 18. Factor a**3 - a**2 - a - 2*a**3 - a**j.
-a*(a + 1)**2
Let c(t) be the second derivative of 5*t**7/42 + t**6/3 - 5*t**4/6 - 5*t**3/6 - 17*t. Solve c(p) = 0.
-1, 0, 1
Let r(o) be the first derivative of -5*o**3/3 + 5*o**2 - 5*o + 13. Find a such that r(a) = 0.
1
Let c(k) be the second derivative of 0*k**2 + 0 - 1/3*k**3 + 3*k + 1/3*k**4 - 1/10*k**5. What is q in c(q) = 0?
0, 1
Let a(k) be the second derivative of 0 - 5/2*k**3 + k - 3/20*k**5 + k**4 + 3*k**2. Factor a(r).
-3*(r - 2)*(r - 1)**2
Let t(f) be the second derivative of -7*f**5/100 + f**4/6 + f**3/30 - 2*f**2/5 - 6*f. Factor t(a).
-(a - 1)**2*(7*a + 4)/5
Find q such that 0*q**2 + 3*q**2 - 7 + 23 - 4 + 12*q = 0.
-2
Let t be (2/1)/((-5)/(-5)). Factor 1 + y**3 + y - 143*y**2 + 142*y**2 - t*y**3.
-(y - 1)*(y + 1)**2
Let i(r) = r**2 - 8*r + 14. Let n(b) = -b**2 + 14*b - 18. Let l be n(12). Let a be i(l). Factor 0 + 4/9*o - 2/9*o**3 + 2/9*o**a.
-2*o*(o - 2)*(o + 1)/9
Find p such that 15/2*p**2 - 5 - 5/2*p + 5/2*p**3 - 5/2*p**4 = 0.
-1, 1, 2
Factor -27*x**2 - 4 + 12*x**3 + 18*x + 0*x**3 + 1.
3*(x - 1)**2*(4*x - 1)
Let o(g) be the third derivative of g**7/210 + g**6/60 + 17*g**5/60 + g**4/2 + g**2. Let x(i) = i**3 - i**2 + 1. Let c(a) = o(a) + 4*x(a). Factor c(t).
(t + 1)**2*(t + 2)**2
Suppose -10*u = -12*u + 22. Factor -r + 7*r + 3 + 12*r**2 - 2*r + u*r.
3*(r + 1)*(4*r + 1)
Let c(z) be the first derivative of -z**4 - 8*z**3/3 + 2*z**2 + 8*z + 3. What is q in c(q) = 0?
-2, -1, 1
Suppose m - 4*j + 8 = 0, -2*m + 23 = 3*j + 2*j. Suppose -m*k = 20, c + 2*k - 1 = -8. Let -3/2*o + 1 + 0*o**2 + 1/2*o**c = 0. What is o?
-2, 1
Factor -2/3*x**2 - 16/3*x - 32/3.
-2*(x + 4)**2/3
Let b(w) be the first derivative of 1/9*w**4 - 2/15*w**5 + 0*w**2 + 2/27*w**3 - 4 + 0*w. Factor b(r).
-2*r**2*(r - 1)*(3*r + 1)/9
Let r(p) be the third derivative of -1/30*p**5 + 2*p**2 + 1/3*p**3 + 0*p + 0 + 1/12*p**4 - 1/60*p**6. Factor r(z).
-2*(z - 1)*(z + 1)**2
Suppose -4*a - 20 = -5*c - 7, 0 = c + 2*a + 3. Let r(t) = t**2 + t + 1. Let n(j) = -3*j**2 - 3*j - 9. Let d(s) = c*n(s) + 5*r(s). Factor d(v).
2*(v - 1)*(v + 2)
Let r = 2029/7 + -289. Factor -r*g**2 + 2/7*g + 6/7*g**3 - 2/7*g**4 + 0.
-2*g*(g - 1)**3/7
Let z be ((-72)/112)/(3/(-6)). Factor z*c + c**2 + 2/7.
(c + 1)*(7*c + 2)/7
What is s in -2*s - 3*s**2 - s**2 + s**2 + s**2 = 0?
-1, 0
Let a(n) be the second derivative of -2*n**7/21 - 7*n**6/15 - 4*n**5/5 - n**4/3 + 2*n**3/3 + n**2 + 8*n. What is t in a(t) = 0?
-1, 1/2
Let z(x) be the second derivative of x**8/33600 - x**7/4200 + x**6/1200 - x**5/600 - x**4/6 - 3*x. Let k(n) be the third derivative of z(n). Factor k(w).
(w - 1)**3/5
Let c = -3 - -6. Factor 0*y**c - 5*y**3 + 5*y**2 + y**2 + 2*y**3.
-3*y**2*(y - 2)
Let l be (-28)/70*1*-15*1. Let o(x) be the third derivative of 0*x - 1/300*x**l - 1/15*x**3 + 1/60*x**4 + 0 + 4*x**2 + 1/150*x**5. Find n such that o(n) = 0.
-1, 1
Let u(q) be the first derivative of q**6/15 + 6*q**5/25 + q**4/5 - 4*q**3/15 - 3*q**2/5 - 2*q/5 + 5. Factor u(a).
2*(a - 1)*(a + 1)**4/5
Let x(u) be the second derivative of -u**6/40 + 3*u**4/8 + u**3 + u**2 + 4*u. Let y(o) be the first derivative of x(o). Factor y(h).
-3*(h - 2)*(h + 1)**2
Let n = 3 - 3. Let i be (-3)/(-6) - -3 - 3. Let i*b**5 - b**4 - 1/2*b + n + 0*b**3 + b**2 = 0. Calculate b.
-1, 0, 1
Let y(a) be the second derivative of 0*a**2 - a - 1/16*a**5 + 0*a**3 - 1/24*a**4 + 7/120*a**6 + 0. Let y(h) = 0. What is h?
-2/7, 0, 1
Let d be (-6)/7*-7*3/15. Suppose 8/5*j - 2/5*j**4 - 4/5*j**3 + d*j**2 - 8/5 = 0. What is j?
-2, 1
Let q be ((-1)/(-1))/((-2)/(-10)). Let v = q + -5. Factor -o**2 + o**4 - 3*o**3 + v*o**2 - o + 4*o**3.
o*(o - 1)*(o + 1)**2
Let b(w) be the second derivative of -w**6/45 + w**5/30 + w**4/18 - w**3/9 - 5*w. Let b(m) = 0. What is m?
-1, 0, 1
Let x(c) be the second derivative of -c**8/20160 + c**7/7560 - c**4/12 + c. Let y(r) be the third derivative of x(r). Factor y(o).
-o**2*(o - 1)/3
Suppose 5*n + 5*k + 15 = 0, -3*n = 2*k + 7 - 3. Let l(v) be the first derivative of -2/15*v**3 + 0*v + 3 - 3/5*v**n. Factor l(i).
-2*i*(i + 3)/5
Let y(r) be the first derivative of -5*r**5/12 + 5*r**4/4 - 3*r**3/2 + 5*r**2/2 + 5. Let o(z) be the second derivative of y(z). Find n, given that o(n) = 0.
3/5
Let p = -2/111 - -80/333. What is l in 0 - 4/9*l - 10/9*l**2 - 8/9*l**3 - p*l**4 = 0?
-2, -1, 0
Let v be 0 - (1 + 1 - -6). Let p = -3 - v. Factor 2*x**3 + 2*x**4 - x**3 + 4*x - 2 - p*x**3.
2*(x - 1)**3*(x + 1)
Determine i so that -2*i - 4/7 - 10/7*i**2 = 0.
-1, -2/5
Let l(c) be the first derivative of c**6 - 2*c**5 - c**4/2 + 10*c**3/3 - 2*c**2 - 12. Solve l(n) = 0 for n.
-1, 0, 2/3, 1
Let y(r) be the second derivative of -r**5/60 - r**4/12 + 2*r**2 + 3*r. Let f(q) be the first derivative of y(q). Solve f(p) = 0.
-2, 0
Let i(z) = z**3 - 11*z**2 - 2*z + 22. Let l be i(11). What is k in 1/2*k - k**3 + l*k**2 + 0 + 0*k**4 + 1/2*k**5 = 0?
-1, 0, 1
Let v(a) = 2*a**2 - 3*a + 2. Suppose 4 + 0 = 2*p. Let i be v(p). Suppose i*n - 2*n**2 + 4*n**2 - n**2 + 4 = 0. Calculate n.
-2
Let q = 488 + -485. Find m such that 2/5*m**q - 4/5*m**2 + 0 + 2/5*m = 0.
0, 1
Suppose 1 + 17*u**3 - 2*u - 1 - 15*u**3 = 0. Calculate u.
-1, 0, 1
Let w = 31 + -31. Let p(b) be the third derivative of b**2 + 1/60*b**5 + w*b**4 + 0*b + 0 + 1/120*b**6 + 0*b**3. Find l such that p(l) = 0.
-1, 0
Let w(k) = 9*k - 13. Let p(c) = 4*c - 6. Let q(s) = 7*p(s) - 3*w(s). Let j be q(3). Factor 5*y**3 + y**3 + 2*y + 8*y**2 + j*y**3.
2*y*(y + 1)*(3*y + 1)
Let n(i) = 6*i**2 + 13*i + 11. Let w(d) be the third derivative of -d**4/24 + d**3/6 - d**2. Let b(u) = 2*n(u) - 6*w(u). Determine s so that b(s) = 0.
-2, -2/3
Let q be (-2)/3*-2*(-9)/(-6). Let u(h) be the first derivative of 2/5*h**5 - 2/3*h**3 + 1 + 0*h - q*h**2 + h**4. Factor u(b).
2*b*(b - 1)*(b + 1)*(b + 2)
Suppose 0 = 4*k - 3*k - 4. Factor 3*i**5 + 0*i**3 + 2*i**3 - 3*i**3 - 4*i**5 - 2*i**k.
-i**3*(i + 1)**2
Let m be (-4)/(-10) + (-63)/(-180). Let f be 2 - ((-14)/(-8) - 0). Find y, given that 0*y + 1/4*y**2 + m*y**3 + 3/4*y**4 + f*y**5 + 0 = 0.
-1, 0
Let p(o) be the first derivative of o**6/90 - o**5/10 - 8*o**3/3 + 4. Let t(b) be the third derivative of p(b). Find l such that t(l) = 0.
0, 3
Let y(x) = -3*x + 2. Let i(r) = -9 + 3*r**2 + 13*r + 4*r**2 - 8*r**2. Let b(d) = -4*i(d) - 18*y(d). Suppose b(o) = 0. What is o?
-1/2, 0
Suppose 3*v - 4*v = 3*q + 2, 2*v + 4 = -2*q. Let s be 0 - q - (-8 + 4). Factor 1/5 - 2/5*z - 8/5*z**2 + 4/5*z**5 - 2/5*z**3 + 7/5*z**s.
(z - 1)*(z + 1)**3*(4*z - 1)/5
Let -2/3 + 1/3*z**3 - 1/3*z + 2/3*z**2 = 0. Calculate z.
-2, -1, 1
Let s be (10/35)/(8/14). Let j(v) be the first derivative of 2 + 0*v**3 + s*v**2 + 0*v - 1/4*v**4. Factor j(y).
-y*(y - 1)*(y + 1)
Let a(c) be the second derivative of 2*c**7/63 + c**6/5 + 11*c**5/30 - 4*c**3/9 + 3*c. What is n in a(n) = 0?
-2, -1, 0, 1/2
Suppose -5*u + 5 = -2*u - 5*n, -5*u = n - 27. Let -2*x**4 + 3/4*x**u + 1/2 + 3/2*x**2 + x**3 - 7/4*x = 0. Calculate x.
-