. Let m(t) = 0. Calculate t.
0, 1, 4
Let b be 8 + 2 + 312/(-36). Factor 1/3*o**2 + 0*o - b.
(o - 2)*(o + 2)/3
Suppose -6 = 2*w - 4*w. Let p = 5 - w. Determine h so that 1/4*h**3 + 0 + 0*h**p - 1/4*h = 0.
-1, 0, 1
Let f = 53/300 - 4/25. Let x(r) be the third derivative of 1/12*r**4 + 0 - 1/6*r**3 - f*r**5 - r**2 + 0*r. Factor x(i).
-(i - 1)**2
Solve -m**2 - 10*m + m**4 + 4*m**3 + 9*m - 3*m**3 = 0 for m.
-1, 0, 1
Let u = -17 - -17. Let d(v) be the third derivative of 0*v**5 + 0 + 0*v + u*v**3 + 1/24*v**4 - v**2 - 1/120*v**6. Let d(o) = 0. What is o?
-1, 0, 1
Factor 2/7*t**3 + 0*t + 0 - 4/7*t**4 + 0*t**2.
-2*t**3*(2*t - 1)/7
Let b(h) be the third derivative of -h**9/60480 + h**8/20160 + h**7/2520 + h**5/15 + 2*h**2. Let l(d) be the third derivative of b(d). Factor l(g).
-g*(g - 2)*(g + 1)
Suppose -2*z = 5*h + z, 2*h - z = 0. What is n in h + 3/2*n**2 - n**3 - 1/2*n = 0?
0, 1/2, 1
Suppose 4*k - 69 = -5*s, -s + 60 = 3*k + 22. Suppose -5*d + 27 = 3*b, 0*d + d - k = -2*b. Factor -15*h**4 + 16*h**4 - 3*h**3 + 2*h**d + h**5 - h**2.
h**2*(h - 1)*(h + 1)**2
Let b be 4/14 - ((-525)/49 + 9). Solve 2*r - 4/3 + 4/3*r**b = 0 for r.
-2, 1/2
Let b(x) be the first derivative of x**8/168 - 2*x**7/105 + x**6/60 - x**2/2 + 2. Let g(w) be the second derivative of b(w). What is q in g(q) = 0?
0, 1
Let u = 3 + -1. Suppose -2*w + 2 = -u. Factor 0 - 2/3*b + 2/3*b**w.
2*b*(b - 1)/3
Let b(f) = f**2 + 7*f. Let l be b(-7). Let w be (l + -1)/((-3)/15). Factor -4/5*z + 2/5 - 14/5*z**4 - 4/5*z**2 + 4/5*z**w + 16/5*z**3.
2*(z - 1)**4*(2*z + 1)/5
Find v, given that -7*v**2 + 7*v + 8*v**2 - v - 4*v**2 - 3 = 0.
1
Let a(l) = -16*l**3 - 32*l**2 - 24*l - 8. Let t(u) = -16*u**3 - 31*u**2 - 24*u - 9. Let d(q) = -5*a(q) + 4*t(q). Factor d(f).
4*(f + 1)**2*(4*f + 1)
Find p such that -1/2*p**3 + 0*p + 4*p**2 + 0 = 0.
0, 8
Solve 2 + 12*j**3 - 6*j + 12*j**4 - 4*j**2 - 5 - 5*j**2 - 6*j = 0 for j.
-1, -1/2, 1
Let v(b) = -2*b**2 + 4*b - 2. Suppose -2*q + 4*j - 5 = -q, 5*q + 5*j = 0. Let g = 4 + q. Let d(f) = 2*f**2 - 4*f + 3. Let u(w) = g*v(w) + 2*d(w). Factor u(i).
-2*i*(i - 2)
Let w(v) be the second derivative of -2*v**7/7 - 2*v**6/3 + 4*v**5/5 + 4*v**4/3 + 58*v. Suppose w(u) = 0. What is u?
-2, -2/3, 0, 1
Let f(i) be the first derivative of -i**6/6 - 2*i**5/5 - i**4/4 - 22. Factor f(g).
-g**3*(g + 1)**2
Suppose -6 = 3*i - 3*d, 7*i - 2*i + 3*d = 22. Factor 15*g**3 + 2*g**i - 17*g**3 + 2*g - 1 - 1.
-2*(g - 1)**2*(g + 1)
Factor 9 - 10*n - 2*n + 7 - 4*n**2.
-4*(n - 1)*(n + 4)
Suppose -u - 16 = -7*v + 2*v, 20 = 4*v + u. Suppose 15/2*d**3 + 3 + 27/2*d**2 + 21/2*d + 3/2*d**v = 0. Calculate d.
-2, -1
Let n(t) = 4*t - 13. Let p be n(-6). Let v = 37 + p. Factor -2/3*r**3 + 0 + v*r + 4/3*r**2.
-2*r**2*(r - 2)/3
Let b = 57/5 + -503/45. Let t(c) be the third derivative of -1/36*c**4 - b*c**3 + 0*c + 0 - c**2 + 1/9*c**5. Find r such that t(r) = 0.
-2/5, 1/2
Suppose -5*y + 4*d = -20, 7 = -3*y - 5*d - 18. Let n be y/3 + (-4)/(-6). Factor 1/3 + 1/3*g**2 + n*g.
(g + 1)**2/3
Let w(v) = -v**2 + v. Let c(j) = -j**2 + 8*j + 2. Let f be c(8). Let h(g) = 5*g**2 - 6*g + 1. Let d(b) = f*h(b) + 11*w(b). Factor d(r).
-(r - 1)*(r + 2)
Let w(a) = a**2 + a. Let t be w(2). Let r(s) = -s + 8. Let h be r(t). Find z, given that 0*z**h - z**2 + 4*z + 3*z**2 = 0.
-2, 0
Let 0 + 8/3*z - 2/3*z**2 = 0. What is z?
0, 4
Suppose -3*u + 8 = 2. Factor -r**u + r + r**4 - 7*r**5 + 6*r**5 - r**2 + r**4.
-r*(r - 1)**3*(r + 1)
Suppose 3*y + 2 = 14. Let d(m) be the second derivative of 0*m**y - m - 1/30*m**6 + 0*m**3 + 0*m**2 + 1/20*m**5 + 0. Factor d(x).
-x**3*(x - 1)
Determine i so that 2/7*i**2 + 0 + 2/7*i = 0.
-1, 0
Suppose z + 0 - 6 = 0. Let m(c) = c**3 - 6*c**2 + c - 6. Let l be m(z). Factor -p**5 + 0*p - p**5 + l*p**3 - 2*p + 4*p**3.
-2*p*(p - 1)**2*(p + 1)**2
Suppose q + 2*k = -2 - 5, 0 = -2*q + 4*k + 26. Suppose 9 = -0*d + q*d. Factor 1 + d*h + h**2 - 2*h - 3*h.
(h - 1)**2
Suppose -5*v + 0*v - 5*p = -35, 0 = -v - 3*p + 17. Suppose v*c - 4 = c. Find k, given that 3/2*k**2 + 5/4*k**3 + 1/4*k**c - 2 - k = 0.
-2, 1
Let m = -8 + 9. Let j be -2 + m + (2 - -1). Factor -6*q + 6*q**2 + 2 + 0*q**3 + 2*q**3 - j*q**3 - 2*q**3.
-2*(q - 1)**3
Determine u so that 48*u**4 - 33*u**4 - 15*u**3 - 5*u**5 + 2*u**2 + 3*u**2 = 0.
0, 1
Let z be (2 + 2)*1/2. Factor -31 + 2*d**3 + 31 + z*d**2.
2*d**2*(d + 1)
Factor 4*c**4 - 10*c**2 - c**2 + 4 - c**2 + 4*c**2.
4*(c - 1)**2*(c + 1)**2
Suppose -8 = -r - 6. Factor -2/7 + 2*x - 16/7*x**r - 32/7*x**3.
-2*(x + 1)*(4*x - 1)**2/7
Factor 0 + 5/2*q - 5/2*q**2.
-5*q*(q - 1)/2
Let f(q) = q**2 + q - 1. Suppose 4*o = 17 - 1, 3*o = -3*i + 15. Let c(k) = -7*k**2 - k + 5. Let m(p) = i*c(p) + 5*f(p). Suppose m(b) = 0. Calculate b.
0, 2
Let 0*r**3 - 2/3*r + 4/3*r**2 + 2/3*r**5 + 0 - 4/3*r**4 = 0. Calculate r.
-1, 0, 1
Factor 16/3*o - 4 - 4/3*o**2.
-4*(o - 3)*(o - 1)/3
Let s(c) be the first derivative of -2 + 1/360*c**6 + 0*c + 2/3*c**3 + 0*c**5 + 0*c**2 - 1/24*c**4. Let o(j) be the third derivative of s(j). Factor o(d).
(d - 1)*(d + 1)
Let y = -16 - -21. Let g(n) be the first derivative of 0*n + 0*n**3 + 22/25*n**y + 0*n**2 - 4/5*n**6 - 1/5*n**4 + 2. Let g(o) = 0. What is o?
0, 1/4, 2/3
Let k(y) be the second derivative of -y**8/26880 + y**6/960 - y**5/240 + y**4/4 + 4*y. Let m(b) be the third derivative of k(b). Let m(l) = 0. Calculate l.
-2, 1
Let f(l) be the first derivative of l**3/3 - l**2/2 - l - 2. Let t(q) = 2*q**3 + 2*q**2 + 8*q + 4. Let u(d) = -4*f(d) - t(d). Factor u(z).
-2*z*(z + 1)*(z + 2)
Let h(r) = -33*r**5 + 27*r**3 + 3*r**2 - 15*r - 3. Let j(m) = 8*m**5 - 7*m**3 - m**2 + 4*m + 1. Let b(i) = -5*h(i) - 21*j(i). Factor b(t).
-3*(t - 2)*(t - 1)*(t + 1)**3
Let i be ((48/6)/8)/5. Factor -i - 1/5*r**2 - 2/5*r.
-(r + 1)**2/5
Let f be -1*(3 + -3) + 4 - 1. Factor 1/3*h**4 - 1/3*h**2 + 0*h**f + 0 + 0*h.
h**2*(h - 1)*(h + 1)/3
Let q(r) = -4*r**2 - 2*r - 1. Let o(u) = 3*u**2 + 2*u + 1. Suppose -w = -6*w + 10. Let j(b) = w*q(b) + 3*o(b). Determine n, given that j(n) = 0.
-1
Let x(d) be the second derivative of d**5/5 + 2*d**4/3 + 2*d**3/3 + 29*d. Suppose x(a) = 0. What is a?
-1, 0
Let c(j) be the second derivative of 2*j + 16/9*j**3 + 8/3*j**2 + 1/42*j**7 + 0 - 1/3*j**5 - 1/90*j**6 + 0*j**4. Let c(d) = 0. Calculate d.
-2, -1, -2/3, 2
Let d(k) be the first derivative of 1 + 2*k + 1/2*k**2 - 1/3*k**3. Find a, given that d(a) = 0.
-1, 2
Let x(a) = a - 1. Let g(t) = t**2 + 3*t + 5. Let r(y) = -g(y) - x(y). Factor r(c).
-(c + 2)**2
Let x be 1/(3/(-3)) + 0 + 1. Let -2/3*s**2 + 1/3*s + x = 0. What is s?
0, 1/2
Let t(o) = o**3 - o - 1. Let w(u) = -6*u**3 - u**2 + 7*u + 5. Let m(g) = 5*t(g) + w(g). Solve m(y) = 0.
-2, 0, 1
Let m(u) be the first derivative of u**4/4 - 11*u**3/3 + 16*u**2 - 28*u - 7. Factor m(o).
(o - 7)*(o - 2)**2
Let q(y) be the third derivative of y**8/1176 + y**7/147 + y**6/70 - y**5/105 - y**4/12 - y**3/7 - 9*y**2. Factor q(g).
2*(g - 1)*(g + 1)**3*(g + 3)/7
Let f(z) = -4 + 7*z + 15*z**2 - 5 - 4 + 4*z. Let i(o) = -7*o**2 - 5*o + 6. Let b(k) = -6*f(k) - 13*i(k). Let b(g) = 0. Calculate g.
0, 1
Let n(d) be the second derivative of -4*d + 1/54*d**4 + 0*d**2 - 1/27*d**3 + 0. Factor n(g).
2*g*(g - 1)/9
Suppose 5*y + 2*z = 13, y + 2*z + 2*z = -1. Let t(g) be the first derivative of 2/3*g**2 + 2/9*g**y + 2/3*g - 1. Factor t(l).
2*(l + 1)**2/3
Let r = 5399/231 - 255/11. Let c(p) be the first derivative of r*p**3 + 0*p - 1/14*p**4 - 1/7*p**2 + 1. Find q, given that c(q) = 0.
0, 1
Let f(j) be the second derivative of j**5/80 - j**4/48 + j. Determine k, given that f(k) = 0.
0, 1
Let n(q) be the third derivative of -3*q**2 + 0 + 0*q - 2/105*q**7 + 0*q**3 + 0*q**5 + 1/30*q**6 + 0*q**4. Let n(v) = 0. What is v?
0, 1
Let z(j) be the first derivative of -j**5/5 - j**4/4 + 4*j**3/3 + 2*j**2 - 43. What is v in z(v) = 0?
-2, -1, 0, 2
Find z such that 4/3 + z - 1/3*z**2 = 0.
-1, 4
Let x(i) be the second derivative of -i**6/360 - i**5/180 + i**2/2 - 4*i. Let l(z) be the first derivative of x(z). Factor l(c).
-c**2*(c + 1)/3
Let d(z) be the third derivative of z**6/120 - 7*z**5/60 + 5*z**4/8 - 3*z**3/2 + 2*z**2. Solve d(s) = 0 for s.
1, 3
Let j(o) = o + 5. Let z be j(-3). Factor 4 - 6*c + 5*c**2 + 3*c**2 - 6*c**z.
2*(c - 2)*(c - 1)
Let o(z) be the first derivative of -5 + 1/18*z**3 + 1/6*z - 1/6*z**2. Factor o(a).
(a - 1)**2/6
Let