- 1)*(5*a - 4)/2
Let n be 6 - (69/12 - (-9)/36). Factor 0 + 0*y + n*y**2 + 2/11*y**3.
2*y**3/11
Let q(n) be the first derivative of n**3 - 3*n**2 + 3*n - 1. Suppose q(w) = 0. What is w?
1
Let k = 35 - 22. Factor -13 + 4*f**2 + k - 2*f**3.
-2*f**2*(f - 2)
Let t be 8 - 2/(-3)*-3. Let j be (t/8)/(2/8). Let 0 + 0*c**4 + 0*c**2 - 2/3*c**j + 1/3*c + 1/3*c**5 = 0. Calculate c.
-1, 0, 1
Let k(i) be the third derivative of 2*i**2 + 1/105*i**7 + 0*i**3 - 1/12*i**4 + 0 - 1/30*i**5 + 1/60*i**6 + 0*i. Factor k(q).
2*q*(q - 1)*(q + 1)**2
Let c(h) = 3*h**4 + 9*h**2 - 6*h - 6. Let w(l) = 4*l**4 + 10*l**2 - 7*l - 7. Let z(m) = 7*c(m) - 6*w(m). Find t, given that z(t) = 0.
-1, 0, 1
Factor 0 - 1/5*r + 0*r**2 + 1/5*r**3.
r*(r - 1)*(r + 1)/5
Determine s, given that 2/5*s + 2/5*s**2 + 0 = 0.
-1, 0
Let h = -6 - -4. Let j(p) = -3*p**4 + 1 - 2*p**4 - 4*p**3 + 1 + 4*p. Let a(n) = 4*n**4 + 4*n**3 - 4*n - 2. Let x(k) = h*j(k) - 3*a(k). Factor x(m).
-2*(m - 1)*(m + 1)**3
Let l = -32 + 34. Suppose l*b - 2*u + 21 = -7*u, 5*u = -3*b - 19. What is s in 2/9*s**b + 2/3*s + 4/9 = 0?
-2, -1
Let w(q) = -82*q**4 + 360*q**3 - 127*q**2 - 137*q - 22. Let p(g) = -575*g**4 + 2520*g**3 - 890*g**2 - 960*g - 155. Let x(t) = 2*p(t) - 15*w(t). Factor x(s).
5*(s - 4)*(s - 1)*(4*s + 1)**2
Let x = -24 + 28. Factor -2/3*t**x + 0 + 2/3*t**2 + 0*t**3 + 0*t.
-2*t**2*(t - 1)*(t + 1)/3
Suppose 6*b - 5*z = b, 5*b = -2*z + 14. Solve 4*y + 2 - 9/2*y**3 - 3/2*y**b = 0.
-2/3, 1
Let p(q) be the first derivative of q**2 - 1/3*q**3 + 3 + 0*q. Factor p(f).
-f*(f - 2)
Let w(u) be the first derivative of -u**6/720 - u**5/120 - 8*u**3/3 + 11. Let i(p) be the third derivative of w(p). Solve i(c) = 0 for c.
-2, 0
Let x(t) be the third derivative of -t**8/3360 + t**6/720 + t**3/2 - 3*t**2. Let i(m) be the first derivative of x(m). Factor i(k).
-k**2*(k - 1)*(k + 1)/2
Let k(s) be the second derivative of 3*s**5/20 + 10*s. Find z, given that k(z) = 0.
0
Suppose 2*v + 0*v + 3*h - 15 = 0, -4*v + 4*h - 20 = 0. Suppose v = 4*x - x. Factor x + 0*c + 0*c**4 + 0*c**2 + 2/5*c**5 - 2/5*c**3.
2*c**3*(c - 1)*(c + 1)/5
Let y = 2129/5 - 425. Factor -2/5*k**2 + 2/5*k + y.
-2*(k - 2)*(k + 1)/5
Factor -2/3*b**3 - 200*b + 2000/3 + 20*b**2.
-2*(b - 10)**3/3
Let r(k) = 3*k. Let h be r(1). Factor -y**5 + 2*y**4 - 3*y**2 - h*y**2 + y**3 + 0*y**3 + 4*y**2.
-y**2*(y - 2)*(y - 1)*(y + 1)
Let z = 377/5 + -75. What is r in -2/5 + 4/5*r - z*r**2 = 0?
1
Let 2/3 - y + 1/3*y**2 = 0. Calculate y.
1, 2
Let h(z) = 2*z**2 - 6*z - 2. Let y(g) = g**2 - g + 1. Let s(f) = h(f) + 2*y(f). What is x in s(x) = 0?
0, 2
Suppose -2*f + 16 + 2 = 0. Suppose -6 - 11 = 4*r + 5*s, 0 = -3*r - 5*s - 19. Factor -x + x**2 - f - r*x + 11.
(x - 2)*(x - 1)
Let a = 78 - 75. What is t in -2/7 + 0*t**2 - 3/7*t + 1/7*t**a = 0?
-1, 2
Let k be (100/6)/((-28)/42). Let j = k + 28. Find q, given that -3/4*q + 1/4 - 1/4*q**j + 3/4*q**2 = 0.
1
Let b(t) = 8*t**2 + 41*t + 108. Let p(r) = 33*r**2 + 165*r + 432. Let c(f) = -21*b(f) + 5*p(f). Factor c(d).
-3*(d + 6)**2
Let w = 18 + -20. Let v be ((-6)/w)/((-270)/(-20)). Find n such that -v*n**2 - 4/9*n - 2/9 = 0.
-1
Let j(x) be the first derivative of -x**5/10 + x**4/8 + x**3/6 - x**2/4 + 8. Suppose j(r) = 0. Calculate r.
-1, 0, 1
Let k(f) = f**2 - 10*f + 12. Let i be k(9). Let 2*y + 5*y - i*y - 2*y**2 + 0*y = 0. What is y?
0, 2
Let s(m) = 4*m**2 + m + 1. Let j be s(-1). Suppose 3*c + 5 + 1 = j*v, 0 = -3*c - 2*v + 12. Solve 2/9*z**c + 2/9*z - 2/9*z**4 - 2/9*z**3 + 0 = 0 for z.
-1, 0, 1
Suppose 5*z + 3*q = 3*z + 1, -3*z - q + 5 = 0. Determine g, given that 0 + 2/9*g**z + 2/3*g = 0.
-3, 0
Let a = 28 + -26. Determine l, given that 0*l**a - 1/4*l**4 + 0 + 0*l**3 + 0*l = 0.
0
Suppose -36 = -4*k + 4*s, 3*k = k + 5*s + 30. Suppose -2*z - r = -2, 6 = z - 2*r + k*r. Suppose z*t + 0 - 3/7*t**3 - 6/7*t**2 = 0. What is t?
-2, 0
Let n = 1801/12 + -150. Let y(p) be the third derivative of n*p**6 + 11/15*p**4 - 7/15*p**5 + 0*p - 8/15*p**3 + 0 - 2*p**2. Suppose y(v) = 0. Calculate v.
2/5, 2
Solve 10/9*a**2 + 2/3 - 14/9*a - 2/9*a**3 = 0 for a.
1, 3
Let l(d) = -2*d**2 - d - 5. Let f(i) be the first derivative of i**3 + i**2 + 8*i + 2. Let v(y) = -5*f(y) - 8*l(y). Suppose v(n) = 0. What is n?
0, 2
Let t(j) be the first derivative of -1/18*j**4 + 0*j + 0*j**3 + 4 + 2/45*j**5 + 0*j**2. What is u in t(u) = 0?
0, 1
Let q be 14/(-5) - (-3)/(-15). Let n be q/(-2)*(-4 - -10). Solve -2*h**4 - 9*h**2 - 3*h**5 + n*h**2 = 0.
-2/3, 0
Factor 0*q - 1/2*q**4 + 0*q**2 + 0*q**3 + 0.
-q**4/2
Let f(w) be the first derivative of 1/14*w**4 + 0*w + 6 - 4/21*w**3 + 0*w**2. Factor f(g).
2*g**2*(g - 2)/7
Factor 0*v - 6*v + 16 - v**2 + 2*v - v**2.
-2*(v - 2)*(v + 4)
Let x(p) be the third derivative of p**6/420 - p**5/70 + p**4/28 - p**3/21 + 3*p**2. Solve x(r) = 0 for r.
1
Let 0 + 0*p - 4/5*p**2 = 0. Calculate p.
0
Let j(s) be the first derivative of 77/36*s**4 + 2/3*s**2 - 16/9*s**3 + 2*s - 49/60*s**5 + 2. Let d(x) be the first derivative of j(x). What is f in d(f) = 0?
2/7, 1
Let l(g) = g**2 + 1. Let f(s) be the third derivative of s**7/105 + s**3 + 2*s**2. Let n(i) = f(i) - 4*l(i). Factor n(x).
2*(x - 1)**2*(x + 1)**2
Factor 4/5*z**2 - 1/5*z**3 - 3/5*z + 0.
-z*(z - 3)*(z - 1)/5
Let d = -7/6 - -43/30. Find q, given that 8/15*q**3 + d - 6/5*q + 2/5*q**2 = 0.
-2, 1/4, 1
Let o = -18/13 - -121/78. Let d(r) be the second derivative of 0*r**2 - 2*r + 1/12*r**4 + 0 - o*r**3. Find a such that d(a) = 0.
0, 1
Let z(f) = -f**3 + 2*f - 1. Let p be z(-2). Find q such that -2*q**5 + p*q**3 + 3*q**5 + 0*q**3 - 4*q**3 = 0.
-1, 0, 1
Let z = 9 + -3. Let u(t) = -t**2 + 7*t - 3. Let m be u(z). Factor g**m + 12*g**4 + 9*g**5 + 3*g + 0*g**2 - 8*g**3 - 18*g**2 - 5*g**3 + 6.
3*(g - 1)*(g + 1)**3*(3*g - 2)
Let h(v) be the second derivative of -3*v**6/40 - 29*v**5/80 - 11*v**4/16 - 5*v**3/8 - v**2/4 - 9*v. Factor h(p).
-(p + 1)**3*(9*p + 2)/4
Let p(u) be the first derivative of 4 + 2/7*u**3 + 0*u + 2/7*u**2. Factor p(l).
2*l*(3*l + 2)/7
Let d be 0/(-5)*2/6. Let b(n) be the third derivative of 0*n - 1/10*n**5 + 0*n**3 + 2*n**2 + 1/12*n**4 + d + 3/80*n**6. Factor b(p).
p*(3*p - 2)**2/2
Let y = 1316/29 - -2526/145. Let h = 63 - y. Determine u so that 1/5*u + 2/5 - h*u**2 = 0.
-1, 2
Let b be (-4)/(-2) + 2 - 4. Determine k so that 2/5*k**3 + 4/5*k**4 - 2/5*k**2 + 0 + b*k = 0.
-1, 0, 1/2
Let h be 110/20 - (-1)/(-2). Suppose 14*v**3 - 2*v**3 + 3*v**2 - 7*v**5 - 5*v**h - 3*v**4 = 0. Calculate v.
-1, -1/4, 0, 1
Suppose 3*z - r - 6 = -0*r, 3*z - 6 = 4*r. Determine c, given that -z*c + c - 9*c**3 - 6*c**2 - 3*c + 3*c = 0.
-1/3, 0
Let i be -2 + 0 - (-26)/12. Let u = 43/276 + 1/92. Factor 1/3*m - i - u*m**2.
-(m - 1)**2/6
Let j(d) be the third derivative of 4/3*d**3 + 0 - 1/6*d**5 + 3*d**2 + 0*d - 2/3*d**4. Let j(y) = 0. Calculate y.
-2, 2/5
Let o(y) be the second derivative of -1/36*y**4 - y + 1/120*y**5 + 0*y**2 + 1/36*y**3 + 0. Factor o(v).
v*(v - 1)**2/6
Let h(d) be the first derivative of -1/2*d**4 - 5 + 0*d + 4/3*d**3 + 0*d**2. Determine v, given that h(v) = 0.
0, 2
Suppose -3*g - 16 = -5*v, -3*g + 8 = -7*g. Factor 2/9*d**3 + 0*d + 8/9 - 2/3*d**v.
2*(d - 2)**2*(d + 1)/9
Let x(r) = r + 1. Let v(l) = -2*l**4 - 4*l**3 + 8*l + 6. Let h(j) = v(j) - 4*x(j). Find o such that h(o) = 0.
-1, 1
Let i = -2/2075 + 24914/14525. Factor 36/7*y - i - 15/7*y**2.
-3*(y - 2)*(5*y - 2)/7
Let g = -4 - -6. Suppose 0 = g*b + 10, -3*a = -8*a - b + 35. Solve 2*f**2 - 8*f + a + 0*f**2 + 0 = 0 for f.
2
Let q(m) = -13*m**3 - 63*m**2 - 423*m - 864. Let g(w) = 6*w**3 + 32*w**2 + 212*w + 432. Let z(v) = 9*g(v) + 4*q(v). Suppose z(n) = 0. Calculate n.
-6
Let o(u) = -u**3 - 8*u**2 - 8*u + 5. Let k be o(-7). Let r = -9 + k. Determine a so that -2/9*a**r + 2/9*a + 0*a**2 + 0 = 0.
-1, 0, 1
Let f(t) be the third derivative of -5*t**2 - 1/180*t**5 + 0*t + 0*t**3 + 0 + 1/72*t**4. Factor f(v).
-v*(v - 1)/3
Let q(i) = 14*i**4 + 13*i**3 - 7*i**2 - 17*i - 1. Let d(k) = 225*k**4 + 207*k**3 - 111*k**2 - 273*k - 15. Let b(j) = 2*d(j) - 33*q(j). Solve b(o) = 0.
-1, -1/4, 1
Let b(n) be the second derivative of -5*n**9/3024 + n**8/560 + n**7/420 + n**3 - 3*n. Let q(r) be the second derivative of b(r). Determine k so that q(k) = 0.
-2/5, 0, 1
Suppose 35*w - 30*w - 25 = 0. Suppose -2*v**4 + 1/2*v**w + 1/2*v + 3*v**3 - 2*v**2 + 0 = 0. What is v?
0, 1
Let t(o) 