is z in -2/5*z**3 + 8/5*z**2 + 0 - 6/5*z = 0?
0, 1, 3
Factor 3/4*g**3 + 3/2*g**2 - 3/2 - 3/4*g.
3*(g - 1)*(g + 1)*(g + 2)/4
Let g(z) be the third derivative of z**8/294 - 23*z**6/420 + 11*z**5/70 - 17*z**4/84 + z**3/7 + 22*z**2. What is p in g(p) = 0?
-3, 1/2, 1
Let i(w) = -2*w + 4. Let q(m) = -4*m + 8. Let y(k) = 5*i(k) - 2*q(k). Let b be y(2). What is g in 0*g - 1/3*g**3 + b + 0*g**2 = 0?
0
Let k(x) be the second derivative of 0 + 2*x + 0*x**2 - 3/50*x**5 + 0*x**3 - 1/30*x**4 - 2/75*x**6. Factor k(w).
-2*w**2*(w + 1)*(2*w + 1)/5
Let w(b) be the third derivative of -b**4/24 - 5*b**3/6 - b**2. Let u be w(-9). Let s**2 + 5/3*s + 1/3 - 4/3*s**u - 5/3*s**3 = 0. What is s?
-1, -1/4, 1
Let q(v) = 4*v**2 - v - 1. Let m be q(-1). Let u = -150 - -150. Find g, given that -14/3*g**m - 6*g**3 - 4/3*g**2 + 0*g + u = 0.
-1, -2/7, 0
Suppose 5*o - 5 = -3*l, 2*l + 4 = -2*o + 2. Factor 1 - 1 - o*x + x + x**2.
x*(x - 3)
Let j(r) be the first derivative of -1/5*r**5 + 1/6*r**4 + 2/9*r**3 + 1 - 1/2*r**2 + 1/3*r + 1/18*r**6. Factor j(p).
(p - 1)**4*(p + 1)/3
Let l = 84 - 78. Let y(d) be the third derivative of 0 - d**2 + 0*d + 1/945*d**7 + 0*d**l + 0*d**4 + 1/27*d**3 - 1/135*d**5. Factor y(g).
2*(g - 1)**2*(g + 1)**2/9
Let r(f) = -1 + 3*f + 3*f**3 - 4*f**3 - 7*f - 4*f**2. Let j be r(-3). Factor 1 + v**2 + 1 - 1 - 2*v**j.
-(v - 1)*(v + 1)
Let x(m) be the second derivative of m**4/72 + m**3/9 - m**2 - 27*m. Factor x(p).
(p - 2)*(p + 6)/6
Let u(d) be the third derivative of 1/12*d**3 - 1/168*d**8 - 1/240*d**6 - 2/105*d**7 + 2*d**2 + 0 + 7/120*d**5 + 0*d + 5/48*d**4. Find w, given that u(w) = 0.
-1, -1/2, 1
Let w be 2/9 - (-3776)/504. Let f = -158 - -1108/7. Factor -54/7*d + 18/7*d**2 - f*d**3 + w.
-2*(d - 3)**3/7
Factor -1/2 + 0*j + 1/2*j**2.
(j - 1)*(j + 1)/2
Let b be 3/18*-5*6/(-180). Let q(z) be the third derivative of 0*z + 0 + 0*z**3 + 3*z**2 + b*z**4 + 1/180*z**6 - 1/45*z**5. Find c such that q(c) = 0.
0, 1
Let t = 421/6 + -70. Let y(l) be the second derivative of 0 + 1/4*l**5 + 0*l**2 + 0*l**3 - 2*l + t*l**4 + 1/10*l**6. Suppose y(m) = 0. Calculate m.
-1, -2/3, 0
Factor 0 - 2/17*k - 4/17*k**2 - 2/17*k**3.
-2*k*(k + 1)**2/17
Let a = -41/4 + 43/4. Factor a*z**2 + z + 0.
z*(z + 2)/2
Suppose 2*m - 10 = -2. Let v(i) be the first derivative of -3/4*i**m + 2 - 1/6*i**6 - 1/3*i**3 + 0*i + 0*i**2 - 3/5*i**5. Solve v(g) = 0.
-1, 0
Let u = 130 - 124. Let t(d) be the third derivative of -1/30*d**5 + 1/210*d**7 + 0 + 1/60*d**u - 1/336*d**8 + 0*d - 1/24*d**4 + 1/6*d**3 - 2*d**2. Factor t(b).
-(b - 1)**3*(b + 1)**2
Factor 8/11 + 8/11*k + 2/11*k**4 - 4/11*k**3 - 6/11*k**2.
2*(k - 2)**2*(k + 1)**2/11
Let y = 220/747 + -6/83. Factor 0*q + 0 + y*q**2.
2*q**2/9
Let f(r) = -9*r**5 - 7*r**4 + 9*r**3 + 11*r**2 - 6*r - 7. Let z(l) = -8*l**5 - 6*l**4 + 10*l**3 + 10*l**2 - 6*l - 6. Let t(y) = 4*f(y) - 6*z(y). Solve t(n) = 0.
-1, -2/3, 1
Let t(u) = -10*u**3 + 40*u**2 - 110*u + 95. Let f(s) = -9*s**3 + 40*s**2 - 109*s + 94. Let h(n) = 5*f(n) - 4*t(n). Find v, given that h(v) = 0.
2, 3
Let l(o) be the first derivative of 3*o**4/20 - o**3/5 + 2. Find q such that l(q) = 0.
0, 1
Let v(i) be the third derivative of 1/45*i**5 + 0*i**3 + 0 + 1/180*i**6 + 0*i + i**2 + 1/36*i**4. Find h, given that v(h) = 0.
-1, 0
Let r = -2 - -2. Let f(b) be the third derivative of 1/24*b**4 - 1/120*b**6 + 0 + 2*b**2 + 0*b + 0*b**5 + r*b**3. Find y, given that f(y) = 0.
-1, 0, 1
Let r = -115/2 - -58. Factor 1/2 + r*k**2 - k.
(k - 1)**2/2
Suppose -2*c + 7 = 3. Let w(u) = -u**3 + 5*u**2 + 6*u + 4. Let k be w(6). Factor c*p**5 - 3*p**4 + p**k + 0*p**4.
2*p**4*(p - 1)
Let x be (-54)/(-45)*(-10)/2. Let d be (x + 2)/2 + 2. Determine y so that -y**3 + d - 1/2*y**2 + y**5 + 0*y + 1/2*y**4 = 0.
-1, -1/2, 0, 1
Let v be -11 + (-1)/(-1) - -2. Let x = v - -15. What is d in -d**2 - 9 + x - 2*d**4 + 5*d**2 = 0?
-1, 1
Let s(j) = -2*j - 2. Let n be s(-3). Suppose 30 = n*l + l. Determine p so that -2*p**4 - 6 + l + p**5 + p**3 = 0.
0, 1
Let q(p) be the second derivative of 2*p**7/21 - 14*p**6/15 + 18*p**5/5 - 22*p**4/3 + 26*p**3/3 - 6*p**2 - 5*p. Factor q(i).
4*(i - 3)*(i - 1)**4
Let v(x) = -x**5 + x**4 - x**3 - x. Let w(g) = 2*g**2 + g**3 + 2*g**2 + 2 - 8*g**5 - 11*g**3. Let y(s) = -6*v(s) + w(s). Factor y(k).
-2*(k - 1)*(k + 1)**4
Let r(v) be the first derivative of -v**9/4032 + 3*v**8/2240 - 3*v**7/1120 + v**6/480 - 4*v**3/3 + 5. Let d(y) be the third derivative of r(y). Factor d(l).
-3*l**2*(l - 1)**3/4
Let p(v) be the first derivative of v**2/2 + 12*v - 1. Let w be p(-10). Factor -4/9 + 2/3*x**3 + w*x - 20/9*x**2.
2*(x - 2)*(x - 1)*(3*x - 1)/9
Find z, given that 0 + 34/3*z**4 - 32/3*z**3 - 10/3*z**5 + 8/3*z**2 + 0*z = 0.
0, 2/5, 1, 2
Let a(b) = -14*b**2 - 4*b + 4. Let g be a(2). Let t = g - -182/3. Find h such that t*h**2 - 2/3*h + 0 = 0.
0, 1
Factor 1/9*y**3 + 0*y**2 - 1/3*y - 2/9.
(y - 2)*(y + 1)**2/9
Let b(p) be the second derivative of 0 + 0*p**3 + 0*p**4 + 0*p**2 + 1/100*p**5 + 4*p. Find n, given that b(n) = 0.
0
Let m(n) = 7*n**3 - 23*n**2 + 49*n - 59. Let c(v) = -3*v**3 + 11*v**2 - 25*v + 29. Let p(d) = -15*c(d) - 6*m(d). Factor p(f).
3*(f - 3)**3
Let t = -36 - -36. Let p(s) be the first derivative of -1/3*s**3 + 1 + 4/3*s**6 + 1/4*s**4 + t*s**2 + 0*s + 2*s**5. Solve p(u) = 0.
-1, -1/2, 0, 1/4
Factor -11*i**5 - 11*i**3 - 8*i**5 + 15*i**5 + 16*i**4 - i**3.
-4*i**3*(i - 3)*(i - 1)
Let w = -18 + 22. Let p(k) be the second derivative of -1/9*k**3 + 0 + 1/36*k**w + 1/6*k**2 - 2*k. Factor p(y).
(y - 1)**2/3
Let x be ((-36)/9)/(1 + -7). Let y(r) be the second derivative of 0 + x*r**4 + 1/9*r**2 + 3/5*r**5 + 1/5*r**6 + 10/27*r**3 + 3*r. Determine q so that y(q) = 0.
-1, -1/3
Factor -5*h**2 - 20*h**3 - 10*h**2 + 76*h - 26*h + 40 + 5*h**4.
5*(h - 4)*(h - 2)*(h + 1)**2
Suppose -2*k = 4*q - 4, 0*q = -3*q. Let u(x) be the first derivative of 0*x**3 - 1/14*x**4 + 2 + 0*x**k + 0*x. Find y such that u(y) = 0.
0
Let v(b) be the first derivative of 0*b**4 + 2 + 1/10*b**5 - 2*b**2 - 2*b - b**3. Let o(z) be the first derivative of v(z). Suppose o(a) = 0. Calculate a.
-1, 2
Let v(k) be the second derivative of -k**4/72 + k**3/36 + 24*k. Let v(f) = 0. Calculate f.
0, 1
Let q(w) be the first derivative of 5*w**6/6 + 6*w**5 + 65*w**4/4 + 20*w**3 + 10*w**2 - 11. Find f, given that q(f) = 0.
-2, -1, 0
Suppose -3*q + 15 = 2*q. Let x = -1 + q. Factor 2*a - 3*a - a**x + a**3 - 1 + 2*a**2.
(a - 1)*(a + 1)**2
Let o = 607 - 607. Factor -2/3 + o*h + 2/3*h**2.
2*(h - 1)*(h + 1)/3
Let l(b) be the second derivative of b**4/12 - b**2/2 - 8*b. Solve l(h) = 0.
-1, 1
Let o(l) = -3*l**4 - 3*l**3 + 6*l**2 - 6. Let z(c) = -3*c**4 - 4*c**3 + 6*c**2 - 7. Let f(n) = 4*o(n) - 3*z(n). Solve f(k) = 0 for k.
-1, 1
Let i(b) = b**3 + 11*b**2 - 13*b - 9. Let x be i(-12). Let 0*f**x - 1/2*f + 1/2*f**5 + 0 + f**4 - f**2 = 0. What is f?
-1, 0, 1
Suppose -414 + 9 = 9*v. Let l = v + 47. Factor -2/3*q**l - 2/3 - 4/3*q.
-2*(q + 1)**2/3
Let m(z) be the third derivative of z**5/240 - z**4/48 + 4*z**2. Factor m(c).
c*(c - 2)/4
Let u(w) be the third derivative of -w**7/630 - w**6/180 - w**5/180 - 6*w**2. What is t in u(t) = 0?
-1, 0
Suppose 85*a - 97*a = -24. Factor 2*y**3 - 4/7*y - 10/7*y**a + 0.
2*y*(y - 1)*(7*y + 2)/7
Let b = 201/2 + -105. Let h = -4 - b. Find z such that z + 1/2*z**2 + h = 0.
-1
Factor -2/3 + y**3 + 2/3*y**2 - y.
(y - 1)*(y + 1)*(3*y + 2)/3
Let h(k) = -4*k**3 + 1. Let w = -3 - -2. Let n be h(w). Suppose 2*a**4 - 3 + 5 - n*a**2 + a**2 = 0. What is a?
-1, 1
Let l(a) be the third derivative of a**5/20 - 5*a**4/2 + 50*a**3 - 34*a**2. What is p in l(p) = 0?
10
Suppose -4*i = -1 - 11. Let s = 3 - i. Factor 0*h**2 + s*h**2 - h + h**2 - 2.
(h - 2)*(h + 1)
Let b(v) = 2*v**3 + 6*v**2 + 14*v + 10. Let l be 2/(-10) - (-24)/20. Let g(o) = o + 1. Let n(c) = l*b(c) - 8*g(c). Let n(u) = 0. Calculate u.
-1
Let y(x) = x**2 - 5*x - 4. Let w(j) = 2*j**2 - 11*j - 9. Let b(m) = 4*w(m) - 9*y(m). Let s(k) = 2*k**3 - 4*k**2 + 2*k. Let q(d) = 4*b(d) - s(d). Factor q(n).
-2*n*(n - 1)*(n + 1)
Let o be (8/(-60))/((-2)/5). Factor 1/3*q**2 + 0 - o*q.
q*(q - 1)/3
Let w(g) be the third derivative of -g**7/1260 - g**6/180 - g**5/180 + g**4/36 + g**3/12 + 20*g**2. Factor w(s).
-(s - 1)*(s + 1)**2*(s + 3)/6
Factor -9*f + 1 + 9*f**2 + f + 2*f**2 + 5*f**2.
(4*f - 1)**2
Let a(r) be the third d