2*p**5 - 228*p**2 - 3*p**4 - 7*p**5 + 0 + 366*p**3 = 0. What is p?
1/5, 2/5, 1
Let s(d) = -9*d**3 + 57*d**2 - 51*d + 15. Let k(h) = -8*h**3 + 56*h**2 - 51*h + 16. Let p(b) = 3*k(b) - 4*s(b). Factor p(x).
3*(x - 4)*(2*x - 1)**2
Let q(s) be the second derivative of -1/2*s**4 + 2/15*s**6 + 5*s - 1/10*s**5 + 1/3*s**3 + s**2 + 0. Determine h so that q(h) = 0.
-1, -1/2, 1
Let a(r) = r**3 - r**2. Let s(v) = 5*v**3 - 14*v**2 - 13*v - 6. Let l(i) = -6*a(i) + s(i). Suppose l(q) = 0. What is q?
-6, -1
Let r(z) = -5*z**2 - 2*z - 1. Let w(j) = 2*j**2 + j. Let d(m) = -3*r(m) - 8*w(m). Factor d(k).
-(k - 1)*(k + 3)
Let j be (-4)/3*3*(-6)/8. Let c(i) be the first derivative of -12/7*i**j + 8/7*i**2 - 2/7*i - 1 + 0*i**4 + 54/35*i**5. Factor c(w).
2*(w + 1)*(3*w - 1)**3/7
Let j(q) be the first derivative of 2*q**3/3 - 11*q**2 + 20*q + 33. Determine i so that j(i) = 0.
1, 10
Let r(v) be the third derivative of 0*v - 1/32*v**4 + 1/240*v**5 + 1/12*v**3 + 4*v**2 + 0. Let r(a) = 0. What is a?
1, 2
Let d(r) be the first derivative of 1/6*r**4 + 4*r - 2 + 1/27*r**3 - 1/9*r**2 - 1/10*r**5. Let u(f) be the first derivative of d(f). Let u(k) = 0. Calculate k.
-1/3, 1/3, 1
Suppose -y = -6*y + 25. Suppose -y*v + 2 = -4*v. Solve 1/2 + 2*w + v*w**2 = 0 for w.
-1/2
Let p(c) = -c**3 - 18*c**2 + 39*c - 17. Let b be p(-20). Suppose 5*z**2 + 8*z**b + 0 + 2/3*z - 16/3*z**4 = 0. What is z?
-1/4, 0, 2
Let c(d) be the third derivative of 1/180*d**5 + 0*d + 1/12*d**4 + 1/2*d**3 + 0 + 8*d**2. Find s, given that c(s) = 0.
-3
Let z = 471 + -469. Determine o, given that -4/3*o**3 - 2*o**z + 0*o + 2/3 = 0.
-1, 1/2
Let l = -1822/7 + 262. Suppose -2/7*r**2 + l*r - 18/7 = 0. What is r?
3
Let x(d) be the third derivative of -d**8/2240 + d**7/420 - d**4/24 - 6*d**2. Let a(g) be the second derivative of x(g). Let a(q) = 0. Calculate q.
0, 2
Find m, given that -4*m - 1/2*m**4 + 2 + 1/2*m**2 - 1/2*m**5 + 5/2*m**3 = 0.
-2, 1
Factor 5*t**2 - 7*t - 40 + 162*t + 15*t**2.
5*(t + 8)*(4*t - 1)
Let i(z) be the second derivative of 1/2*z**2 + 2/3*z**4 + 1/5*z**5 - z + 5/6*z**3 + 0. Factor i(d).
(d + 1)*(2*d + 1)**2
Let p(v) be the second derivative of 7/30*v**5 - 3/20*v**6 + 0 + 0*v**3 + 1/2*v**2 + 1/6*v**4 + 2*v. Let i(w) be the first derivative of p(w). Factor i(q).
-2*q*(q - 1)*(9*q + 2)
Let v(k) = -4*k**4 + 8*k**3 - 6*k. Let z(b) = -9*b**4 + 17*b**3 - 11*b. Let g(o) = 5*v(o) - 2*z(o). Determine x, given that g(x) = 0.
-1, 0, 2
Suppose 0 = 5*h - 2*r - 7 - 8, 4*h = -4*r + 12. Suppose -s - 4*s + 9 = -3*z, -3*s = -z - 7. Factor -b**2 - h*b + z*b + 0*b**2.
-b*(b + 1)
Suppose -5*i = -2*n + 17, -n + 0*i + i + 4 = 0. Let m(u) = 2*u**3 + 1. Let l be m(n). Factor f**2 + 1/2 - 3/2*f**4 - f**l - 1/2*f**5 + 3/2*f.
-(f - 1)*(f + 1)**4/2
Suppose -4*o + 2*o + 4 = 0. Factor -14*b**3 - 7 + 0 + 19*b**3 - 1 + b**4 + 6*b**o - 4*b.
(b - 1)*(b + 2)**3
Factor 2*f**5 + 25*f**4 - 17*f**4 - 7*f**3 + 15*f**3.
2*f**3*(f + 2)**2
Let z(x) be the third derivative of -1/75*x**5 + 0 - 1/60*x**4 + 0*x - 2*x**2 - 1/300*x**6 + 0*x**3. Factor z(w).
-2*w*(w + 1)**2/5
Let d = 0 + -6. Let u be (d/(-4))/(2/12). Solve -14*z**3 + 5*z**2 - u*z**2 - 6*z**5 - 16*z**4 + 0*z**5 = 0.
-1, -2/3, 0
Let n(q) be the first derivative of 8*q**5/5 + q**4 - 20*q**3/3 + 4*q**2 + 45. Factor n(l).
4*l*(l - 1)*(l + 2)*(2*l - 1)
Factor 0*v**2 + 0*v - 8/7*v**3 + 2/7*v**4 + 0.
2*v**3*(v - 4)/7
Let n(o) be the third derivative of o**7/140 - o**6/90 + o**3/6 - o**2. Let z(u) be the first derivative of n(u). Factor z(g).
2*g**2*(3*g - 2)
Let -6*d**2 + 9*d**5 - 4*d**4 - 2*d**4 - 14*d**3 - 7*d**3 = 0. Calculate d.
-1, -1/3, 0, 2
Let j(y) be the first derivative of -1/6*y**3 + 3/4*y**2 + 4 - y. Factor j(b).
-(b - 2)*(b - 1)/2
Suppose 2 - 18 = -4*v. What is h in -2*h + h + h**2 - v*h + h**3 + 3*h = 0?
-2, 0, 1
Factor -q**2 - 2*q**3 + 0*q**2 + 2*q + q**2.
-2*q*(q - 1)*(q + 1)
Let m(g) be the second derivative of -2*g**7/21 + g**6/10 + 13*g**5/20 - 17*g**4/12 + g**3/2 + g**2 + 8*g. Factor m(t).
-(t - 1)**3*(t + 2)*(4*t + 1)
Determine j, given that 96/5*j - 24/5*j**3 - 4/5*j**4 - 64/5 - 4/5*j**2 = 0.
-4, 1
Let y be (-37 - -35)*5/(-18)*2. Solve 10/9*d**4 + 0 - y*d**2 - 4/9*d + 4/9*d**3 = 0.
-1, -2/5, 0, 1
Let f(m) = -2*m + 17. Let k be f(7). Let o(p) be the second derivative of p + 0 - 1/66*p**4 + 1/11*p**k - 2/11*p**2. Find a such that o(a) = 0.
1, 2
What is j in -366 - 222 - j**2 + 84*j + 3*j**2 - 5*j**2 = 0?
14
Let g be (-180)/(-2070) + ((-88)/23)/(-2). Factor 0*n**g + 2/11*n**3 + 0 - 2/11*n.
2*n*(n - 1)*(n + 1)/11
Let p(c) be the second derivative of -c**4/48 + c**2/2 + 7*c. Factor p(y).
-(y - 2)*(y + 2)/4
Let y = -283/4 + 71. Factor -j - j**3 + 3/2*j**2 + 1/4 + y*j**4.
(j - 1)**4/4
Factor 0*o**2 + 0 - 1/4*o + 1/4*o**3.
o*(o - 1)*(o + 1)/4
Let b(d) be the second derivative of -d**9/30240 + d**8/13440 + d**4/3 - 2*d. Let z(o) be the third derivative of b(o). What is m in z(m) = 0?
0, 1
Factor -2*p**2 - 3*p + 11*p**2 - 2*p**4 - p**4 + 9*p.
-3*p*(p - 2)*(p + 1)**2
Let z(r) be the second derivative of r**5/120 + r**4/24 + r**3/12 + r**2/12 + r. Factor z(u).
(u + 1)**3/6
Let t(r) = 4*r**2 + 2. Let l(u) = 3*u**2 - u + 2. Let k(f) = 3*l(f) - 4*t(f). Let b(c) = -c**2 - c. Let s(v) = -6*b(v) + k(v). Solve s(a) = 0 for a.
1, 2
Let s = 165/4 + -41. Let c(n) be the first derivative of -s*n**2 + 0*n - 1/6*n**3 - 1. Factor c(i).
-i*(i + 1)/2
Suppose 25*l - 7*l + 70 + 3*l**2 - 43 = 0. What is l?
-3
Suppose 0 = -5*v + 21 + 44. Solve -4*c**4 - 9*c**3 + v*c**4 - 17*c**2 - 3*c**5 + 20*c**2 = 0.
0, 1
Suppose t + 8*w - 3*w = -13, -5*t - 2*w = -4. Suppose 10/3*z**3 + 5/3*z + 1/3*z**5 + 5/3*z**4 + 10/3*z**t + 1/3 = 0. Calculate z.
-1
Let y(u) be the second derivative of u**6/135 - u**4/6 - 4*u**3/27 + 4*u**2/3 - 47*u. Determine b, given that y(b) = 0.
-2, 1, 3
Solve 3/5*o + 3/5*o**2 + 0 = 0 for o.
-1, 0
Let q(p) = p**3 - p - 2. Let d be q(0). Let g be (0/(-3))/(d - 1). Factor 0*i - 2/7*i**2 + g.
-2*i**2/7
Suppose -2*o = 2*o - 96. Let u be 0/1 + o/108. Let -4/9*a**3 + u*a**4 + 2/9*a**2 + 0*a + 0 = 0. What is a?
0, 1
Let m(v) = v**2 + 10*v + 9. Let i be m(-6). Let g be (2/(-3))/(i/9). Suppose 0 + 4*d**3 - g*d**2 - 4/5*d = 0. What is d?
-2/5, 0, 1/2
Let f(l) = -4*l**3 + 28*l**2 + 2*l - 10. Let m be f(7). Let 0 - 1/2*i - 3/4*i**2 + 1/4*i**m + 0*i**3 = 0. What is i?
-1, 0, 2
Let i(c) be the first derivative of -4*c**6/9 + 4*c**5/5 - 4*c**3/9 - 16. Factor i(y).
-4*y**2*(y - 1)**2*(2*y + 1)/3
Let t(v) = v**3 - v**2 + v. Let a(r) = 4*r**4 + 4*r**3 - 16*r**2 + 20*r. Let c(d) = a(d) - 12*t(d). Factor c(k).
4*k*(k - 2)*(k - 1)*(k + 1)
Let o(n) = 7*n**4 + 3*n**3 + n**2 - 9*n + 4. Let m(p) = -p**4 + p - 1. Let x(w) = 6*m(w) + o(w). Suppose x(s) = 0. Calculate s.
-2, -1, 1
Let x(w) = 4*w. Let u be x(1). Suppose 0 = -a + 1 + 2. Suppose -2*h**3 - 3*h**3 + u*h**a = 0. What is h?
0
Let a(u) = -u. Let i be a(0). Suppose i*y = -5*y. Factor 1/2*r**5 + 0*r**2 + 0*r**4 - 1/2*r**3 + 0 + y*r.
r**3*(r - 1)*(r + 1)/2
Let u(z) be the first derivative of 0*z**2 - 1/48*z**4 - 1/40*z**5 - 1/120*z**6 - 4*z + 0*z**3 - 2. Let r(a) be the first derivative of u(a). Factor r(t).
-t**2*(t + 1)**2/4
Let y(q) be the third derivative of -q**9/1008 - q**8/560 + q**7/840 - 5*q**4/24 - 3*q**2. Let j(r) be the second derivative of y(r). Factor j(k).
-3*k**2*(k + 1)*(5*k - 1)
Let 125*d**4 + 12*d**3 + 2*d**2 + 4*d**5 - 137*d**4 - 6*d**2 = 0. What is d?
0, 1
Let i(x) be the first derivative of 4/7*x + 1/14*x**4 - 1/7*x**2 - 4/21*x**3 - 6. Factor i(j).
2*(j - 2)*(j - 1)*(j + 1)/7
Suppose 3*m = -2*m. Let z = m - -3. Find y, given that -3*y**3 - 4*y**z + 4*y**3 + y**2 + 2*y**3 = 0.
0, 1
Suppose -25 + 0 = 5*m. Let p be -1*1 - (m + 2). Suppose -10/3*j**3 + 12*j**2 + p*j**5 + 8/3*j - 16/3 - 16/3*j**4 = 0. What is j?
-1, 2/3, 2
Let i(t) = -3*t**2 + 4*t - 5. Let w(p) = 6*p**2 - 9*p + 12. Let j(f) = -9*i(f) - 4*w(f). Determine h, given that j(h) = 0.
-1, 1
Let a(y) be the third derivative of 1/8*y**4 - y**2 + 0 + 0*y**3 + 1/20*y**5 + 0*y. Factor a(b).
3*b*(b + 1)
Let j(b) = -11*b**4 + 12*b**3 + 8*b**2 - 19*b - 9. Let k(n) = n**4 + n**3 - n**2 - n + 1. Let m(o) = j(o) + 5*k(o). Factor m(y).
-(y - 2)**2*(y + 1)*(6*y + 1)
Let h(m) be the first derivative of -1/4*m**4 - 1/36*m**6 - 1/12*m**2 + 0*m + 3 + 2/15*m**5 + 2/9*m**3. Suppose h(c) = 0. Calculat