/135*p**5 + 0*p**4. Factor b(m).
2*m**2*(m - 2)/9
Suppose -10 = -3*k - 2*k. Suppose 8*t + 14*t**2 + 2*t**3 + 2*t**4 + 6*t**3 - k*t**2 + 0 + 2 = 0. What is t?
-1
Suppose 2*k - 7*k = 40. Let h(i) = 3*i**3 - 4*i**2 + 3*i - 5. Let x(p) = 5*p**3 - 6*p**2 + 5*p - 8. Let v(t) = k*h(t) + 5*x(t). Determine d so that v(d) = 0.
-1, 0
Let q(u) be the second derivative of 0 - 5/6*u**3 - 1/20*u**5 - u**2 - u - 1/3*u**4. Find d such that q(d) = 0.
-2, -1
Let u(j) = -j - 4. Let t be u(-4). Suppose n - 3*x - 21 = 0, -3*n + 4*x = -16 - 22. Factor n - 13*l**2 + 40*l - 70*l**3 + t + 2 + 35*l**2.
-2*(l - 1)*(5*l + 2)*(7*l + 2)
Suppose 2 = -2*f, 5*f = -0*i + 2*i + 51. Let q be (-15)/i - 4/14. What is v in 1/4*v**2 + 0 - q*v + 1/4*v**3 - 1/4*v**4 = 0?
-1, 0, 1
Suppose -2 - 4/3*d + 2/3*d**2 = 0. Calculate d.
-1, 3
Let h(y) be the first derivative of 0*y**2 + 1/5*y**3 - 3/10*y**4 + 0*y + 2. Factor h(i).
-3*i**2*(2*i - 1)/5
Suppose 4*q + 7 + 7 = -3*v, 0 = 3*v + 3*q + 9. Let u(g) be the first derivative of 1/2*g + 1/6*g**3 - v - 1/2*g**2. Determine n, given that u(n) = 0.
1
Let f(j) = 3*j**2 - 4*j + 1. Let u(g) = -g**2 + 1. Let r(t) = f(t) + u(t). Factor r(z).
2*(z - 1)**2
Let x = -64 + 64. Let n(k) be the third derivative of 0*k**3 + 4/105*k**7 + x*k**4 - 1/15*k**5 - 4*k**2 + 0 - 7/60*k**6 + 0*k. Suppose n(y) = 0. Calculate y.
-1/4, 0, 2
Let f(s) be the first derivative of 1 + 1/2*s**2 + 2/3*s**3 + 0*s + 1/4*s**4. Factor f(b).
b*(b + 1)**2
Let u(m) be the second derivative of -1/6*m**3 - 3*m + 0 + 0*m**2 + 1/12*m**4. Factor u(n).
n*(n - 1)
What is c in -12*c - 26*c**2 + 2 - 8*c**4 - 271*c**3 - 4 + 247*c**3 = 0?
-1, -1/2
Let l(w) = 7*w**2 - w + 4. Let n = 3 - 1. Suppose n*f + f = -12. Let q(g) = -13*g**2 + 2*g - 7. Let v(h) = f*q(h) - 7*l(h). Let v(s) = 0. Calculate s.
0, 1/3
Let r = -13 - -17. Solve r*u**5 + 3*u**4 + 0*u**4 - u**5 = 0 for u.
-1, 0
Let b be (1*3)/((-4)/(-4)). Factor b*r - 7*r**4 - 5*r**4 - 16*r**2 + 4*r**2 + 14*r**3 + 3*r**5 + 4*r**3.
3*r*(r - 1)**4
Solve -20 + 2*a**2 + 8 + a**2 + 10 - 5*a = 0.
-1/3, 2
Suppose q - 3*w - 12 = -q, -2*q - 4*w = 2. Determine i so that 2/3*i**4 + 0 + 2*i**2 + 2*i**q + 2/3*i = 0.
-1, 0
Let w = 27 + -24. Let h(x) be the second derivative of -2*x**2 + 0 + x**w - 2*x + 0*x**4 - 1/10*x**5. Factor h(r).
-2*(r - 1)**2*(r + 2)
Let c(h) be the first derivative of -1/18*h**3 + 5/12*h**2 - 4 - 1/2*h - 1/24*h**4. Determine r, given that c(r) = 0.
-3, 1
Let a(p) be the first derivative of 4 - 1/6*p**4 - 1/5*p**5 + 2/9*p**3 - 1/18*p**6 + 1/3*p + 1/2*p**2. Find q such that a(q) = 0.
-1, 1
Let f be -2*-2*(-3)/(-4). Suppose 4*m + 4*h + 8 = 0, 5*m + f*h = -h - 5. Suppose 0 - 1/3*i**2 + 0*i + 2/3*i**m - 1/3*i**4 = 0. What is i?
0, 1
Let t(y) be the third derivative of y**6/60 - y**4/12 + 3*y**2. Factor t(x).
2*x*(x - 1)*(x + 1)
Suppose -3*y - 47 = 1. Let j be 3/((-12)/y) + -2. Factor 6/5 - 9/5*o + 3/5*o**j.
3*(o - 2)*(o - 1)/5
Let x = 1 - 1/2. Factor -x*b**3 + 1/4*b - 1/2*b**2 + 1/4*b**5 + 1/4*b**4 + 1/4.
(b - 1)**2*(b + 1)**3/4
Let k be 9 - 8 - (-2)/2. Let j be 2/(k/(-1)*-4). Factor -3/4*w**2 - j*w**3 - 3/4*w - 1/4.
-(w + 1)**3/4
Let k be 287/392 - 2/(-16). Factor -4/7 - k*w - 2/7*w**2.
-2*(w + 1)*(w + 2)/7
Let r(b) = 6*b**2 - 6. Let u(s) = 5*s**2 - 5. Let c(y) = -3*r(y) + 4*u(y). Factor c(k).
2*(k - 1)*(k + 1)
Let m = 2224/513 + -1/513. Solve -m*a**2 - 5*a - 2/3 = 0.
-1, -2/13
Let x be (-36)/162 + 38/90. Factor 0 + x*w**3 + 0*w + 0*w**2.
w**3/5
Let n = 36 + -26. Factor 240*j**4 - 36*j**2 + n*j + 8*j - 6*j + 1200*j**5 + 120*j**4 - 213*j**3.
3*j*(4*j - 1)**2*(5*j + 2)**2
Let n(c) be the third derivative of -c**7/120 - 23*c**6/480 - c**5/40 - 3*c**2. Factor n(f).
-f**2*(f + 3)*(7*f + 2)/4
Determine x, given that 0 - 6*x + 18*x**2 - 15/2*x**3 = 0.
0, 2/5, 2
Let q(j) = -21*j**2 - 37*j - 12. Let g(u) = 7*u**2 + 12*u + 4. Let l(k) = -11*g(k) - 4*q(k). Factor l(p).
(p + 2)*(7*p + 2)
Let r(u) be the third derivative of 0 - 5/24*u**4 - 3*u**2 + 1/24*u**6 + 0*u + 1/3*u**3 - 1/30*u**5. Suppose r(q) = 0. Calculate q.
-1, 2/5, 1
Find p such that 12*p - 2*p**2 - 7*p + 4*p**2 - 3*p = 0.
-1, 0
Factor -p**4 - 2*p**2 - 17*p**3 + 4*p**4 - 16*p**3 + 32*p**3.
p**2*(p - 1)*(3*p + 2)
Let d(w) be the first derivative of -14*w**3/15 - 12*w**2/5 + 8*w/5 - 13. Factor d(g).
-2*(g + 2)*(7*g - 2)/5
Let g = 433/12 + -36. Let n(t) be the first derivative of 0*t**2 - g*t**4 + 0*t**3 + 0*t - 1. Factor n(k).
-k**3/3
Let o(z) be the first derivative of -z**7/21 + z**6/5 - z**5/5 - z**4/3 + z**3 - z**2 - 3*z - 1. Let c(t) be the first derivative of o(t). Factor c(y).
-2*(y - 1)**4*(y + 1)
Suppose r = 4*r. Let v(d) be the second derivative of r*d**2 - 1/6*d**3 + 0 - 2*d + 2/15*d**6 - 1/4*d**4 + 0*d**5. Suppose v(k) = 0. What is k?
-1/2, 0, 1
Suppose -4 = -4*p + 2*p. Suppose -2*j = -p - 10. Let b(o) = 7*o**2 + 2*o + 1. Let w(l) = 20*l**2 + 6*l + 3. Let n(d) = j*w(d) - 17*b(d). Factor n(k).
(k + 1)**2
Suppose 2*q = 3*q - 4*x, -15 = 5*q - 5*x. Let j be (-1 + -5)/(6/q). Factor -r**2 - 3*r**2 - j*r - 2*r**2.
-2*r*(3*r + 2)
Let p(c) be the first derivative of -c - 4/3*c**3 - 2 + 5/2*c**2. Find s such that p(s) = 0.
1/4, 1
Let x(l) = -l**2 - 4*l + 7. Let r be x(-6). Let y be 1*(0 + 1 - r). Factor 0*h**3 + 4*h**2 - 2*h**3 - y*h**2.
-2*h**2*(h + 1)
Let a(w) = -5*w**2 + 8*w + 7. Let i(u) = 5*u**2 - 7*u - 8. Let s(o) = -2*a(o) - 3*i(o). Factor s(x).
-5*(x - 2)*(x + 1)
Let c = -5 + 7. Solve -17*k - 6*k - 2*k**3 + 19*k**2 - k - 7*k**c + 16 = 0 for k.
2
Let s = 100 + -199/2. What is n in 0*n**2 - 3/4*n - s + 1/4*n**3 = 0?
-1, 2
Let k(y) = y + 9. Let d = -2 + -5. Let n be k(d). What is x in -x**2 + 0*x**2 - 2*x**3 - x**n = 0?
-1, 0
Let h be -8 - ((-217)/21 + -1). Suppose 26/3*m - 12*m**4 - h*m**2 - 38*m**3 + 2 = 0. What is m?
-3, -1/3, 1/2
Let o(n) = 6*n**3 - 4*n**2 - 2*n. Let y(q) = q**3 - 1. Let j(h) = -o(h) + 4*y(h). Let j(s) = 0. What is s?
-1, 1, 2
Let f be ((-1 - 0) + (-4 - -7))/1. Let t(x) be the first derivative of 3*x**f + 1/2*x**4 - 3 + 2*x**3 + 2*x. Factor t(s).
2*(s + 1)**3
Let g(w) be the second derivative of -w**6/15 + w**5/3 - w**4/3 + 11*w**2/2 + 8*w. Let d(h) be the first derivative of g(h). Let d(i) = 0. What is i?
0, 1/2, 2
Let c be 0/1 + -1 + -8. Let t be (-1)/(2 - (-21)/c). Solve -18*v**2 - 7*v**4 - 3*v**t - 23*v**3 + 1 + 2*v - 3*v**4 + 3 = 0.
-1, 2/5
Let d be (-72)/(-7) + (-18)/63. Factor -d*j - 3*j**5 - 3*j**4 + 4*j**5 + 2*j**3 + 10*j.
j**3*(j - 2)*(j - 1)
Let u(k) be the third derivative of -4*k**2 + 0*k**5 + 3/8*k**4 + 0*k - 1/40*k**6 + 0 + k**3. Let u(q) = 0. Calculate q.
-1, 2
Let x(p) be the second derivative of 1/4*p**4 + 3/2*p**3 + 0 - 2*p + 0*p**2. Suppose x(a) = 0. Calculate a.
-3, 0
Let -12/7 + 4/7*j**2 + 2/7*j**3 - 10/7*j = 0. Calculate j.
-3, -1, 2
Let d = 13 + -8. Let m(w) = 2*w**2 + 6*w**3 + 5*w + d + w**3 + w**2. Let x(a) = -4*a**3 - 2*a**2 - 3*a - 3. Let n(p) = 6*m(p) + 10*x(p). Solve n(q) = 0.
0, 1
Let b(f) be the first derivative of -2/5*f**3 - 1/10*f**4 + 6/5*f - 4 + 1/5*f**2. Factor b(j).
-2*(j - 1)*(j + 1)*(j + 3)/5
Let c(s) be the third derivative of s**7/420 + s**6/120 - s**5/120 - s**4/24 - 27*s**2. Solve c(w) = 0.
-2, -1, 0, 1
Let s = -30 - -14. Let g be 4/s*10 + 3. Solve -1/4*t**2 - 1/4 + g*t = 0.
1
Let -1/5*o**3 - 3/5*o**2 + 1/5*o**4 + 1/5*o + 2/5 = 0. Calculate o.
-1, 1, 2
Factor 6/7*k**3 + 2/7*k**4 + 4/7*k**2 + 0 + 0*k.
2*k**2*(k + 1)*(k + 2)/7
Let r(g) = 6*g**5 - 21*g**4 + 18*g**3 - 3*g + 3. Let v(d) = -7*d**5 + 22*d**4 - 18*d**3 + 3*d - 2. Let p(b) = -2*r(b) - 3*v(b). Factor p(s).
3*s*(s - 1)**3*(3*s + 1)
Let b(l) be the third derivative of -l**8/28 + 17*l**7/70 - 3*l**6/10 - 7*l**5/10 + 2*l**4 - 3*l**3/2 - 23*l**2. Find v such that b(v) = 0.
-1, 1/4, 1, 3
Let i = 89 + -443/5. Factor i*m**4 + 0*m**3 - 6/5*m**2 - 4/5*m + 0.
2*m*(m - 2)*(m + 1)**2/5
Suppose -2*v + 5*h - 4 = 0, -5*v + 3*h + 5 = -2*h. Factor -3 + 2*d**3 + 0*d**3 + 2*d**2 + v.
2*d**2*(d + 1)
Let r = -23 + 117/5. Let n = -6 + 32/5. Let -6/5*p**2 + 6/5*p - n + r*p**3 = 0. What is p?
1
Find t such that 1/5*t + 0*t**2 + 0 - 13/5*t**3 + 12/5*t**4 = 0.
-1/4, 0, 1/3, 1
Let o be (10 - 1)*6/9. Let r(q) = 7*q**3 - q**2 + 9*q - 9. Let y(s) = 15*s**3 - s**2 + 17*s - 18. Let l(z) = o*y(z) - 13*r(z). Factor l(d).
-(d - 3)**2*(d - 1)
Factor 4*x**2 + 25/6*x**4 + 32/3*x - 40/3*x**3 + 8/3.
(x