p + 2)/3
Suppose -21*q + 60*q + 9 - 31*q - 20*q + 3*q**2 = 0. Calculate q.
1, 3
Factor -7301*i**3 - 1936*i**2 + 32 + 256*i + 1744*i**3 + 46818*i**4 - 4235*i**3.
2*(9*i - 2)**2*(17*i + 2)**2
Let v(p) = p. Let i(r) = r**2 - 8*r - 10. Let u(g) = -i(g) - 2*v(g). Let s be u(7). Factor 15*w + 31*w**2 + 5*w**3 + 3*w**3 + 3*w**s + 2 - 7*w**2.
(w + 1)**2*(11*w + 2)
Let v(a) be the first derivative of -a**5/20 + 3*a**4/8 - a**3 + 6*a**2 + 8. Let d(y) be the second derivative of v(y). Factor d(q).
-3*(q - 2)*(q - 1)
Suppose -7*i = -9*i. Let c be (-7 + 3)/(i + -2). Let -11 - 4*u**c - 1 - 20*u - 4 = 0. What is u?
-4, -1
Let y(h) = -16*h**2 - 17*h - 9. Let s(n) = 62*n**2 + 70*n + 35. Let g(a) = 6*s(a) + 22*y(a). Determine f, given that g(f) = 0.
-2, -3/10
Let h(z) be the second derivative of 1/168*z**7 + 1/120*z**6 - 1/40*z**5 + 0 + 0*z**2 + 0*z**3 + 8*z + 0*z**4. Factor h(k).
k**3*(k - 1)*(k + 2)/4
What is k in 3/4*k - 25/8*k**2 + 0 - 9/8*k**3 = 0?
-3, 0, 2/9
Let p(b) be the third derivative of -b**5/150 - 19*b**4/60 + 4*b**3/3 + 26*b**2 + 2*b. Determine s, given that p(s) = 0.
-20, 1
Suppose 68*c + 24 = 74*c. Let h(y) be the third derivative of 1/24*y**4 + 0*y + 0*y**3 + 1/360*y**6 + c*y**2 + 1/45*y**5 + 0. Determine o, given that h(o) = 0.
-3, -1, 0
Let j(l) be the first derivative of l**4/18 - 8*l**3/27 - 4*l**2/9 + 32*l/9 - 328. Solve j(u) = 0 for u.
-2, 2, 4
Let x(m) be the first derivative of 2/3*m**3 - 19 + 50*m + 10*m**2. Factor x(q).
2*(q + 5)**2
Let t = 39 + -37. Suppose -i = v + t, -v = -i - 2*i - 6. Determine j so that v*j - 3/2*j**2 + 0 + 3/2*j**3 = 0.
0, 1
Let m(u) = -29*u**2 + 62*u - 8. Let f(c) = c**2 - c - 2. Let r(n) = -2*f(n) - m(n). Solve r(s) = 0 for s.
2/9, 2
Let r be ((-10)/(-35))/(110/77). Let n(x) be the second derivative of 1/30*x**3 + 0 - 1/20*x**4 + x + r*x**2. Factor n(g).
-(g - 1)*(3*g + 2)/5
Let w be 2/(48/(-27) - -2). Let i = 16 - w. Factor 0*v + 6 - i*v + 0*v - v + 2*v**2.
2*(v - 3)*(v - 1)
Let m(v) be the second derivative of -5/12*v**4 + v + 20/3*v**3 - 40*v**2 + 0. Factor m(i).
-5*(i - 4)**2
Let w(g) = 3*g**5 + 24*g**4 + 30*g**3 + 30*g**2 - 6*g - 6. Let a(b) = b**4 - b**3 + b**2 - b - 1. Let p = 27 + -26. Let x(s) = p*w(s) - 6*a(s). Factor x(z).
3*z**2*(z + 2)**3
Let o(t) be the first derivative of -1/20*t**4 + 1 + 1/6*t**3 - 1/5*t**2 - 5*t. Let v(u) be the first derivative of o(u). Solve v(h) = 0.
2/3, 1
Suppose 8*h = 17 - 1. What is x in -x**2 + 12*x**3 - 2*x**4 - 32 - 5*x**2 + 13*x - 61*x + 4*x**h = 0?
-1, 4
Let n(o) = 15*o - 27. Let l be n(6). Let w = -60 + l. Find f, given that 0 + 0*f - 2/3*f**w + 2/3*f**2 = 0.
0, 1
Suppose -3*u = -u - 20. Factor -2 - 7*w**3 + u + 15*w**2 + 3*w**2 + 7*w**4 - 6*w**4 - 20*w.
(w - 2)**3*(w - 1)
Let a be 0/4 + ((-3)/6 - -1). Let y(w) be the third derivative of -1/80*w**6 + 0*w + 0 + 2*w**2 + 1/16*w**4 + a*w**3 - 1/20*w**5. Suppose y(f) = 0. What is f?
-2, -1, 1
Let n(w) be the second derivative of 16*w**2 - 18*w + 9/5*w**5 + 2*w**4 - 40/3*w**3 + 0. Factor n(l).
4*(l + 2)*(3*l - 2)**2
Determine o so that -63/2*o**2 + 30 + 12*o**3 - 12*o + 3/2*o**4 = 0.
-10, -1, 1, 2
Let 102 - 2*p**3 - 30 + 5*p**3 - 32*p**2 - 6*p**3 + 66*p + 23*p**2 = 0. Calculate p.
-6, -1, 4
Let x be (-6)/8 - (-417)/(-4). Let m be -1*27/x + (-3)/(-21). Factor -m*k - 8/5*k**2 - 8/5*k**4 + 0 - 12/5*k**3 - 2/5*k**5.
-2*k*(k + 1)**4/5
Let s be (-1 - (1 - 2))/(-4). Let d = s + 1. Determine p so that -3*p**3 - 4*p - 3*p**2 + 0*p**3 + 7*p + 2 + d = 0.
-1, 1
Let s be (6/(-4))/((-9)/12). Suppose -a**s - 5*a + a - 4 + 4*a**3 + 5*a**2 = 0. Calculate a.
-1, 1
Let s(m) be the first derivative of 3/2*m**2 + 5/2*m + 25 + 1/6*m**3. Factor s(u).
(u + 1)*(u + 5)/2
Determine t so that -3/5*t - 1/5*t**4 - 4/5 + t**2 + 3/5*t**3 = 0.
-1, 1, 4
Let u be 729/(-108)*-1*(-16)/(-12). Let q(t) be the second derivative of u*t + 1/170*t**5 + 3/17*t**2 - 5/51*t**3 + 0 + 1/102*t**4. Factor q(b).
2*(b - 1)**2*(b + 3)/17
Let d(g) = g**2 - g + 2. Let b(a) = -3*a**2 - 1. Let h(p) = 5*b(p) + 10*d(p). Suppose h(s) = 0. Calculate s.
-3, 1
Let y(q) be the first derivative of 1 + 9/2*q**2 - 3/4*q**4 - 6*q + 0*q**3. Factor y(b).
-3*(b - 1)**2*(b + 2)
Let k = -81 - -85. Let y(t) be the third derivative of -1/15*t**3 + 0 - 1/30*t**k - 1/150*t**5 + 4*t**2 + 0*t. Factor y(x).
-2*(x + 1)**2/5
Suppose -v + 29*v - 112 = 0. Let z(f) be the first derivative of 0*f + 1 + 0*f**2 + 1/6*f**v + 4/9*f**3. Determine r, given that z(r) = 0.
-2, 0
Let m(k) be the third derivative of 19*k**2 + 0*k - 1/420*k**7 + 0 + 0*k**3 + 1/120*k**6 - 1/672*k**8 + 0*k**4 + 0*k**5. Factor m(x).
-x**3*(x - 1)*(x + 2)/2
Let o(a) be the third derivative of a**8/2520 - a**7/560 + a**6/360 - a**5/720 + 3*a**3/2 + 2*a**2. Let i(n) be the first derivative of o(n). Factor i(s).
s*(s - 1)**2*(4*s - 1)/6
Let q(u) be the first derivative of -4*u**5/5 + u**4 + 28*u**3/3 - 26*u**2 + 24*u - 112. Factor q(z).
-4*(z - 2)*(z - 1)**2*(z + 3)
Let c(a) = a**4 - 2*a**3 - 9*a**2 - 9*a - 3. Let r(k) = -2*k**4 + 5*k**3 + 18*k**2 + 18*k + 7. Let z(o) = -14*c(o) - 6*r(o). Determine s so that z(s) = 0.
-3, -1, 0, 3
Suppose -11*p - 52 = 58. Let t be (-12 - -10)/(4 + 1)*p. Factor -3/5*v**2 + 0 + 1/5*v**t + 2/5*v + 0*v**3.
v*(v - 1)**2*(v + 2)/5
Let q = -50 + 59. Let o be (-16)/(-4) + (-24)/q. Find a such that 4/3*a - o - 1/3*a**2 = 0.
2
Let z be ((-3)/43 - 0)*(-2)/(-2). Let i = z - -55/172. Solve 1/4*p**3 - 1/4*p**2 + 0*p - 1/4*p**5 + i*p**4 + 0 = 0.
-1, 0, 1
Let q(t) be the second derivative of t**5/4 + 35*t**4/12 - 25*t**3/3 - 40*t**2 - 121*t. What is a in q(a) = 0?
-8, -1, 2
Let b(x) be the second derivative of 4*x**5/75 - 3*x**4/10 + 4*x**3/15 + 2*x**2 - 20*x. Let h(j) be the first derivative of b(j). Factor h(d).
4*(d - 2)*(4*d - 1)/5
Let t = -4 + 6. Let y be (6 - (4 - 4)) + (-12)/3. Factor c**2 - y - 3*c**t + 4*c**2 + c - c**3 + 0*c**3.
-(c - 2)*(c - 1)*(c + 1)
Let d = 384 - 384. Let x(o) be the second derivative of 0*o**4 + 1/10*o**5 + d*o**2 + 3*o + 0 - 1/3*o**3. Factor x(r).
2*r*(r - 1)*(r + 1)
Let z(g) = -6*g**3 - 3. Let s be (-4)/12 + 13/3. Suppose s = -w - 3*w. Let t(k) = -k**5 - k**3 - 1. Let u(a) = w*z(a) + 3*t(a). Let u(p) = 0. What is p?
-1, 0, 1
Factor 2/11*h**5 + 0*h + 4/11*h**4 + 0*h**2 + 0 - 6/11*h**3.
2*h**3*(h - 1)*(h + 3)/11
Let s = 37 + -34. Solve 5*q**2 - 3*q**3 + 4*q**2 - 3*q**3 - s = 0.
-1/2, 1
Let g = -776 - -1555/2. Let l(i) be the first derivative of -g*i - 1/18*i**3 - 1/2*i**2 + 1. Factor l(u).
-(u + 3)**2/6
Let m be 4/5 - (28/(-5))/2. Determine a so that m*a**4 + 78/5*a**3 + 16/5 + 116/5*a**2 + 72/5*a = 0.
-2, -1, -2/3
Let p(w) be the first derivative of -8*w**5/15 - 9*w**4/2 + 76*w**3/9 - 21*w**2/4 + 4*w/3 + 78. Solve p(s) = 0.
-8, 1/4, 1/2
Suppose 0 = -37*j - 26 + 100. Factor 0 + 2/5*i**4 + 0*i - 2/5*i**3 + 0*i**j.
2*i**3*(i - 1)/5
Let n be (10 - (-1 - (-608)/56))*14. Solve 0*w + 1/7*w**n - 1/7 = 0 for w.
-1, 1
Suppose 0 = -w - 7 + 11. Let s be -2 - (w/(-6))/(4/22). Solve -7/3*r**5 + s*r**4 - 2/3*r - 5/3*r**2 + 0 + 3*r**3 = 0.
-1, -2/7, 0, 1
Let p(i) be the second derivative of -i + 0 - 1/21*i**4 + 4/7*i**3 + 0*i**2. Solve p(k) = 0 for k.
0, 6
Let a(z) be the third derivative of z**7/210 - z**6/24 + 7*z**5/60 - z**4/8 - 214*z**2. Factor a(w).
w*(w - 3)*(w - 1)**2
Let r(n) = 4*n**5 + 4*n**4 - 26*n**3 - 15*n**2 - 22. Let f(p) = -p**5 - p**4 + 9*p**3 + 5*p**2 + 8. Let c(x) = 11*f(x) + 4*r(x). Factor c(b).
5*b**2*(b - 1)*(b + 1)**2
Find o, given that -145633*o + 29205536 + 1591*o**2 + 737*o**2 + 597265*o + 2*o**3 + o**3 + o**3 = 0.
-194
Let w(a) = 226*a - 45 - 117*a - 122*a + 11*a**2 - 21*a**3. Let q(s) = -10*s**3 + 6*s**2 - 6*s - 22. Let m(g) = 13*q(g) - 6*w(g). Let m(d) = 0. What is d?
-1, 2
Suppose -12*m - 7*m + 510 = 472. Factor 1/3*f**m + 1 - 4/3*f.
(f - 3)*(f - 1)/3
Suppose -25*j**3 - 279*j**4 + 136*j**4 + 138*j**4 + 160*j**2 - 180*j = 0. What is j?
-9, 0, 2
Suppose 25*r = -8*r - 8 + 8. Suppose 0*q - 4/5*q**5 + 4/5*q**3 + 4/5*q**2 + r - 4/5*q**4 = 0. What is q?
-1, 0, 1
Factor 3/2*z**4 + 75 - 9/2*z**2 + 165/2*z - 21/2*z**3.
3*(z - 5)**2*(z + 1)*(z + 2)/2
Let n be 4/14 - 78/(-21). Suppose 15 = n*c + c. Let -3 - 13*l**2 + c - 2*l**2 + 6*l = 0. Calculate l.
0, 2/5
Let s(x) = 7*x**2 - 2*x - 17. Let d(y) = -6*y**2 + 2*y + 16. Let c = 27 - 31. Let t(i) = c*s(i) - 5*d(i). Factor t(p).
2*(p