 1
Factor 1/5*q**5 + 76832/5 + 60368/5*q + 1288/5*q**3 + 13328/5*q**2 + 58/5*q**4.
(q + 2)*(q + 14)**4/5
Let l(u) = -u**3 - 4*u**2 + 11*u - 4. Let b be l(-6). Determine j, given that 48*j - 2*j**b - 8 + 6*j**3 + 51*j - 115*j = 0.
-1, -2/3, 2
Let i(s) = 10*s**2 + 65*s - 28. Let j be i(-7). Let c(w) be the first derivative of 0*w**2 - 2/7*w**3 + 1/14*w**4 + 0*w - j. Let c(f) = 0. What is f?
0, 3
Let l(r) = -4*r**2 + 62*r - 964. Let s(o) = -5*o**2 + 62*o - 965. Let k(w) = -4*l(w) + 3*s(w). Factor k(u).
(u - 31)**2
Let w = -82 - -40. Let v be (w/49)/(1/(-7)). Factor 32*a - 4*a**2 + 8 + v*a**2 + 28*a**2.
2*(3*a + 2)*(5*a + 2)
Suppose -10*v = -22*v + 60. Let k(u) be the third derivative of 2*u**3 + 0 + 1/2*u**4 + v*u**2 + 1/20*u**5 + 0*u. Suppose k(h) = 0. What is h?
-2
Let n(d) be the first derivative of -d**4/14 - 10*d**3/7 - 9*d**2 - 14*d + 135. Factor n(w).
-2*(w + 1)*(w + 7)**2/7
Suppose -13*y - 35*y = -9*y - 78. Determine o so that -1/2*o + 0 - 1/2*o**y = 0.
-1, 0
Find l such that 8/3*l**4 + 64/3*l**3 + 30*l**2 - 36 - 18*l = 0.
-6, -3/2, 1
Solve -3/4*z**2 - 21/4*z - 9 = 0 for z.
-4, -3
Factor 2/5*k**2 - 4/5 - 2/5*k.
2*(k - 2)*(k + 1)/5
Find k such that 16/7*k**3 + 0*k**4 + 8/7*k**2 - 4/7*k**5 - 12/7*k - 8/7 = 0.
-1, 1, 2
Determine n so that 3 - 1/2*n - 1/2*n**2 = 0.
-3, 2
Suppose 0 = -5*k - 4*y, 0*y = 3*k - y. Factor 0*i + 0 + 1/3*i**3 + k*i**2.
i**3/3
Factor 392/9 + 448/9*l + 58/9*l**2 + 2/9*l**3.
2*(l + 1)*(l + 14)**2/9
Find u such that -13/10*u**3 + 7/5*u - 7/10*u**4 - 1/10*u**5 - 1/10*u**2 + 4/5 = 0.
-4, -2, -1, 1
Let j = -10522/5 - -2108. Solve -54/5*i**5 + 30*i**4 + 0 - 126/5*i**3 + 12/5*i + j*i**2 = 0 for i.
-2/9, 0, 1
Suppose 3*j = -5*d + 21, 7*d - 5*j - 9 = 8*d. Let w be 1/d + 6/36. What is f in w*f**2 + 0*f - 1/3 = 0?
-1, 1
Factor 3/5*g**2 + 9 - 48/5*g.
3*(g - 15)*(g - 1)/5
Let h(d) = -2*d**3 - 6*d + 24. Let a(w) = -6*w**3 - w**2 - 17*w + 68. Let i(f) = 6*a(f) - 17*h(f). Factor i(y).
-2*y**2*(y + 3)
Let x(i) = 13*i**2 + 4*i - 3. Let b be x(1). Find d such that -10 - 21*d - 15*d**3 + 35*d**2 - 11*d**4 - b*d**4 + 36*d = 0.
-1, 2/5, 1
Factor -3*s**3 + 3*s**2 - 2*s**4 - s**4 + 117*s + 3*s**5 - 117*s.
3*s**2*(s - 1)**2*(s + 1)
Let p(a) be the third derivative of a**7/280 - a**5/10 + 2*a**3 + 5*a**2 + 7. Let p(s) = 0. Calculate s.
-2, 2
Factor 2/7*v**2 + 288/7 - 48/7*v.
2*(v - 12)**2/7
Let h(m) = -2*m**4 - 16*m**3 + 14*m**2 - 8*m - 3. Let f(p) = -5*p**4 - 45*p**3 + 42*p**2 - 24*p - 8. Let n(l) = 3*f(l) - 8*h(l). Suppose n(x) = 0. What is x?
0, 1, 2, 4
Let y = 39 - 43. Let j(p) = p**3 + 6*p**2 + 6*p - 5. Let h be j(y). Factor 4/3*c + 0 + 2/3*c**2 - 2/3*c**h.
-2*c*(c - 2)*(c + 1)/3
Let w = 166/15 - 14/3. Let k(n) be the first derivative of 6 + 56*n**2 - w*n**5 + 25*n**4 + 2/3*n**6 - 152/3*n**3 - 32*n. Determine l so that k(l) = 0.
1, 2
Let b(p) = p**2 + p. Let w be b(1). Suppose 0 = -5*y - 3*k - 25 + 10, 2*k = -w*y - 10. Factor -6*q**2 + 0*q**2 + 0 + y - 3*q**3.
-3*q**2*(q + 2)
Let k(q) be the third derivative of -q**6/120 - q**5/4 + q**2 + 25. Factor k(z).
-z**2*(z + 15)
Let y(j) be the first derivative of -1/36*j**6 + 9/4*j**2 + 0*j - 3/4*j**4 - 16 + 4/15*j**5 + 0*j**3. Suppose y(r) = 0. What is r?
-1, 0, 3
Let l(j) = -206*j**2 - 163*j + 165. Let z(v) = -73*v**2 - 54*v + 55. Let g(n) = 6*l(n) - 17*z(n). Factor g(y).
5*(y - 11)*(y - 1)
Let u(c) be the third derivative of -c**7/945 + 7*c**5/270 - c**4/18 + 14*c**2 + 2. Factor u(g).
-2*g*(g - 2)*(g - 1)*(g + 3)/9
Let x be (-4)/15*(-6150)/820. Factor -4/5*y**4 + 8/5*y**x - 8/5*y**3 + 4/5*y - 4/5 + 4/5*y**5.
4*(y - 1)**3*(y + 1)**2/5
Let j(g) be the second derivative of g**4/8 - 37*g**3/4 + 27*g**2 + 17*g + 18. Determine x, given that j(x) = 0.
1, 36
Let c be (-81)/(-108) + (-33)/(-4). Suppose -c*s + 20 = s. Factor -147/5*p**3 + 231/5*p**s - 96/5*p + 12/5.
-3*(p - 1)*(7*p - 2)**2/5
Let w(d) be the third derivative of d**11/332640 - 3*d**5/20 - 7*d**2. Let x(f) be the third derivative of w(f). Let x(y) = 0. What is y?
0
Suppose i = -0*i + 16. Find m, given that -m**3 + 39*m**2 - 5*m**2 + i*m**2 + 32 - 5*m**3 - 112*m = 0.
1/3, 4
Suppose 0*d + 2*d - 12 = 0. Suppose -d*w + 14 = w. Determine z so that -2/9*z**5 + 10/9*z - 4/9*z**w - 8/9*z**3 - 4/9 + 8/9*z**4 = 0.
-1, 1, 2
Let l(o) be the third derivative of 1/80*o**6 - 3/16*o**4 - 17*o**2 + 1/20*o**5 + 0 + 0*o**3 + 0*o. Factor l(g).
3*g*(g - 1)*(g + 3)/2
Suppose i = -0 + 3. Factor 0*q**3 - q**i - 2*q**2 - 5*q + 4*q + 0*q.
-q*(q + 1)**2
Factor -2/7*m**5 - 16/7*m**3 + 0*m**2 + 12/7*m**4 + 0 + 0*m.
-2*m**3*(m - 4)*(m - 2)/7
Let b(p) be the second derivative of -p**7/20160 - p**6/5760 + p**5/480 + 5*p**4/12 - 17*p. Let a(k) be the third derivative of b(k). Factor a(o).
-(o - 1)*(o + 2)/8
Let n be (-58)/29*(-1 + 0). Let d(j) be the second derivative of 0*j**3 + 0 - 1/40*j**5 + 1/60*j**6 + 0*j**4 + 0*j**n - 3*j. Factor d(b).
b**3*(b - 1)/2
Let m(x) = x**2 - 10*x - 15. Let f(h) = -2*h - 63. Let u be f(-30). Let j(k) = -k**2 + 20*k + 29. Let l(v) = u*j(v) - 5*m(v). Determine c so that l(c) = 0.
-3, -2
Suppose 87 - 87 = -s. Suppose s = 12*x + 5*x - 51. Determine t, given that -2/5*t**x - 2/5*t**2 + 0 + 0*t = 0.
-1, 0
Let k = 74 + -220/3. Suppose -2*l - 9 + 28 = -5*g, -4*l + 23 = -5*g. Let -k*j**5 + 2/3*j**2 + 0*j - l*j**3 + 2*j**4 + 0 = 0. What is j?
0, 1
Let k(t) be the second derivative of 3*t**5/4 - 29*t**4/4 + 39*t**3/2 + 27*t**2/2 - 959*t. Factor k(y).
3*(y - 3)**2*(5*y + 1)
Suppose 24*y = 11*y. Suppose y + 2/5*g**2 + 2/5*g**3 + 0*g = 0. What is g?
-1, 0
Suppose -11 = 4*w + 1. Let p be ((-2 - w) + -3)*-1. What is b in b**3 + 1/4*b**4 + b + 1/4 + 3/2*b**p = 0?
-1
Let g(z) be the second derivative of z**8/1680 + z**7/70 - 7*z**6/60 + 11*z**5/30 - 17*z**4/12 - 38*z. Let t(a) be the third derivative of g(a). Factor t(h).
4*(h - 1)**2*(h + 11)
Suppose -q = 5*q - 24. Let 87*p**2 + 41*p**3 + 45*p - 6*p**3 - 12*p**2 + 5*p**q = 0. What is p?
-3, -1, 0
Let w(u) be the first derivative of u**5/50 - u**4/5 + 4*u**3/5 - 8*u**2/5 - 47*u + 22. Let b(l) be the first derivative of w(l). Factor b(d).
2*(d - 2)**3/5
Let d(x) be the first derivative of -x**6/360 + x**5/60 - x**4/24 + x**3/18 + 3*x**2 - 17. Let a(i) be the second derivative of d(i). What is p in a(p) = 0?
1
Let q = -507 + 509. Let s(f) be the first derivative of -2 + 1/3*f**3 + q*f + 3/2*f**2. Factor s(a).
(a + 1)*(a + 2)
Let d(q) be the second derivative of 0*q**5 + 0 + 0*q**2 - 1/105*q**6 + 0*q**3 - 7*q + 1/42*q**4. Suppose d(m) = 0. Calculate m.
-1, 0, 1
Let l(k) be the second derivative of -k**8/1008 - k**7/315 - k**6/360 - 5*k**2/2 - 13*k. Let i(g) be the first derivative of l(g). Find s, given that i(s) = 0.
-1, 0
Let n be (-3 + -1 + ((-1430)/44)/(-13))*-1. Determine g, given that 0*g - 13/2*g**3 - 2*g**5 + 0 - 8*g**4 - n*g**2 = 0.
-3, -1/2, 0
Let r = -111 + 116. Suppose 5 = 3*b - j, 0 = 2*b - 4*j + r*j + 5. Find v such that 0*v - 4/5*v**3 + 12/5*v**2 + b = 0.
0, 3
Let z = -2428/7 - -347. Suppose 0*a**2 + 3/7*a - z*a**3 - 2/7 = 0. What is a?
-2, 1
Suppose 3/4*o + 1/4 - 5/4*o**2 - 3/4*o**3 + o**4 = 0. Calculate o.
-1, -1/4, 1
Let g(z) = 6*z**3 - 35*z**2 - 114*z - 64. Let u(n) = 12*n**3 - 71*n**2 - 226*n - 128. Let q(b) = 7*g(b) - 3*u(b). Suppose q(p) = 0. Calculate p.
-2, -2/3, 8
Factor c**2 + 11 + 276/5*c.
(c + 55)*(5*c + 1)/5
Let v be 1 - 4*(-2 + 1). Let t(d) be the first derivative of 0*d + 0*d**2 + d**4 + 0*d**3 + 4/5*d**v - 7. Determine c so that t(c) = 0.
-1, 0
Let q(g) be the first derivative of -32/21*g**3 + 0*g - 18 + 1/7*g**4 + 32/7*g**2. Find t, given that q(t) = 0.
0, 4
Suppose -4*n = b + n - 17, 0 = 2*b - 4*n + 8. What is x in -497 - 5*x**b - 17*x - 3 + 0*x**2 - 83*x = 0?
-10
Factor -19683 + 0*u**3 - 8*u**3 + 2187*u - 81*u**2 + 9*u**3.
(u - 27)**3
Factor -1 - 41*t - 2*t**3 - 24*t**2 - 32 - 32 + 17 - 29*t.
-2*(t + 1)*(t + 3)*(t + 8)
Let j(u) be the first derivative of u**5/660 - u**4/44 + 3*u**3/22 + 17*u**2/2 + 17. Let r(f) be the second derivative of j(f). Factor r(y).
(y - 3)**2/11
Suppose -25 = 2*q + 5*c, -2*q + c = -6*q - 5. Let w(f) be the first derivative of 0*f + 1/4*f**2 + q*f**3 - 3 - 1/8*f**4. Let w(x) = 0. Calculate x.
-1, 0, 1
Let r(b) = 3*b**2 + 4*b - 2. Let j be r(-2). Suppose 3*x + 5*n + 11 = j, -x = n + 1. Let 1/4*o - 1/4*o**3 + 1/4*o**x + 0 - 1/4*o**4 = 0. Calculate o