).
-2*y**2*(y - 2)**2/7
Suppose -20 = -5*i, -7*y + 2*i = -2*y - 2. Let -11/2*b + y*b**2 - 3/2 = 0. Calculate b.
-1/4, 3
Let o(b) be the second derivative of -b**4/6 - b**3 + 192*b + 1. Factor o(m).
-2*m*(m + 3)
Suppose -35*i + 40 + 40*i + 24*i**3 - 40*i**2 - 29*i**3 = 0. Calculate i.
-8, -1, 1
Let x(l) be the second derivative of -l**4/30 + 6*l**3/5 - 32*l**2/5 - 47*l. Factor x(m).
-2*(m - 16)*(m - 2)/5
Let r(p) = p**3 + p**2 - 4*p - 2. Let m be r(2). Let g(z) be the second derivative of z**3 - 5*z + 3/4*z**4 + 0 + 0*z**m + 3/20*z**5. Solve g(t) = 0 for t.
-2, -1, 0
Suppose 0 = 5*q + 2*a - 1100, 4*q - 821 - 42 = -5*a. Let t = q + -144. Determine d, given that -3*d**3 - 3*d**4 + d**4 + 81*d**5 - t*d**5 + 2*d**2 = 0.
-1, 0, 2/3, 1
Factor -2/7*o**3 - 6/7 - 2/7*o**2 + 10/7*o.
-2*(o - 1)**2*(o + 3)/7
Let b be ((-6)/(-63))/((-7)/(-49)). Let f be -2 - (44/(-12) + -1). Factor b*w**3 + f*w**2 + 4/3 + 10/3*w.
2*(w + 1)**2*(w + 2)/3
Let u(a) be the first derivative of -a**6/2 + 48*a**5/5 - 69*a**4/2 - 36*a**3 + 405*a**2/2 + 324*a + 414. Let u(y) = 0. What is y?
-1, 3, 12
Let c(n) be the second derivative of n**7/105 - 4*n**6/75 - 19*n**5/50 - 7*n**4/15 - n + 179. What is t in c(t) = 0?
-2, -1, 0, 7
Let u(c) be the second derivative of 5*c**4/12 - 35*c**3/3 + 60*c**2 + 61*c. Let u(f) = 0. What is f?
2, 12
Let l be 12/(-14)*(-26)/78. Let i be ((-1)/(-14))/(1/4). Factor 2/7*a**2 + 0*a - l*a**4 + 0 + i*a**3 - 2/7*a**5.
-2*a**2*(a - 1)*(a + 1)**2/7
Let n = 4956 + -4956. Factor n + 4/3*p**3 + 4/3*p - 8/3*p**2.
4*p*(p - 1)**2/3
Let k(s) be the third derivative of -s**7/210 + 13*s**6/60 - 14*s**5/5 - 13*s**4/12 + 169*s**3/6 - 313*s**2. Suppose k(d) = 0. Calculate d.
-1, 1, 13
What is q in -27/5*q**2 + 48/5 - 18/5*q - 3/5*q**3 = 0?
-8, -2, 1
Let g be -1 - 0 - -68 - -3. Let r be 28/5 + (-42)/g. Factor 55*z**4 - 3*z**3 + 4*z**5 + 3*z**2 - 58*z**4 - z**r.
3*z**2*(z - 1)**2*(z + 1)
Suppose -4*a + 63 + 93 = 0. Let x be 130/a - 5/(15/(-2)). Solve 0*b + 0 - 1/3*b**x - 1/3*b**3 + 0*b**2 = 0.
-1, 0
Let g = -1936 - -1936. Factor -1/6*d**5 - 1/3 + 2/3*d**3 + g*d**4 - 1/2*d + 1/3*d**2.
-(d - 2)*(d - 1)*(d + 1)**3/6
Factor 93*h + 72*h - 5*h**2 - 130*h.
-5*h*(h - 7)
Let x(m) = m**2 + 19*m + 20. Let a be x(-18). Factor -678*i**2 + i - 4*i**5 + 3*i**5 + 680*i**2 - a*i**4.
-i*(i - 1)*(i + 1)**3
Factor 64/3*d - 2/3*d**2 - 512/3.
-2*(d - 16)**2/3
Suppose 3*z - 2*k = -46, z + k + 4*k - 13 = 0. Let y = -8 - z. Factor -y*o - 7*o**2 + 2*o**2 + o**2 + 0*o**2.
-4*o*(o + 1)
Suppose 5*t - 3 - 7 = 0. Let r = t + 1. Find f, given that -3*f**4 + 3*f**5 - 3*f**r + 3*f**2 - 10 + 10 = 0.
-1, 0, 1
Let k(u) = -u**3 + u**2 + u + 2. Let p be k(-2). Let n = p - 59/5. Find b such that 0*b + n*b**3 + 0 - 2/5*b**2 = 0.
0, 2
Factor 0 - 2/5*y**4 + 0*y**2 + 0*y + 42/5*y**3.
-2*y**3*(y - 21)/5
Let b(a) be the second derivative of a**9/22680 - a**8/5040 + a**7/3780 - a**4/2 - 13*a. Let k(q) be the third derivative of b(q). Let k(c) = 0. What is c?
0, 1
Find j, given that -1026 + 9*j + j**2 - 4*j**2 - 1026 + 2064 = 0.
-1, 4
Let i(x) = -10*x**2 + 6*x - 4. Let r(y) = 2*y**2 - 2*y + 1. Let d(h) = -i(h) - 4*r(h). Factor d(k).
2*k*(k + 1)
Let 260/3*s**3 - 9*s**4 + 1/3*s**5 + 2048/3 + 256*s - 992/3*s**2 = 0. What is s?
-1, 4, 8
Suppose 0 = 4*l + 5*m - 10, 2*l - 26*m + 25*m + 2 = 0. Determine g so that -1/4*g**2 + 0*g - 3/4*g**3 + g**4 + l = 0.
-1/4, 0, 1
Let u(b) be the second derivative of -b**6/40 + 13*b**5/60 + 5*b**4/12 + 11*b**2/2 - 21*b + 2. Let w(z) be the first derivative of u(z). Factor w(q).
-q*(q - 5)*(3*q + 2)
Let i(a) be the first derivative of a + 1/15*a**5 - 1/6*a**4 - 4/9*a**3 + 1/3*a**2 - 22. Factor i(t).
(t - 3)*(t - 1)*(t + 1)**2/3
Let a(f) = 2*f**3 - 2*f**2 - 3*f + 2. Let b be a(2). Factor 2*i**2 + i**2 - 12*i + b + 0*i + 5.
3*(i - 3)*(i - 1)
Let v(u) = 5*u**3 + 75*u**2 - 35*u - 90. Let y(c) = c**3 + 19*c**2 - 9*c - 23. Let a(o) = 4*v(o) - 15*y(o). What is t in a(t) = 0?
-3, -1, 1
Let w(m) = 13*m**3 + 677*m**2 + 54*m + 107. Let o be w(-52). Solve -6/19*x**2 - 2/19 + 6/19*x + 2/19*x**o = 0.
1
Let n = 9910/11169 - -2/1241. Suppose 10/9*l - 2/9 - 10/9*l**3 + n*l**4 - 2/3*l**2 = 0. What is l?
-1, 1/4, 1
Let d(i) be the second derivative of 49*i**6/120 + 77*i**5/60 + 4*i**4/3 + 2*i**3/3 + 7*i**2/2 + 4*i. Let q(j) be the first derivative of d(j). Factor q(y).
(y + 1)*(7*y + 2)**2
Suppose -1/2*v**2 + 3*v + 0 = 0. What is v?
0, 6
Let q(p) = -5*p. Let a be q(-1). Let g be (20/50)/(2/25). Factor -32 - a*w**2 + g*w**2 - 3*w**2 - 16*w + w**2.
-2*(w + 4)**2
Let o(g) = 5*g**5 + 26*g**4 - 31*g**3 - 7*g + 7. Let y(k) = 2*k**5 + 13*k**4 - 15*k**3 - 3*k + 3. Let p(l) = -3*o(l) + 7*y(l). Solve p(w) = 0 for w.
0, 1, 12
Suppose 0 = 1226*o - 1263*o. Determine n, given that 18/11*n**3 - 18/11*n**5 + 0*n + o - 4/11*n**4 + 4/11*n**2 = 0.
-1, -2/9, 0, 1
Let -578/13*o**2 + 510/13*o**3 + 0 + 66/13*o**4 + 2/13*o**5 + 0*o = 0. What is o?
-17, 0, 1
Suppose -2*i - 18 = -4*o, 3*o = -i + 12 + 4. Solve -15*a**4 + 7*a**3 - a**2 + 0*a**2 - o*a**2 + 14*a**3 = 0 for a.
0, 2/5, 1
Let m = -32 - -36. Suppose -8*t**2 - 15 + 6*t**4 - 18 - 2*t**m + 37 = 0. Calculate t.
-1, 1
Factor 0*g**3 + 12 - g**2 + 2*g - 7*g**2 - 4*g**2 - 2*g**3.
-2*(g - 1)*(g + 1)*(g + 6)
What is v in 0 + 42*v + 819/5*v**3 - 9/5*v**5 - 291/5*v**4 - 729/5*v**2 = 0?
-35, 0, 2/3, 1
Let -106*s + 155*s + 200 + 156*s + 5*s**2 = 0. Calculate s.
-40, -1
Let d be -4*(6 - (-28)/(-4)). Let w(m) be the third derivative of -1/60*m**5 + 0*m**d + 0 + 0*m + 0*m**3 + 3*m**2. Factor w(j).
-j**2
Let h(s) be the second derivative of 0 - 1/3*s**4 - 4*s + 1/3*s**3 - 3/2*s**2 - 1/6*s**5. Let g(i) be the first derivative of h(i). Let g(f) = 0. What is f?
-1, 1/5
Let m(n) = 4*n**3 - 16*n**2 - 28*n + 84. Let b(s) = -4*s**3 + 17*s**2 + 25*s - 83. Let u(o) = 4*b(o) + 3*m(o). Factor u(a).
-4*(a - 5)*(a - 2)*(a + 2)
What is z in 8/3*z**3 + 86/15*z**2 + 44/15*z - 2/15*z**4 + 0 = 0?
-1, 0, 22
Let a(h) = -3*h - 6. Let p be a(-1). Let l be -3*p/3*6/9. Find t such that -24/5*t**4 - l*t**5 + 4*t**2 + 18/5*t - 8/5*t**3 + 4/5 = 0.
-1, -2/5, 1
Let o(t) = 5*t**2 - 20*t + 52. Let q(u) = 6*u**2 - 20*u + 53. Let z(k) = -5*o(k) + 4*q(k). Let i be z(17). Factor 0*p + 0*p**i + 2/7 - 4/7*p**2 + 2/7*p**4.
2*(p - 1)**2*(p + 1)**2/7
Factor -3*l**3 - 4/7 + 23/7*l**2 + 40/7*l.
-(l - 2)*(l + 1)*(21*l - 2)/7
Let w(i) be the third derivative of -i**7/1680 + i**6/240 + i**5/240 - i**4/16 + 13*i**3/6 - 2*i**2. Let g(d) be the first derivative of w(d). Factor g(m).
-(m - 3)*(m - 1)*(m + 1)/2
Let m(b) be the second derivative of 35*b**4/8 - 31*b**3/6 + 2*b**2 - 208*b. Determine o so that m(o) = 0.
4/21, 2/5
Suppose 5*r = 3*t + 114, -5*r - 4*t = -135 + 42. Factor -4*c**2 + c - 13*c + 13 - r.
-4*(c + 1)*(c + 2)
Let t be 627/(-315) + 16/8. Let o(n) be the third derivative of -1/210*n**6 - t*n**5 + 0 + 0*n + 5/42*n**4 - 2/7*n**3 - 2*n**2. Find y, given that o(y) = 0.
-3, 1
Let p(l) = 14*l**3 + 26*l**2 + 8*l + 6. Let m(x) = x**2 - 1. Suppose -46 = -12*n + 26. Let w(v) = n*m(v) + p(v). Factor w(k).
2*k*(k + 2)*(7*k + 2)
Let w(m) = m**3 - 14*m**2 + 23*m - 27. Let q be w(9). Let u be (25/q)/((-2)/84). Factor u*j - 8/3*j**2 - 2.
-2*(j - 1)*(4*j - 3)/3
Let q be (4/10 - (-69)/(-60))*4. Let n be ((3/2)/q)/(3/(-3)). Factor n*m**4 + 1/3*m**3 - 1/6 + 1/6*m**5 - 1/3*m**2 - 1/2*m.
(m - 1)*(m + 1)**4/6
Suppose -11 = -n - 2*m + 1, -4*n + 4*m = 0. Let 3/4*l**2 - 1/2*l**3 - 1/4*l**n + 1 + 2*l = 0. What is l?
-2, -1, 2
Suppose 0 = 6*f - 2 - 10. Factor s**4 - s**2 + 0*s**f - 4 + 8*s - 4*s**3 + 2*s**3 - 2*s**2.
(s - 2)*(s - 1)**2*(s + 2)
Let b(k) = -2*k**2 + 212*k - 5406. Let q(a) = 2*a + 1. Let j(x) = b(x) - 2*q(x). Solve j(z) = 0.
52
Let n be (5 + -314)/(-3)*-1. Let c = n - -105. Let c*t**3 + 11/2*t**2 + 5*t + 3/2 = 0. What is t?
-1, -3/4
Suppose 115*g - 117*g = -128. Suppose 62*f = g*f. Factor 12/5*a**2 + 0 + f*a + 4/5*a**3.
4*a**2*(a + 3)/5
Let a(v) be the first derivative of -v**4/3 + 2*v**2 + v + 4. Let i(c) be the first derivative of a(c). Factor i(f).
-4*(f - 1)*(f + 1)
Let q = -341 + 341. Let b(p) be the third derivative of 8*p**2 + 0*p**3 + 0*p**5 - 1/144*p**4 + q + 1/720*p**6 + 0*p. Factor b(c).
c*(c - 1)*(c + 1)/6
Solve -24/7*j**2 - 144/7*j**3 - 12/7*j**5 - 104/7*j**4 + 0 + 4*j = 0.
-7, -1, 0, 1/3
Let n = -170/3 + 284/5. Let q = -15