 x(q) = -9*q**5 + 26*q**4 - 12*q**3 - 80*q**2 + 108*q - 32. Let y(a) = -a**5 + a**4 - a**3 - a. Let t(v) = x(v) - 4*y(v). Suppose t(s) = 0. What is s?
-2, 2/5, 2
Let 38*q**4 - 9*q**4 + 240*q**2 - 20*q**4 - 3*q**5 - 240*q + 21*q**4 - 120*q**3 + 96 = 0. What is q?
2
Let f be -3 - ((-1)/(-4) + (-693)/204). Let c = f + 1043/306. Factor 14/9*x**4 - 32/9*x**3 - 32/9 + c*x - 2/9*x**5 + 16/9*x**2.
-2*(x - 2)**4*(x + 1)/9
Let c(q) = q**2 + 26*q + 31. Let f be c(-23). Let l be (-246)/287*70/f. Suppose 12/19 - 2/19*j - l*j**2 = 0. Calculate j.
-2/3, 3/5
Let y(p) be the third derivative of -1/1365*p**7 - 9*p**2 + 7/156*p**4 + 0*p - 2/39*p**3 + 1/156*p**6 + 0 - 3/130*p**5. Determine s so that y(s) = 0.
1, 2
Let o be 2 + (-1 + 1)/(-1). Suppose 0 = -4*p + 3*x + 21, -8 = -3*p + x + 4. Determine r, given that 0*r + 0*r**o - 1/4*r**p + 0 = 0.
0
Let c(f) = f**4 - 5*f**2 - 2. Let t(q) = 2*q**4 - 11*q**2 - q - 5. Let n(v) = -5*c(v) + 2*t(v). Factor n(k).
-k*(k - 1)**2*(k + 2)
Suppose 2*n - 175 - 7 = 0. Factor -14 + 10*a**3 - n*a**2 - 30*a**3 - 55*a + 4 + 26*a**2.
-5*(a + 1)*(a + 2)*(4*a + 1)
Let w(b) = 9*b**3 + b**2 - 37*b + 43. Let c(l) = 4*l**3 - 18*l + 22. Let v = 4 - 9. Let k(q) = v*c(q) + 2*w(q). Solve k(s) = 0 for s.
-3, 2
Let k be 7 - (-2 - 18/(-9)). Let o(x) be the first derivative of -4/3*x**3 + 4*x - 1/2*x**4 + x**2 + k. Factor o(g).
-2*(g - 1)*(g + 1)*(g + 2)
Let w be 1 + 1 + 121 + -118. Let u(d) be the third derivative of -9*d**2 + 0*d - 1/9*d**3 - 1/90*d**w + 0 - 1/18*d**4. Factor u(v).
-2*(v + 1)**2/3
Let p(t) be the third derivative of -t**5/120 - 9*t**4/4 - 243*t**3 + 347*t**2. Solve p(b) = 0.
-54
Suppose -35*r = -62*r + 162. Let k(t) be the second derivative of 1/5*t**5 + 0*t**4 + t**2 - 2/3*t**3 - 14*t - 1/15*t**r + 0. Factor k(s).
-2*(s - 1)**3*(s + 1)
Factor 12*o**2 - o**2 + 24*o - 15*o**2 - 36.
-4*(o - 3)**2
Determine p, given that 0 + 0*p - 68/11*p**3 - 1/11*p**4 - 1156/11*p**2 = 0.
-34, 0
Let b(u) be the third derivative of u**8/1344 + u**7/216 + 5*u**6/432 + u**5/72 + 7*u**4/12 - 4*u**2. Let i(a) be the second derivative of b(a). Factor i(x).
5*(x + 1)**2*(3*x + 1)/3
Let b(m) = 3*m**5 + 27*m**4 + 67*m**3 + 53*m**2 - 5*m - 20. Let s(p) = p**3 - p**2 + p + 4. Let k(t) = b(t) + 5*s(t). Determine x, given that k(x) = 0.
-4, -1, 0
Let v(y) = 3*y**3 + 18*y**2 + 12*y - 11. Let n be v(-5). Factor -5*c**3 + 0 - 5/3*c**n - 5/3*c - 5*c**2.
-5*c*(c + 1)**3/3
Let p = 39181/3 + -13060. Find l, given that 0 - 1/3*l**2 + 2*l**3 + p*l**4 - 2*l = 0.
-6, -1, 0, 1
Let s(n) = n - 2. Let k(l) = l**2 + 4*l + 6. Let t(r) = 2*k(r) + 22*s(r). Determine w so that t(w) = 0.
-16, 1
Let p(v) be the first derivative of v**6/18 + 3*v**5/5 + 7*v**4/12 - v**3 - 4*v**2/3 - 113. Factor p(l).
l*(l - 1)*(l + 1)**2*(l + 8)/3
Let i(s) = -3*s**3 - 24*s**2 - 33*s - 18. Let g(c) = -9*c**3 - 71*c**2 - 99*c - 53. Let h(r) = 3*g(r) - 8*i(r). Factor h(d).
-3*(d + 1)**2*(d + 5)
Suppose -z - z + 6 = 0. Let r(j) be the second derivative of 0 - 11/120*j**5 - 1/12*j**2 + 1/8*j**4 - 1/36*j**3 + z*j + 1/45*j**6. Let r(v) = 0. What is v?
-1/4, 1
Let m(l) be the third derivative of -3*l**6/320 - l**5/160 + l**4/8 - l**3/4 - 261*l**2. Factor m(h).
-3*(h - 1)*(h + 2)*(3*h - 2)/8
Let z = 41 - 38. Factor 32*g**3 - 16*g**3 - 11*g**z.
5*g**3
Let a(f) = -222*f - 882. Let h be a(-4). What is q in 12/5*q**2 + 3*q**5 - 6/5 + 3*q - 6/5*q**4 - h*q**3 = 0?
-1, 2/5, 1
Factor 15/2*x**2 - 1/2*x**3 + 125/2 - 75/2*x.
-(x - 5)**3/2
Suppose 221/12*c**2 + 91/12*c**4 - 1 - 88/3*c**3 + 13/3*c = 0. Calculate c.
-2/7, 2/13, 1, 3
Suppose 102*d + 30*d**3 + 69/2 - 3/2*d**4 + 99*d**2 = 0. Calculate d.
-1, 23
Let g(j) be the first derivative of 4*j**5/5 + 2*j**4 - 4*j**3/3 - 4*j**2 - 110. Factor g(z).
4*z*(z - 1)*(z + 1)*(z + 2)
Let j(l) be the first derivative of l**6/2 - 9*l**5 - 99*l**4/4 - 17*l**3 - 95. Factor j(g).
3*g**2*(g - 17)*(g + 1)**2
Solve -75*v**4 - 20 - 46*v**3 + 95*v**2 + 37*v - 116*v**3 + 83*v - 23*v**3 + 65*v**5 = 0 for v.
-1, 2/13, 1, 2
Factor -s**3 + s**4 - s**5 + 24*s**2 - 25*s**2 + 2*s**5.
s**2*(s - 1)*(s + 1)**2
Suppose 0*p + 0 - 1/4*p**4 + 0*p**3 + 1/4*p**2 = 0. Calculate p.
-1, 0, 1
Let s(m) be the second derivative of -2/105*m**6 + 13*m + 0*m**4 - 1/70*m**5 - 1/147*m**7 + 0 + 0*m**3 + 0*m**2. Factor s(k).
-2*k**3*(k + 1)**2/7
Let w(a) be the third derivative of 26*a**2 + 1/12*a**6 + 0 + 0*a + 1/24*a**4 + 0*a**3 - 13/120*a**5 - 3/140*a**7. Solve w(i) = 0.
0, 2/9, 1
Let r be (-3 - -2)/(1/3). Let u be (3/9)/(r/(-27)). Find x such that 6*x**2 - 3*x**3 + 9*x**u - 2*x**3 - 2*x**2 = 0.
-1, 0
Let q(h) = -24*h - 470. Let y be q(-20). Suppose -2 - y*c - 21/2*c**2 = 0. What is c?
-2/3, -2/7
Factor 0 + 35/3*a**3 + 55/3*a**2 + 25/3*a + 5/3*a**4.
5*a*(a + 1)**2*(a + 5)/3
Let z(p) be the second derivative of p**5/90 + p**4/9 + 5*p**3/27 - 4*p**2/3 + 269*p. Factor z(h).
2*(h - 1)*(h + 3)*(h + 4)/9
Let r(k) be the second derivative of k**5/20 - 5*k**4/12 + 4*k**3/3 - 2*k**2 + 21*k - 2. What is f in r(f) = 0?
1, 2
Solve 12*t**3 + 0*t**4 - 12*t**2 + 11*t - 18*t**2 - 6*t + 11*t + 2*t**4 = 0 for t.
-8, 0, 1
Let o(k) be the second derivative of -k**6/360 + k**5/36 - k**4/24 - k**3/2 - 7*k**2 - 8*k. Let s(z) be the first derivative of o(z). Find a such that s(a) = 0.
-1, 3
Let w be (-81)/12 - (-51 - -44). Factor 0 + 1/4*b**3 - w*b**4 - 1/4*b + 1/4*b**2.
-b*(b - 1)**2*(b + 1)/4
Suppose 3*x + 2*j + 2 - 16 = 0, 0 = 4*j - 16. Suppose k - 2*a + 2 = 3*k, -2*a = -2*k + 22. Factor -k*o**2 + x - 5 - 3*o + 3*o**3 + 6 + 3.
3*(o - 2)*(o - 1)*(o + 1)
Suppose -972 - 858 = 10*t. Let z = -183 - t. Factor -3/2*s + 3/2*s**3 + 3/4 + z*s**2 - 3/4*s**4.
-3*(s - 1)**3*(s + 1)/4
Let d be ((-22)/(-8) + -2)/((-9)/(-24)). Let x(r) be the first derivative of -3 - r - 16/3*r**3 - 4*r**d. Factor x(v).
-(4*v + 1)**2
Suppose 0 = -9*m + 113 + 112. Let u**3 + 85*u**4 - m*u**5 - 10*u + 16*u**2 + 39*u**2 - 106*u**3 = 0. Calculate u.
0, 2/5, 1
Suppose h + 0*h = -1. Let g be 4/(112/(-76)) - 3*h. Determine u, given that 0 + 0*u - g*u**3 + 6/7*u**2 = 0.
0, 3
Let o(p) be the third derivative of 55*p**8/2184 + 373*p**7/1365 + 77*p**6/130 - 74*p**5/195 - 10*p**4/39 - 191*p**2. Find y, given that o(y) = 0.
-5, -2, -2/11, 0, 2/5
Let s(h) be the first derivative of h**7/4200 - h**6/1800 + h**3 - 2. Let r(o) be the third derivative of s(o). What is v in r(v) = 0?
0, 1
Factor 4/15*n**4 + 0*n**2 - 2/15*n**5 + 0*n**3 + 0*n + 0.
-2*n**4*(n - 2)/15
Let t(c) be the third derivative of c**6/660 - c**4/33 - 38*c**2. Factor t(a).
2*a*(a - 2)*(a + 2)/11
Let w be (-588)/(-1170) + 3*1/(-6). Let n(t) be the third derivative of 0*t - 1/78*t**4 + 1/39*t**3 - 4*t**2 + 0 + w*t**5. Factor n(v).
2*(v - 1)**2/13
Factor -4/3*c**2 - 2/3*c**5 + 4/3*c**4 + 0*c**3 + 0 + 2/3*c.
-2*c*(c - 1)**3*(c + 1)/3
Suppose 56 + 49 = 3*p - 2*k, 5*p = -3*k + 156. Let z = p + -14. Determine f so that -f + z*f + 0 - 13*f**2 - 4 + 10*f**3 - 11*f**2 = 0.
2/5, 1
Suppose 5*d - 4 = a, 178*a + 8 = d + 179*a. Determine x so that -12/5*x**4 + 12/5*x**3 + 36/5 + 2/5*x**5 + 8*x**d - 78/5*x = 0.
-2, 1, 3
Suppose -4*d + 4 = 7*x - 3*x, -d - 9 = -x. Let v be (-14 - -14)*2/d. Factor -2/19 + 2/19*t**2 + v*t.
2*(t - 1)*(t + 1)/19
Let y be 33 + (0 - 3) - (2 + 1). Suppose -y + 149*k**4 - 24*k**3 - 66*k**2 - 304*k**4 + 152*k**4 - 72*k = 0. What is k?
-3, -1
Let i(m) be the first derivative of -m**5/20 + m**4 - 2*m**3 - 8*m**2 + 28*m + 44. Factor i(v).
-(v - 14)*(v - 2)**2*(v + 2)/4
Suppose -8 = 4*w - 8*w. Factor -2*z - 3 - z - z**2 - w*z - 1.
-(z + 1)*(z + 4)
Suppose 4*w + 4*a + 11 = -9, -a = 3*w + 5. Suppose 0*z - 1/2*z**3 + w + 1/2*z**2 = 0. Calculate z.
0, 1
Let s(f) be the second derivative of f**7/21 - 2*f**6/5 + 13*f**5/10 - 2*f**4 + 4*f**3/3 - 4*f + 42. What is d in s(d) = 0?
0, 1, 2
Let n(p) = 5*p**3 - 10*p**2 - p. Suppose 3*d - 6*d = -3*z - 12, 5*z + 3*d + 36 = 0. Let f(s) = s. Let r(u) = z*f(u) - n(u). Find o, given that r(o) = 0.
0, 1
Let f(l) be the first derivative of 14*l**6/9 + 8*l**5/15 - 28*l**4/3 - 32*l**3/9 + 95. Determine k, given that f(k) = 0.
-2, -2/7, 0, 2
Let c(q) be the first derivative of -6/7*q**2 - 36/7*q + 0*q**4 + 9/7*q**3 + 46 - 3/35*q**5. Solve c(x) = 0 for x.
-3, -1, 2
Let p(c) = 4*c + 0*c - 2 + 4*c - 6*c. Let d be p(3). Let 79 + 12*b**4 - 79 + d*b**2 - 16*b**3 = 0. What is b?
0, 1/3, 1
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