
Let s(p) = p**3 - p**2 + 2. Let k(n) = 9*n**3 - 39*n**2 - 5*n + 43. Let q(a) = k(a) - 4*s(a). Find c, given that q(c) = 0.
-1, 1, 7
Let f = -886/11 + 888/11. Let 4/11*a - f*a**4 - 4/11*a**3 + 0*a**2 + 2/11 = 0. What is a?
-1, 1
Let t(b) be the first derivative of b**4/4 + 8*b**3/3 - 19*b**2/2 + 10*b + 65. Factor t(k).
(k - 1)**2*(k + 10)
Let h = -72 + 75. Suppose -5*m - h = -n, 4*n - 2*m - m = 12. Factor 0*v + 2/3*v**2 + 0 + 2/3*v**n.
2*v**2*(v + 1)/3
Let r be -2*(5 - 60/8). Let v(p) be the second derivative of 1/12*p**3 - 1/80*p**r + 0 + 6*p - 1/48*p**4 + 0*p**2. Let v(b) = 0. Calculate b.
-2, 0, 1
Let a = -88 - -84. Let f be a/1*(-3 + 102/36). Factor 0 - s**3 - 1/6*s - 2/3*s**2 - f*s**4 - 1/6*s**5.
-s*(s + 1)**4/6
Suppose -s - 2 = -o, -4*s - 2 = -14. Let k = o - 2. Find p such that -29*p**3 + 27*p**k + 2*p + 0*p = 0.
-1, 0, 1
Let g = -30/637 - -59453/637. Let y = g - 93. Factor 0 + 0*k + y*k**2.
2*k**2/7
Factor 11/4*x + 1/4*x**3 + 3/2*x**2 + 3/2.
(x + 1)*(x + 2)*(x + 3)/4
Let o(p) be the third derivative of p**6/360 - 13*p**5/90 + 169*p**4/72 - 34*p**2. Factor o(n).
n*(n - 13)**2/3
Let c = -21266 - -21266. Factor 8/3*o**2 - 10/3*o + c.
2*o*(4*o - 5)/3
Suppose 12*d - 6 = 10*d. What is a in 5 + 4*a**d + a + 2*a**4 - 3*a**2 - 5*a**3 - 4 = 0?
-1, -1/2, 1
Suppose -141 = 155*z - 202*z. Factor -3 - 9/2*r + 3/2*r**z + 0*r**2.
3*(r - 2)*(r + 1)**2/2
Let g(o) = -o**2 - 6*o. Let h be (-21)/4 + 1/4. Let z be g(h). Determine i so that -12*i**5 - 2*i**4 + 5*i**5 + 5*i**z = 0.
-1, 0
Let w = -1193 + 1195. Find i, given that 15/8*i**w + 3/4*i + 3/2*i**3 + 0 + 3/8*i**4 = 0.
-2, -1, 0
Let r(j) be the first derivative of -j**3 + 261*j**2 - 22707*j - 398. Factor r(b).
-3*(b - 87)**2
Solve s - 11*s - 17*s**2 + 0*s**2 - 8*s**3 - 6*s**4 + 5*s**4 = 0 for s.
-5, -2, -1, 0
Let o(r) be the first derivative of -2*r**5/35 - 13*r**4/14 - 110*r**3/21 - 75*r**2/7 + 242. What is h in o(h) = 0?
-5, -3, 0
Let s(w) be the second derivative of -7*w**5/25 + 46*w**4/15 - 14*w**3/5 - 36*w**2/5 + 166*w. Determine t so that s(t) = 0.
-3/7, 1, 6
Let c(t) = t**3 + 28*t**2 - 21*t - 8. Let v be c(-29). Let o = 1684/7 + v. Factor 8/7*w + o*w**2 + 4/7.
4*(w + 1)**2/7
Let n(j) be the first derivative of 10*j**2 - 2/3*j**6 + 16/5*j**5 - 8*j - 4*j**4 + 8 - 8/3*j**3. Factor n(x).
-4*(x - 2)*(x - 1)**3*(x + 1)
Let c(a) = 1250*a**3 + 1648*a**2 + 434*a + 36. Let s(z) = 2500*z**3 + 3295*z**2 + 869*z + 74. Let g(o) = 5*c(o) - 2*s(o). Factor g(d).
2*(d + 1)*(25*d + 4)**2
Let q be (108/32)/(-9)*(-7)/126*8. Factor q*r**2 + 6 + 2*r.
(r + 6)**2/6
Factor 3/2*f + 0 - 45/4*f**2.
-3*f*(15*f - 2)/4
Let k(d) be the first derivative of 3*d**5/20 - 3*d**4/4 + 3*d**3/4 + 3*d**2/2 - 3*d + 103. Solve k(r) = 0 for r.
-1, 1, 2
Let x be -1 + 3/(1 + 0). Let v(a) = 2*a. Let c be v(x). Factor j**2 + c*j + j**2 + 2*j**2.
4*j*(j + 1)
Let v(g) = -g**2 + 15*g - 9. Let r be v(14). Suppose 0 = 3*i - 12, -2*n - 3*i + r = -11. What is d in 0 + 2/9*d**n + 2/3*d = 0?
-3, 0
Let -51/5*v - 39/5*v**2 - 12/5 = 0. What is v?
-1, -4/13
Let z(k) be the second derivative of 2*k**7/21 + 2*k**6/5 - 4*k**4/3 + 679*k. Find r, given that z(r) = 0.
-2, 0, 1
Let y(i) = 7*i**2 + 21*i - 20. Let q(t) = 36*t**2 + 105*t - 99. Let a(p) = -4*q(p) + 21*y(p). Factor a(r).
3*(r - 1)*(r + 8)
Let h be (-2)/(-5) - 8/20. Let x be h*-4*1/(-8). Let v + x*v + 8*v**2 + 2 - 7*v - 4*v = 0. What is v?
1/4, 1
Determine v, given that 1/3*v**5 - 22/3*v**3 - 38/3*v**2 - v**4 - 9*v - 7/3 = 0.
-1, 7
Let x(b) be the first derivative of 3/14*b**4 - 6/7*b**2 + 30 + 3/7*b**3 - 12/7*b - 3/35*b**5. Find q, given that x(q) = 0.
-1, 2
Factor -551 + 545 - 8*t**2 + 5*t + 7*t**2.
-(t - 3)*(t - 2)
Let q(b) = -b**3 + b. Let s(n) = 6*n**3 + 17*n**2 - 43*n. Let g(d) = 5*q(d) + s(d). Suppose g(h) = 0. What is h?
-19, 0, 2
Let g(d) be the first derivative of -d**6/660 + d**4/44 + 2*d**3/33 - 2*d**2 + 5. Let k(x) be the second derivative of g(x). Factor k(s).
-2*(s - 2)*(s + 1)**2/11
Find s, given that 8 - 19*s**3 + 56*s**2 + 16*s**4 + 38*s**3 + 2*s**3 + 34*s + 2*s**5 + 19*s**3 + 4*s**3 = 0.
-4, -1
Let p(d) = d**2 + 2. Let s(j) = -j. Suppose f - 12 = -5*u - f, 3*u - 2*f = 4. Let m(r) = u*p(r) + 6*s(r). Factor m(q).
2*(q - 2)*(q - 1)
Let z(w) be the third derivative of -w**7/105 - w**6/5 - 23*w**5/15 - 5*w**4 - 25*w**3/3 + 35*w**2. Factor z(p).
-2*(p + 1)**2*(p + 5)**2
Let v(u) be the first derivative of -4*u**5/25 - 2*u**4 - 148*u**3/15 - 24*u**2 - 144*u/5 + 512. Suppose v(s) = 0. Calculate s.
-3, -2
Suppose 3*b - n = -2*n + 379, -2*b - 4*n = -266. Suppose -28*u**2 + 1000*u + 40*u**3 - 1250 - b*u**4 + 123*u**4 - 272*u**2 = 0. What is u?
5
Let q(s) = s - 2. Suppose 5*v - 9 = 1. Let d be q(v). Solve 1/5*h - 1/5*h**3 + 0*h**2 + d = 0 for h.
-1, 0, 1
Let z = -6 + 0. Let t = 8 + z. Factor 2*d**2 - 2*d**2 + 0 - d**t - 2*d + 3.
-(d - 1)*(d + 3)
Let t(d) be the third derivative of -d**8/2520 + d**7/252 + 11*d**3/3 + 22*d**2. Let b(q) be the first derivative of t(q). Factor b(j).
-2*j**3*(j - 5)/3
Let i(d) = d**2 - 38*d + 356. Let y be i(22). Let h(q) be the second derivative of -1/70*q**5 + 2/21*q**3 + 1/42*q**y + 0 + 11*q + 0*q**2. Factor h(m).
-2*m*(m - 2)*(m + 1)/7
Let a(s) be the second derivative of 2/39*s**4 + 1/39*s**3 + 1/130*s**5 + 14*s + 0 - 6/13*s**2. Factor a(r).
2*(r - 1)*(r + 2)*(r + 3)/13
Let x be 9*3/36*4. Solve 5*c - 3*c**4 + 2 - 2*c**x + 2*c**4 - 1 - 3*c = 0 for c.
-1, 1
Let n(y) be the first derivative of -2*y**3/3 - y**2 + 24*y + 15. Determine g so that n(g) = 0.
-4, 3
Suppose 0 = -w + 4*t + t + 92, 2*w - 3*t - 191 = 0. Factor -w*v**2 - 24 + 36*v + 39*v**2 + 40*v**2 + 3*v**3.
3*(v - 2)**3
Let x(m) be the second derivative of 0*m**2 - 1/6*m**3 + 0 + 1/12*m**4 - 13*m. Let x(c) = 0. What is c?
0, 1
Let v be (-53)/(-126) + (-430)/70 + 6. Let f(t) be the first derivative of 0*t - 1/12*t**2 + 6 + v*t**3. Determine a, given that f(a) = 0.
0, 1/5
Let b(y) be the first derivative of -y**4/6 + 4*y**3/3 - 4*y**2 + 16*y/3 - 28. Factor b(o).
-2*(o - 2)**3/3
Let b(g) be the third derivative of -7*g**5/20 - g**4/4 + g**2 + 2*g. Factor b(w).
-3*w*(7*w + 2)
Let m(x) be the first derivative of 11*x**5/15 + 3*x**4/4 - 13*x**3/9 - 3*x**2/2 + 2*x/3 - 447. Solve m(t) = 0.
-1, 2/11, 1
Let g(x) be the second derivative of -x**6/45 - x**5/30 + x**4/9 + x - 62. Factor g(s).
-2*s**2*(s - 1)*(s + 2)/3
Let s(o) be the first derivative of -4*o**3/21 - 4*o**2 - 132*o/7 - 195. Find l, given that s(l) = 0.
-11, -3
Let f be (4/(-5) - (-14)/25)*15/(-9). Solve 6/5*d**3 + f*d**4 + 0*d**2 + 0 - 8/5*d = 0 for d.
-2, 0, 1
Factor 0*t + 0 - 2*t**3 + 2/3*t**4 + 0*t**2.
2*t**3*(t - 3)/3
Let r(d) be the third derivative of d**7/120 - d**6/72 - d**5/60 - 7*d**3 + d**2 - 21. Let n(k) be the first derivative of r(k). Factor n(w).
w*(w - 1)*(7*w + 2)
Let m(z) be the third derivative of 0*z**3 + 1/56*z**4 + 0 - 45*z**2 - 1/210*z**5 + 0*z - 1/840*z**6. Factor m(t).
-t*(t - 1)*(t + 3)/7
Suppose -2*m + 6 = -14. Let f = -8 + m. Suppose 15 + 2*j - 15 + 2*j**f = 0. Calculate j.
-1, 0
Let a(d) be the second derivative of d**4 - 5*d. Let o be a(1). Factor 11*b - 3*b**2 - 6*b + 7*b - o.
-3*(b - 2)**2
Let u(g) be the second derivative of g**7/21 + 2*g**6/5 + g**5/2 - 4*g**4 - 12*g**3 - g + 209. Solve u(d) = 0.
-3, -2, 0, 2
Suppose -19*b + 16 = -18*b. Factor 19*l - 3*l**2 + 38 - 20 - b*l.
-3*(l - 3)*(l + 2)
Let r(i) be the first derivative of 21*i**4/16 - i**3/6 - i**2/2 - i - 7. Let x(s) be the first derivative of r(s). Factor x(c).
(7*c - 2)*(9*c + 2)/4
Let u be ((-3)/(-6))/((-2)/(-4)). Let d(g) = 8*g + 2. Let w be d(u). Factor -n + 7*n - 5*n**2 - 12*n**4 - 33*n**3 - w*n**2.
-3*n*(n + 1)*(n + 2)*(4*n - 1)
Let b(m) = -4*m**3 + 2*m - 2. Let o = 17 + -13. Let n(v) = -v**4 - 6 + v**2 - o*v + 11 + 5*v**3 + 4*v**3. Let w(g) = -5*b(g) - 2*n(g). Solve w(q) = 0.
-1, 0, 1
Determine y so that -2*y**2 + 19*y**3 - 17*y**3 - y**2 + 2*y**4 - y**2 = 0.
-2, 0, 1
Suppose 0 = 10*v - 24 + 4. Factor 2383*u + 523*u + 165*u**3 + 272*u**2 - 2087*u**v + 3749*u - 5*u**4.
-5*u*(u - 11)**3
Let i = -323 + 1629/5. Let t(w) = 3*w**3 + 154*w**2 + 43*w - 406. Let k be t(-51). Suppose -4/5*a**k + i*a - 2/5*a**3 - 8/5 = 0. Calculate a.
-4, 1
Factor 2*t**3 - 12*t - 3*t**3 - 11*t**2 - 4*t**2 - 16*t + 5*t**2 - 24.
-(t + 2)**2*(t + 6)
Suppose -s - s = d - 8, 0 = 5*d +