2 + i + 1. Let j(y) = -8*y - 15 - 19*y - 7*y**2 + 9*y - 5*y**2. Let q(x) = u*j(x) + 9*f(x). Suppose q(k) = 0. What is k?
-2, -1
Let v(a) be the first derivative of 7*a**6/3 + 33*a**5 - 104*a**4 + 253*a**3/3 + 6*a**2 - 28*a - 147. Let v(o) = 0. What is o?
-14, -2/7, 1/2, 1
Suppose -693 = -5*q + 1432. Let s = q - 6371/15. Suppose -2/15*o - 2/15*o**3 + 0 - s*o**2 = 0. Calculate o.
-1, 0
Let q = 62 + -65. Let j be q + 0 + 261/81. What is s in j*s**3 + 2/3*s**2 - 8/9 + 0*s = 0?
-2, 1
Let v(k) be the second derivative of k**5/420 + 3*k**4/28 + 27*k**3/14 + 10*k**2 - 12*k. Let h(q) be the first derivative of v(q). Find j, given that h(j) = 0.
-9
Let u be 2/7 - 57/(-21). Factor -18*i**4 + 2*i**u - 14*i**3 + 14*i**4 - 8*i + 24*i.
-4*i*(i - 1)*(i + 2)**2
Let h(q) be the second derivative of 5*q**4/48 - 17*q**3/8 - 11*q**2/2 - 2*q - 288. Determine g so that h(g) = 0.
-4/5, 11
Let y(m) be the first derivative of m**5 - 15*m**4/2 + 20*m**3/3 + 15*m**2 - 25*m - 779. Factor y(t).
5*(t - 5)*(t - 1)**2*(t + 1)
Let m(r) be the first derivative of -r**3/3 - 7*r**2/2 - 6*r - 14. Determine d, given that m(d) = 0.
-6, -1
Determine z, given that -200/3 - 481/6*z**2 + 7*z**3 + 140*z - 1/6*z**4 = 0.
1, 20
Let s(o) be the first derivative of -8*o**5/25 - 14*o**4/5 - 10*o**3/3 - 6*o**2/5 - 402. Factor s(z).
-2*z*(z + 6)*(2*z + 1)**2/5
Let j(n) be the first derivative of n**6/24 - 3*n**5/5 + 47*n**4/16 - 13*n**3/3 - 6*n**2 + 16*n + 202. Solve j(t) = 0.
-1, 1, 4
Let w = 13 + -8. Let u(g) = -g**3 + 7*g**2 - g + 1. Let o be u(w). Solve 4 + 32*s**4 + 3*s + o*s**4 - 102*s**3 - 10 - 21*s**5 - 19*s**2 + 67*s**2 = 0.
-2/7, 1
Let j be (25/10 - 4)/(4 + -9). Let l(f) be the second derivative of 0*f**2 - 6*f + 1/10*f**6 + j*f**5 + 0*f**3 + 1/4*f**4 + 0. Factor l(i).
3*i**2*(i + 1)**2
Suppose 4*o - 3*i = 36, 1035*o + 2*i = 1033*o - 10. Suppose 3*h - 3/2*h**o - 3/2*h**2 + 0 = 0. What is h?
-2, 0, 1
Let k be 210/66 + 2/(-11). Let k*f - 2*f + 20 - 15*f**2 - f + 5*f**3 = 0. Calculate f.
-1, 2
Let c(h) = -10*h**2 + 11*h - 24. Let f(y) = 4*y**2 - 5*y + 12. Let p(z) = -3*c(z) - 7*f(z). Find d, given that p(d) = 0.
-3, 2
Let s(g) = 4*g**3 - 2*g + 2. Let c be s(2). Find k such that 10 - 60*k - 5*k**3 - c*k**2 - 50 + k**3 - k**3 = 0.
-2
Suppose 0 - 20 = -5*b, 10*m - 3*b = 8. Let 0 + 4*d**3 + 2/7*d + 16/7*d**4 + 2*d**m = 0. What is d?
-1, -1/2, -1/4, 0
Let l = -7900/9 + 878. Let d(m) be the first derivative of l*m**3 + 0*m**2 + 1/36*m**6 + 1 + 0*m + 0*m**4 - 1/10*m**5. Suppose d(n) = 0. Calculate n.
-1, 0, 2
Let n(f) = f**2 + 5*f - 21. Let z be n(3). Solve -8*v**z - 4*v**4 + 395 + 4*v**2 - 395 + 8*v = 0.
-2, -1, 0, 1
Let k(x) be the third derivative of 29*x**2 + 1/180*x**5 + 0*x**3 + 0*x**6 - 1/630*x**7 + 0*x**4 + 0*x + 0. Factor k(c).
-c**2*(c - 1)*(c + 1)/3
Let p(j) be the first derivative of -2/3*j**3 + 4*j**2 - 6*j + 11. Factor p(h).
-2*(h - 3)*(h - 1)
Let a = 13 - 7. Let k(v) = -100*v**4 + 90*v**3 - 10*v**2 - 35*v - 55. Let y(m) = -11*m**4 + 10*m**3 - m**2 - 4*m - 6. Let z(x) = a*k(x) - 55*y(x). Factor z(i).
5*i*(i - 2)*(i - 1)*(i + 1)
Let b = -36 + 40. Let t(i) be the third derivative of 1/15*i**5 + 0 - 4/3*i**3 - 5*i**2 + 1/6*i**b + 0*i. Let t(s) = 0. Calculate s.
-2, 1
Suppose -2*d + 3*o + 20 = 0, 5*o + 3 + 5 = -3*d. Let 39*s**2 + 4 + 18*s**3 + d + 0 + 36*s + 4 + 3*s**4 = 0. Calculate s.
-2, -1
Let m(p) be the first derivative of -2*p**6/3 + 16*p**5/5 - 3*p**4 - 16*p**3/3 + 8*p**2 - 26. Let m(f) = 0. What is f?
-1, 0, 1, 2
Let x(a) be the third derivative of -a**6/200 + a**5/100 + 17*a**2. Factor x(j).
-3*j**2*(j - 1)/5
Let o = -10 - -17. Suppose -3*b + o = 1. Let 2*p**3 - 3*p - p - 10*p**b - 2*p**4 - 10*p**3 = 0. What is p?
-2, -1, 0
Let h(s) be the first derivative of -20 - 10/3*s**3 + 0*s - 5/8*s**4 - 15/4*s**2. Factor h(f).
-5*f*(f + 1)*(f + 3)/2
Let f(s) = -16*s**2 - 1100*s - 2108. Let x(y) = 3*y**2 + 200*y + 383. Let h(g) = -5*f(g) - 28*x(g). Factor h(q).
-4*(q + 2)*(q + 23)
Suppose 2/15*y**2 + 0 - 22/15*y = 0. What is y?
0, 11
Let l(y) = 5*y**3 - 40*y**2 + 106*y - 86. Let g(k) = -5*k**3 + 40*k**2 - 105*k + 85. Let o(u) = 6*g(u) + 5*l(u). Factor o(q).
-5*(q - 4)*(q - 2)**2
Suppose 0 = 3*v + 23 - 32. What is j in 2/3*j**v - 2/3*j - 2 + 2*j**2 = 0?
-3, -1, 1
Let f(c) = c**2 - 7*c + 28. Let l(z) = 1 + 11*z - 6*z - 4*z. Let a(i) = -4*f(i) + 12*l(i). Find o, given that a(o) = 0.
5
Factor -206 + 6*q**2 + 150 + 6*q**2 - 88*q + 12*q.
4*(q - 7)*(3*q + 2)
Factor 9*t**3 + 4*t + 36*t**2 - t**4 - 27 - 21 + 0*t.
-(t - 12)*(t - 1)*(t + 2)**2
Suppose -633*h = -1268*h + 630*h + 15. Suppose 2/3*r**h - 8/3*r + 8/3 - 2/3*r**2 = 0. What is r?
-2, 1, 2
Let a(d) be the second derivative of -d**7/1680 + d**6/240 - d**5/80 - 13*d**4/12 + 7*d. Let o(u) be the third derivative of a(u). Solve o(c) = 0.
1
Let o(f) = f**3 - 36*f**2 - 79*f - 2. Let t(g) = 3*g**3 - 36*g**2 - 78*g - 3. Let m(a) = 3*o(a) - 2*t(a). Factor m(d).
-3*d*(d + 3)*(d + 9)
Let p = 584 + -584. Let r(z) be the third derivative of 8*z**2 - 1/90*z**6 + p*z**3 + 0*z**4 + 0*z + 0 + 1/45*z**5. Factor r(i).
-4*i**2*(i - 1)/3
Let h be (25/(-375))/(24/(-15)). Let i(p) be the first derivative of h*p**6 - 5 + 0*p**2 + 0*p - 1/20*p**5 + 1/12*p**3 - 1/16*p**4. Factor i(v).
v**2*(v - 1)**2*(v + 1)/4
Let f(w) be the second derivative of w**8/3360 - w**6/120 + w**5/30 + 13*w**4/12 - 11*w. Let b(g) be the third derivative of f(g). Factor b(i).
2*(i - 1)**2*(i + 2)
Suppose 0*p = -4*p. Let r be (18/(-6))/(p - 1). Factor 10*z**4 - z**5 - 2*z**4 - 2*z**5 - 4*z**2 - r*z**5 + 2*z**3.
-2*z**2*(z - 1)**2*(3*z + 2)
Let f(i) be the third derivative of -5*i**7/28 - 57*i**6/16 - 89*i**5/36 + 95*i**4/12 + 110*i**3/9 + 5*i**2 + 7*i. Find l such that f(l) = 0.
-11, -2/3, -2/5, 2/3
Let j(z) be the first derivative of 3*z**5/35 - 9*z**4/14 + 13*z**3/7 - 18*z**2/7 + 12*z/7 + 100. Solve j(m) = 0.
1, 2
Let l(m) = 14*m**2 - 54*m - 26. Let d(g) = -16*g**2 + 53*g + 27. Let s(b) = -2*d(b) - 3*l(b). Factor s(p).
-2*(p - 6)*(5*p + 2)
Let a(n) = 4*n**2 + 8*n - 8. Let v(t) = 11*t**2 + 22*t - 23. Let i(m) = 17*a(m) - 6*v(m). Factor i(w).
2*(w + 1)**2
Let k(z) = 3*z**2 - 9*z + 2. Let v be k(3). Suppose n = -0*o + o - 1, n - 1 = 0. Let 3*m**3 - 3*m - 3*m + o*m**2 + 5*m - 2*m**3 - v = 0. What is m?
-2, -1, 1
Determine h so that -3/2*h + 51/8*h**3 - 31/8*h**4 + 3/4*h**5 - 11/4*h**2 + 1 = 0.
-1/2, 2/3, 1, 2
Let r(m) be the first derivative of 2*m**5/45 + 4*m**4/9 + 32*m**3/27 - 112. Factor r(k).
2*k**2*(k + 4)**2/9
Let c be (3/(-72))/((-41)/1107). Factor 7/8*m**2 + c + 15/8*m + 1/8*m**3.
(m + 1)*(m + 3)**2/8
Let r(p) be the third derivative of -p**5/300 + 37*p**4/30 - 2738*p**3/15 - 258*p**2. Suppose r(d) = 0. What is d?
74
Let n(a) = a**2 - 7*a + 18. Let q be n(9). Let c be 4/q*2 - (-2)/(-9). Suppose 18*m**4 + 10*m**5 + 8/5*m**2 + 48/5*m**3 + 0*m + c = 0. What is m?
-1, -2/5, 0
Factor 10*r**3 + 0*r - 40*r**2 + 26*r**2 - 2*r**4 + 0*r**4 + 5*r + r.
-2*r*(r - 3)*(r - 1)**2
Let l be ((-4)/2)/((-2)/(-20)). Let q(s) = 2*s**2 + 5*s + 19 + 5*s**2 - 21*s. Let y(o) = 48*o**2 - 112*o + 132. Let u(z) = l*q(z) + 3*y(z). Factor u(r).
4*(r - 2)**2
Let u(j) = 29*j**5 - 110*j**4 + 190*j**3 - 164*j**2 + 69*j - 10. Let f(g) = -g**5 + g**2 - g. Let v(p) = -4*f(p) - u(p). Factor v(a).
-5*(a - 1)**4*(5*a - 2)
Let l(c) be the third derivative of c**6/300 - 23*c**5/75 - 19*c**4/12 - 16*c**3/5 - 532*c**2. Let l(j) = 0. Calculate j.
-1, 48
Let z(u) be the third derivative of 1/21*u**7 + 0*u**6 + 5/24*u**4 + 0*u**3 - 1/6*u**5 + 13*u**2 + 0*u - 5/336*u**8 + 0. Determine y, given that z(y) = 0.
-1, 0, 1
Let u(b) be the second derivative of 1/6*b**3 + 0 - 1/60*b**4 + 0*b**5 - 3*b + 0*b**2 + 1/900*b**6. Let j(p) be the second derivative of u(p). Factor j(w).
2*(w - 1)*(w + 1)/5
Factor 66*g - 3*g**2 - 72*g + 267 - 243.
-3*(g - 2)*(g + 4)
Factor 26/9*d + 8/3*d**2 + 0 - 2/9*d**3.
-2*d*(d - 13)*(d + 1)/9
Suppose -4*f = -5*n - 15 - 35, -f - 5*n = -25. Let m be ((-18)/f)/((-8)/20). Let 4*y**4 - 5*y - 2*y - y + 70*y**m - 4*y**2 - 62*y**3 = 0. What is y?
-2, -1, 0, 1
Suppose -74*r**4 - 75*r**3 + 4*r - 11*r**5 - 25*r**5 - 14*r**2 + 10*r**5 + 9*r**3 = 0. What is r?
-1, 0, 2/13
Factor 168*r**2 + 96*r + 39/2*r**4 + 90*r**3 + 3/2*r**5 + 0.
3*r*(r + 1)*(r + 4)**3/2
Let u be (78/(-10))/(-3) + (-4)/(-10). Let -4*w**2 + 10*w**u - 1