 m(w) = -w**3 - 9*w**2 - 11*w - 21. Let f be m(-8). Let o = -199/20 + 47/4. Factor -4/5*k**f + o*k + 2/5 + 3/5*k**2.
-(k - 2)*(k + 1)*(4*k + 1)/5
Suppose -2*j = -0*j - 344. Factor -172 - 20*z - 5*z**2 + j.
-5*z*(z + 4)
Let u(d) = 7*d**3 + 60*d**2 + 394*d - 1029. Let m(f) = 6*f**3 + 60*f**2 + 392*f - 1028. Let q(i) = 5*m(i) - 4*u(i). Let q(x) = 0. What is x?
-16, 2
Let w(d) be the third derivative of -d**6/220 + 13*d**4/44 - 12*d**3/11 + 229*d**2 - 2*d. Find m such that w(m) = 0.
-4, 1, 3
Let p be ((-34)/(-17))/(2/5). Suppose 3*m = 5*r + 4, -7 = 3*r - p*m + 5. Factor -1/2*i - 1/2*i**2 + r.
-(i - 1)*(i + 2)/2
Let o(i) be the third derivative of -2*i**7/525 + 17*i**6/300 - 13*i**5/50 + 4*i**4/15 + 4*i**3/3 - 104*i**2. What is k in o(k) = 0?
-1/2, 2, 5
Let w = -8 - -11. Let c(a) be the first derivative of a**2 + 4*a + 4*a**2 + 0*a + 30 - 28 - 2*a**w. Suppose c(r) = 0. What is r?
-1/3, 2
Factor -2/5*j**2 + 18/5*j + 4.
-2*(j - 10)*(j + 1)/5
Factor 2/11*l**3 + 300/11 + 32/11*l**2 + 170/11*l.
2*(l + 5)**2*(l + 6)/11
Suppose -5*q = -5*r + 15, 3*q + q + 2*r - 18 = 0. Let w = -1058/287 + 198/41. Suppose w*t + 4/7*t**4 - 8/7*t**3 + 0*t**q - 4/7 = 0. What is t?
-1, 1
Factor -3*q**3 + 0 + 1/3*q**5 + 11/3*q**2 - 4/3*q + 1/3*q**4.
q*(q - 1)**3*(q + 4)/3
Solve 2/7*f**2 + 126 + 12*f = 0 for f.
-21
Let u(m) be the second derivative of m**6/6 + 13*m**5/4 + 20*m**4 + 30*m**3 + m - 32. Let u(j) = 0. What is j?
-6, -1, 0
Let i = 10/129 + 11/43. Factor 0*r + 2/3*r**3 + 0 + 0*r**2 + 1/3*r**4 - i*r**5.
-r**3*(r - 2)*(r + 1)/3
Suppose j + 3 = 0, -3*i = -5*j + 4*j + 9. Let n = 4 + i. Let -9*g**5 + g**3 + 9*g**2 - 15*g**4 + 6*g**2 - 6*g + 14*g**3 + n*g**5 = 0. Calculate g.
-2, -1, 0, 1/3, 1
Let a(z) be the third derivative of -1/90*z**5 - 1/180*z**6 + 0*z**3 + 0*z + 16*z**2 - 1/1260*z**7 + 0*z**4 + 0. Factor a(h).
-h**2*(h + 2)**2/6
Let z = 88256/1565 + 2/313. Let o = z + -56. Factor 2/5 + 4/5*t + o*t**2.
2*(t + 1)**2/5
Let i = 143 - 141. Let -30*z - 118*z**2 + 40 + 65*z**i + 58*z**2 = 0. Calculate z.
2, 4
Suppose 0 = 3*m + s - 6, 0 = -m + 4*s + 2. Solve -m*k**2 + 22*k + 4*k**3 + 2 - 8*k - 6*k**3 - 12*k = 0.
-1, 1
Let n(l) = l + 1. Let k(p) = -p**3 + 7*p**2 - 3*p + 19. Let a(q) = -2*k(q) + 22*n(q). Factor a(i).
2*(i - 4)*(i - 2)*(i - 1)
Let i(z) be the first derivative of -z**6/50 - z**5/50 + z**4/40 + 2*z**3/3 - 1. Let p(f) be the third derivative of i(f). Factor p(d).
-3*(2*d + 1)*(6*d - 1)/5
Let 20/7*k + 1/7*k**2 + 19/7 = 0. What is k?
-19, -1
Find s, given that 1/4*s**4 + 3/2*s + 0 + 11/4*s**2 + 3/2*s**3 = 0.
-3, -2, -1, 0
Let c be (-152)/(-52)*15/18. Let a = c + -23/13. Factor 0*x**4 - 1/3*x**5 - 1/3*x + 0 + 0*x**2 + a*x**3.
-x*(x - 1)**2*(x + 1)**2/3
Let s(o) be the second derivative of 5/9*o**4 - 14*o + 8/3*o**2 - 1/15*o**5 + 0 - 16/9*o**3. Factor s(l).
-4*(l - 2)**2*(l - 1)/3
Let -49/2*i**3 - 763/2*i**2 - 212*i - 30 = 0. Calculate i.
-15, -2/7
Let y(i) = -2*i + 4. Let k be y(0). Suppose 4*q**2 + 0 + k*q + 0*q**2 - 2*q**2 + 2 = 0. What is q?
-1
Let p(q) = q**2 - q - 1. Let g(v) = 8*v**2 + 5*v + 29. Let s(t) = -9*t**2 - 4*t - 28. Let i(w) = 4*g(w) + 3*s(w). Let k(n) = i(n) - 4*p(n). Factor k(c).
(c + 6)**2
Suppose -18*u - 18 = -72. Let p(y) be the first derivative of -1/6*y**2 + 1/12*y**4 + 1/9*y**u + 0*y - 1/15*y**5 + 7. Factor p(n).
-n*(n - 1)**2*(n + 1)/3
Let o(f) be the second derivative of 1/5*f**6 + 0*f**2 - 2/3*f**4 + 0*f**3 + 0*f**5 + 0 - 6*f - 1/21*f**7. Factor o(h).
-2*h**2*(h - 2)**2*(h + 1)
Let m be ((-184)/6*1)/((-12)/18). Factor -12*s**5 - 36*s**3 + 53*s**4 - m*s**5 - 6*s**5 + 43*s**4 + 4*s**2.
-4*s**2*(s - 1)*(4*s - 1)**2
Let j = 19908/5 - 3981. Let q = 1471/5 - 293. Factor -q - 9/5*x - j*x**2.
-3*(x + 1)*(x + 2)/5
Let i(x) be the first derivative of -x**4/36 + 16*x**3/9 - 128*x**2/3 - 6*x - 49. Let m(w) be the first derivative of i(w). Suppose m(g) = 0. Calculate g.
16
Let g = -631288 + 57448304/91. Let p = 544/39 - g. Factor -100/7*w**2 + p*w**3 - 2/21*w**4 + 1000/21*w - 1250/21.
-2*(w - 5)**4/21
Let i = -3/257 + -5391/514. Let o = i - -11. Factor -1/2*w**3 + 0*w**2 + 0 + o*w.
-w*(w - 1)*(w + 1)/2
Let f = -17378 - -17378. Determine p, given that f*p + 2/7*p**2 + 0 + 2/7*p**3 = 0.
-1, 0
Let o(c) = -4*c**5 - 74*c**4 + 66*c**3 + 6*c**2 - 90*c + 40. Let z(i) = i**5 + 15*i**4 - 13*i**3 - i**2 + 18*i - 8. Let u(d) = -3*o(d) - 14*z(d). Factor u(w).
-2*(w - 4)*(w - 1)**3*(w + 1)
Let n = 5/1844 - -3633/20284. Factor 2/11*u**3 + 0 - 2/11*u - 2/11*u**4 + n*u**2.
-2*u*(u - 1)**2*(u + 1)/11
Solve 8*a**2 + 0*a**2 + 24*a - a**2 - 3*a**2 = 0 for a.
-6, 0
Let g be 3 + (-2 - -1) - -3. Suppose 5*h - 4*h + o = 7, -3*o + 27 = g*h. Factor -3*y**5 + 4*y**2 + 2*y**2 + 14*y**3 - 9*y - 9 + h - 2*y**3.
-3*(y - 2)*(y - 1)*(y + 1)**3
Let j be -3*8/12 - 3. Let w(f) = f**3 + 5*f**2 + f + 7. Let d be w(j). What is i in 2*i**2 + 5*i + 2 + 0 + d + i = 0?
-2, -1
Let o = 2372 - 2368. Suppose -6 = -3*l + 3. What is i in -1/6*i**5 + 1/6*i**2 - 1/2*i**l + 1/2*i**o + 0 + 0*i = 0?
0, 1
Let x = -14 + 18. Suppose 0 = -x*g + 12, 0*t - 5*t + 1 = -3*g. Factor -24*k - 61 + 13 - k**2 - t*k**2.
-3*(k + 4)**2
Suppose -4*o + 200 = 160. Let w(r) = -10*r + 102. Let j be w(o). Factor 5/2*f**j - 7/2*f - 1/2*f**3 + 3/2.
-(f - 3)*(f - 1)**2/2
Let v = -21056 - -21058. Determine o, given that -2/7*o + 2/7*o**3 + 10/7*o**v - 10/7 = 0.
-5, -1, 1
Let k(y) = -y**2 + 5*y. Let x be k(4). Suppose 15*f**3 + 3*f**x + 4*f - 19*f - 15*f**2 + 12*f**2 = 0. What is f?
-5, -1, 0, 1
Let j(s) be the first derivative of -5*s**2 - 2*s**3 - 4*s + 1/2*s**4 + 2/5*s**5 + 23. Factor j(d).
2*(d - 2)*(d + 1)**3
Suppose 55 + 8 = 21*o. Let j be (2/(-15))/((-2)/24). Determine w, given that -j*w**2 - 3/5*w**o - 4/5*w + 0 = 0.
-2, -2/3, 0
Let 15*h**2 - 30*h - 52 - 39 - 42 - 57 + 150 + 5*h**3 = 0. Calculate h.
-4, -1, 2
Let n(c) be the first derivative of c**5/20 - 6*c**4 + 429*c**3/2 - 1620*c**2 + 18225*c/4 + 588. Let n(m) = 0. Calculate m.
3, 45
Determine o, given that -34/7*o**2 - 16/7*o - 2/7*o**4 + 0 - 20/7*o**3 = 0.
-8, -1, 0
Let z be (-64)/(-35) - ((-6)/(-14) + -1). Factor 4/5*b**2 - 8/5*b - z.
4*(b - 3)*(b + 1)/5
Let s(v) be the third derivative of v**6/24 + 7*v**5/6 + 25*v**4/2 + 60*v**3 + 11*v**2 - 2. Determine j so that s(j) = 0.
-6, -2
Suppose 0 = -3*i - 3*s + 21 + 3, 4*i - 5*s = 68. Let d be -6 + (-5)/(-1) - i/(-2). Solve 0*n - 3/2*n**4 - 2*n**2 + 0 + 1/4*n**d + 3*n**3 = 0 for n.
0, 2
Let v = 18 - 14. Factor l + v*l - 6*l - 2 + l**2 + 0*l.
(l - 2)*(l + 1)
Let z be 3165/(-150) - -21 - (-2 + 42/(-20)). Find w such that 11*w - 4/3*w**z + 3 - 17/3*w**2 - 7*w**3 = 0.
-3, -1/4, 1
Let b = 83525/6 - 13916. Let 1 + 19/6*v**2 - b*v + 2/3*v**3 = 0. What is v?
-6, 1/4, 1
Let b(s) = -14*s**3 - 59*s**2 - 15*s - 6. Let o(r) = 55*r**3 + 235*r**2 + 60*r + 25. Let m(n) = 25*b(n) + 6*o(n). Suppose m(c) = 0. What is c?
-3, -1/4, 0
Suppose 4*o = 3*c + 14, 7*o - 45 = 4*c - 18. Factor 0 - 2/3*y**3 + 0*y - 4/3*y**c.
-2*y**2*(y + 2)/3
Let d(q) be the first derivative of -q**9/8064 + q**7/2240 + 19*q**3/3 - 12. Let t(l) be the third derivative of d(l). Find a, given that t(a) = 0.
-1, 0, 1
Suppose -16 - 8 = -4*q. Let w be (-2)/(-20) + -3*q/(-45). Factor 1/2*b + 0 - w*b**2.
-b*(b - 1)/2
Let y(p) be the first derivative of 0*p - 1/15*p**3 + 5/2*p**2 - 7 - 1/50*p**5 + 1/15*p**4. Let a(m) be the second derivative of y(m). Solve a(x) = 0 for x.
1/3, 1
Solve -2/5*y + 0 - 9/10*y**3 - 2*y**2 = 0 for y.
-2, -2/9, 0
Let u(k) be the first derivative of 4*k**3/9 + 8*k**2 - 52*k/3 + 84. Factor u(v).
4*(v - 1)*(v + 13)/3
Let y(k) = -5*k**3 + k**2 + 24*k + 28. Let w(m) = -2*m**3 - m**2. Let n(s) = -2*w(s) + y(s). Suppose n(c) = 0. Calculate c.
-2, 7
Let r(o) be the third derivative of -5/12*o**5 + 5/6*o**4 + 0*o**3 + 0*o - 20*o**2 + 1/24*o**6 + 0. Factor r(y).
5*y*(y - 4)*(y - 1)
Let j be 4 + 1 + -3 + 1. Factor 5*l**2 + 8*l + 8 - 3*l**2 + j*l**2 - 3*l**2.
2*(l + 2)**2
Let q(f) be the first derivative of -1/2*f**3 + 3*f**2 + 15/2*f + 16. Factor q(v).
-3*(v - 5)*(v + 1)/2
Let c(m) be the third derivative of -5*m**7/14 - 3*m**6 - 46*m**5/5 - 12*m**4 - 8*m**3 - 59*m**2 - m. Factor c(y).
-3*(y + 2)**2*(5*y + 2)**2
Let l(h) = 9*h + 318. Let t be l(-35). Let f(c) be the first derivative of -4/9*c**t - 1/6*c**4 - 1/3*c**2 + 2 + 0*c. Determine z so that f(z) = 0.
-1, 0
