f - 2)
Let t be (-84)/30 - (545 - 548). Let -13/5 - t*q**2 - 14/5*q = 0. What is q?
-13, -1
Let w(p) = -p**2 + 7*p. Let t(y) = 3*y**2 - 59*y - 54. Let z(g) = 2*t(g) + 10*w(g). Determine c, given that z(c) = 0.
-9, -3
Let u = 21 + -44. Let g = 26 + u. Factor 24*t**2 - 4*t**2 + 4 - g*t + 12*t**2 + 23*t + 16*t**3.
4*(t + 1)*(2*t + 1)**2
Let g be 270/120*20/15. Let z(v) be the first derivative of 2/3*v**2 - 10 - 1/18*v**g + 0*v. Find a such that z(a) = 0.
0, 8
Let o = 10186/4265 - -10/853. Let g(y) be the first derivative of -4/15*y**3 - 8/5*y**2 - o*y + 3. Factor g(s).
-4*(s + 1)*(s + 3)/5
Suppose -14*v + 471 = -33. Factor v*r + 2*r**2 - 271 + 0*r**2 + 10*r**2 + 298.
3*(2*r + 3)**2
Suppose 100 - 55/3*b - 1/3*b**2 = 0. Calculate b.
-60, 5
Suppose 10*y + 64 - 64 = 0. Let m(l) = l**2 - 4*l - 10. Let w be m(-2). Factor 0*q + 1/3*q**4 + y + 0*q**w - 4/3*q**3.
q**3*(q - 4)/3
Let x(h) = 5*h**4 + 34*h**3 - 70*h**2 + 27*h + 132. Let t(j) = -2*j**4 - 5*j**3 - j**2 + 2*j - 2. Let s(o) = -3*t(o) - x(o). Factor s(l).
(l - 14)*(l - 3)**2*(l + 1)
Suppose -425 + 731 = 6*h. Let -h*r**2 + 28*r**2 + 42 - 51*r + 26*r**2 + 26 + 22 = 0. Calculate r.
2, 15
Suppose 0 = 158*m - 290*m + 52*m + 320. Solve 1 + 11/3*j**m - 6*j**3 + 5/3*j**5 + 13/3*j - 14/3*j**2 = 0 for j.
-3, -1, -1/5, 1
Let p(k) = k**2 + 4. Let l be p(6). Let b = l + -29. Solve 36*x**2 - 9 - b - 28*x**4 - 20*x + 20*x**3 - 6 + 18 = 0.
-1, -2/7, 1
Let v(o) = o**3 - 9*o**2 + 8*o + 3. Let d be v(8). Let q be (-6)/2*(-62)/93. Solve -5 + 3*t + 5*t**q - 10*t**4 - 3*t**d + 4*t**4 + 1 + 5*t**4 = 0 for t.
-4, -1, 1
Let d(s) be the second derivative of -5*s**7/3 - 27*s**6/2 - 113*s**5/4 - 45*s**4/2 - 20*s**3/3 + 3*s + 111. Find q such that d(q) = 0.
-4, -1, -1/2, -2/7, 0
Suppose 0 = -4*v + 25*h - 26*h + 6, 5*h - 30 = -2*v. Let f(i) be the second derivative of 1/12*i**4 + v + 2/3*i**3 + 2*i**2 - 17*i. What is m in f(m) = 0?
-2
Let o(y) = -30*y + 62. Let m be o(2). Factor -7*z**2 + z - m*z**3 + z**3 - 11*z - 6*z - 12.
-(z + 2)**2*(z + 3)
Let x(j) = 725*j**3 + 1485*j**2 + 3255*j - 65. Let b(w) = -67*w**3 - 135*w**2 - 296*w + 6. Let f(s) = 65*b(s) + 6*x(s). Factor f(n).
-5*n*(n - 29)*(n + 2)
Let b(d) = 3*d**2 + 129*d - 10707. Let p be b(-85). Suppose 12/7*n**2 - 2/7*n**p + 8/7 - 18/7*n = 0. Calculate n.
1, 4
Determine w so that 3/5*w**3 - 237/5*w**2 + 912/5*w - 180 = 0.
2, 75
Let x be -15 - ((-505)/25 + 16) - -11. Factor 2/5*y**2 + 0 + 3/5*y**3 + 0*y + x*y**4.
y**2*(y + 1)*(y + 2)/5
Let j(n) be the first derivative of 32/9*n - 10/9*n**3 + 8 - 8/9*n**2 + 1/2*n**4. Factor j(p).
2*(p + 1)*(3*p - 4)**2/9
Let k be 2*(643 + (-5 - -2)). Let d = 8966/7 - k. Factor d*q**3 + 0*q + 0 - 9/7*q**4 + 0*q**2.
-3*q**3*(3*q - 2)/7
Let g(u) be the second derivative of -3*u**4/8 + 1403*u**3/4 + 351*u**2 + 3*u + 2348. Factor g(m).
-3*(m - 468)*(3*m + 1)/2
Let k be 4 - ((3 - 0) + (-12 - 2)). Suppose k*h = -10*h. Factor v**2 - 3/2*v**3 + 0*v**4 + h*v + 1/2*v**5 + 0.
v**2*(v - 1)**2*(v + 2)/2
Suppose -13*x + 86 = -31. Suppose 2 + 25 = x*d. Factor -5*r**2 + 8 + 3*r**2 - d - 3*r**2.
-5*(r - 1)*(r + 1)
Suppose -3*o = 5*s + 9, 31*o + 2*s + 4 = 30*o. Let -20 + 11 + 2*t**o + 21 + 2*t + 8*t = 0. Calculate t.
-3, -2
Let p be 0 - 2 - (-10 + (22 - 9)). Let w(a) = 3*a**2 + 45*a + 78. Let h(o) = 2*o**2 + 22*o + 40. Let z(g) = p*w(g) + 9*h(g). Factor z(k).
3*(k - 10)*(k + 1)
Let z(l) be the third derivative of -l**6/96 + 23*l**5/48 + 475*l**4/12 + 5375*l**3/6 - 41*l**2 - 6. Factor z(h).
-5*(h - 43)*(h + 10)**2/4
Let a(c) = 2*c**3 - 12*c**2 - 19*c - 34. Let f be a(11). Factor 466*v + 469*v + 4*v**2 - f*v.
4*v*(v - 8)
Let t(v) be the third derivative of -v**6/30 + 4*v**5/5 - 35*v**4/6 + 16*v**3 + 792*v**2. Solve t(z) = 0.
1, 3, 8
Let s = -233930/9 - -25994. Factor -2/9 - 8/9*p**3 - s*p**2 - 10/9*p.
-2*(p + 1)*(2*p + 1)**2/9
Let y be -103*2/(-112) + (-34)/272. Let z = 62 - 60. Suppose -y*p + 16/7 - 4/7*p**z = 0. What is p?
-4, 1
Let f be (4/6)/((-72)/(-756)). Let v(d) = -2*d**2 + 16*d - 12. Let k be v(f). Determine z, given that 0*z + 0 - 2/11*z**3 + 2/11*z**k = 0.
0, 1
Let h = -49 - -53. Let r be (2/20*h)/((-4)/(-20)). What is z in 11*z**2 - 8*z**3 - 11*z - 4*z**3 + 28*z**r + 6 - 22*z = 0?
1/4, 1, 2
Solve 392/17*g**3 + 388/17*g + 0 + 778/17*g**2 + 2/17*g**4 = 0.
-194, -1, 0
Let r(p) = -13*p**2 - 3545*p - 781384. Let y(g) = -g**2 - g + 8. Let l(j) = -r(j) + 9*y(j). Factor l(t).
4*(t + 442)**2
Let 1053*p**5 + 142*p - 40 + 1056*p**5 + 86*p**3 - 14*p - 154*p**2 - 2107*p**5 - 22*p**4 = 0. What is p?
1, 2, 5
Suppose -104 + 133/5*k**3 + 78*k**2 + 1/5*k**4 - 4/5*k = 0. Calculate k.
-130, -2, 1
Let v(a) be the second derivative of a**4/6 - 22*a**3/3 - 135*a**2 - 9384*a. Solve v(g) = 0.
-5, 27
Suppose 0 = s - p - 4, 1416*s - 1420*s - p + 6 = 0. Determine m, given that -1/5*m**5 + 2/5*m**3 + 7/5*m - 2/5*m**4 + 8/5*m**s + 2/5 = 0.
-1, 2
Let o(t) be the first derivative of -4/3*t**3 + 0*t + 2*t**4 + 4/5*t**5 - 43 - 4*t**2. Factor o(s).
4*s*(s - 1)*(s + 1)*(s + 2)
Let v = -1687 + 1691. Suppose 10*b - 4*b = v*b. Solve 2/17*w**2 + b - 16/17*w = 0 for w.
0, 8
Let y(c) be the second derivative of 13*c**2 - 29*c - 25/78*c**4 + 11/3*c**3 + 0 + 1/130*c**5. Suppose y(m) = 0. What is m?
-1, 13
Let d(b) be the third derivative of 2 + 1/210*b**5 - b**2 + 16/21*b**3 - 2/21*b**4 + 0*b. Factor d(n).
2*(n - 4)**2/7
Let f = 415 - 369. Let t = f - 44. Suppose 2/3 - 2/3*j**t + 0*j = 0. What is j?
-1, 1
Let u(y) = 4*y**2 - 25. Let h be u(5). Suppose -74*g + h*g - 3 = 0. Factor -5*n - 45/2*n**g + 0 - 35/2*n**2 - 5/2*n**5 - 25/2*n**4.
-5*n*(n + 1)**3*(n + 2)/2
Suppose 3/4*o - 27/2*o**2 - 3/4*o**3 + 27/2 = 0. Calculate o.
-18, -1, 1
Suppose 4 = -2*x + 17*n - 13*n, -3*n + 12 = 3*x. Factor -75 - 40 - 74*j + 42 - 3*j**x + 2*j**2.
-(j + 1)*(j + 73)
Let k be (21 + 799/(-34))*(-120)/100. What is i in -6 + 45/4*i + 87/2*i**2 + 117/4*i**k + 3*i**4 = 0?
-8, -1, 1/4
Let t be 2 + -11 - ((-4)/34 + (-28237)/3179). Factor 3/2*g**2 + 0 - 1/6*g**4 + 0*g + t*g**3.
-g**2*(g - 3)*(g + 3)/6
Let c be (-5)/3 - (((-7940)/78)/(-10) + -12). Factor 4/13*x - c - 2/13*x**2.
-2*(x - 1)**2/13
Let a(m) be the second derivative of -m**6/195 - 519*m**5/130 + 347*m**4/26 - 521*m**3/39 + 192*m - 1. What is u in a(u) = 0?
-521, 0, 1
Let p(j) be the first derivative of -3*j**6 + 4*j**5 + 4*j**4 - 20*j**3/3 + j**2 - 4949. Let p(m) = 0. What is m?
-1, 0, 1/9, 1
Let d(s) = s**3 + 4*s**2 + 9*s + 20. Let r be d(-3). Suppose 185*b**3 + 15*b**3 + 73*b**2 - 78*b + 287*b**r + 23 - 19 = 0. Calculate b.
-2, 1/10
Solve 24*r + 4/7*r**2 + 320/7 = 0.
-40, -2
Let m(l) = l**2 + 2*l + 3. Let r be m(-2). Find f such that -3*f**2 - 90*f**r - 3 + 7 + 89*f**3 = 0.
-2, 1
Let f be 1/2*0/(12 - 1). Let g(h) be the first derivative of -2/9*h**3 - 1/4*h**4 + f*h**2 - 1 + 0*h. Factor g(s).
-s**2*(3*s + 2)/3
Let a(l) = -7*l**2 - 15*l + 308. Let r(u) = 186 - 10*u + 47*u**2 - 52*u**2 + 30 - 11. Let k(g) = -5*a(g) + 8*r(g). Determine p, given that k(p) = 0.
-5, 4
Factor -30*i**3 - 57*i**2 + i + 59*i**3 - 49*i**2 + 106 - 30*i**3.
-(i - 1)*(i + 1)*(i + 106)
Let p(c) = 2*c**3 - 5*c**2 + 5*c - 4. Let y be p(3). Suppose -17 - 11 + 2*w**3 - 6 + y - 2*w + 14*w**2 = 0. What is w?
-7, -1, 1
Let a be (-7)/3 + 2 - 20/(-6). Suppose 0 = -a*m + 1 + 8. Suppose 5*u**4 - 5*u - 6*u**2 + 7*u**4 + 3*u**5 + 12*u**m - 9*u - u - 6 = 0. Calculate u.
-2, -1, 1
Let a be 4/(48/(-16857)) - 21/(-28). Let h = -12620/9 - a. Factor 16/9*r + 2/9*r**4 - h*r**3 - 32/9 + 10/3*r**2.
2*(r - 4)**2*(r - 1)*(r + 1)/9
Factor -39*i**2 - 111 - 36*i**2 + 110*i**2 - 32*i**2 + 108*i.
3*(i - 1)*(i + 37)
Let s(a) be the first derivative of -a**6/9 + 12*a**5 - 44*a**4 + 524*a**3/9 - 29*a**2 + 5961. Determine x, given that s(x) = 0.
0, 1, 87
Let k(c) be the third derivative of 0*c**3 + 0 + 1/420*c**6 + 0*c**4 + c**2 - 2*c - 4/105*c**5. Factor k(u).
2*u**2*(u - 8)/7
Suppose -z - 882 = -4*r, 2*r - 900 = z + 7*r. Let f = z - -890. Factor 2/3*x**5 + 0*x + 2/3*x**4 + 0*x**2 + f + 0*x**3.
2*x**4*(x + 1)/3
Suppose 0 = -10*n - 181 + 211. Let l(r) be the second derivative of -1/220*r**5 + 2/11*r**2 - 1/132*r**4 + 2/33*r**n + 0 + 18*r. Factor l(p).
-(p - 2)*(p + 1)*(p + 2)/11
Let i(n) be the first derivative of n**6/40 - n**5/4 + n**4/2 + 17*n**2 + 3*n + 104. Let y(j) be the second derivative of i(j). Find v, given tha