4.
2*(f - 3)**2*(f - 2)**3
Let i(k) = -k**3 + k**2 + 2*k + 4. Let f be i(-2). Let z(t) = t + 6. Let r be z(-3). Find m, given that -3*m**3 + f*m**3 + 12*m**4 - m**r - 4*m**2 = 0.
-1, 0, 1/3
Let k(u) be the third derivative of u**5/140 + 1063*u**4/7 + 9039752*u**3/7 + 4253*u**2. Suppose k(t) = 0. What is t?
-4252
Let c = 199 + -100. Suppose -128 - 128 + c*y - 35*y - 4*y**2 = 0. What is y?
8
Let v(j) be the first derivative of 3*j**4/8 - 11*j**3 + 387*j**2/4 - 162*j + 9. Solve v(p) = 0 for p.
1, 9, 12
Let h(w) be the first derivative of -114 + 0*w**2 + 5/12*w**6 + 0*w**3 + 5/8*w**4 + 0*w - w**5. Find d such that h(d) = 0.
0, 1
Let 86/3*j**2 - 176/3 + 2/3*j**3 - 92/3*j = 0. What is j?
-44, -1, 2
Suppose 233*t - 32 = 231*t + 2*f, -f - 10 = 2*t. Find o, given that 2/7*o**t + 116/7*o + 114/7 = 0.
-57, -1
Suppose o + 3 - 6 = x, 0 = -o + 5*x + 3. Suppose -2*y = 3*l + o*y + 11, 18 = 2*l - 3*y. Factor 6*v**l + 99/2*v - 30*v**2 - 27.
3*(v - 2)*(2*v - 3)**2/2
Let w(y) be the third derivative of y**5/36 - 5915*y**4/36 + 6997445*y**3/18 - y**2 - 1251. Let w(t) = 0. Calculate t.
1183
Let k be 0 + -5 + 0 + (-211 - 2). Let m = k - -220. Factor 1/2*p + 1 - 1/2*p**m.
-(p - 2)*(p + 1)/2
Let u(a) = -a**2 - 5*a - 18. Let b(s) = 2*s**2 + 10*s + 32. Let v be (3/12 - 1)/((-9)/(-36)). Let h(l) = v*b(l) - 5*u(l). What is g in h(g) = 0?
-3, -2
Suppose 4*r + 5*d = -4, -14*r + 72 = 3*d + 28. What is u in 14/5 - 18/5*u**r + 4/5*u**2 + 2/5*u**5 - 6*u + 28/5*u**3 = 0?
-1, 1, 7
Let k(x) = -2*x + 2. Let h be k(0). Suppose o - 3*b - 28 = 38, h*o = b + 117. Let -z**2 + o*z - 3*z**2 - 60*z - 2*z**2 = 0. Calculate z.
-1/2, 0
Let s(p) be the second derivative of p**5/40 - 29*p**4/12 - 119*p**3/12 - 15*p**2 + 358*p. Determine n, given that s(n) = 0.
-1, 60
Let j = 81666 + -571660/7. Determine t so that 4/7*t**2 + 0*t + j*t**3 - 4/7*t**4 + 0 - 2/7*t**5 = 0.
-2, -1, 0, 1
Let o(w) = -3*w**2 + 7*w - 1. Let n(u) = 20*u**2 - 1208*u + 1170. Let s(r) = -n(r) - 6*o(r). Let s(m) = 0. What is m?
1, 582
Factor -201 + 4*y**3 - 119 + 12981*y**2 + 272*y - 13045*y**2.
4*(y - 10)*(y - 4)*(y - 2)
Let z(t) = -39*t**3 - 882*t**2 + 1845*t - 1032. Let p(o) = -11*o**3 - 252*o**2 + 527*o - 294. Let n(u) = -18*p(u) + 5*z(u). Determine l, given that n(l) = 0.
-44, 1
Let f(s) = -s**3 - 12*s**2 - 21*s + 22. Let t(j) = -3*j**3 - 38*j**2 - 68*j + 67. Let w(z) = 7*f(z) - 2*t(z). Factor w(g).
-(g - 1)*(g + 4)*(g + 5)
Let r(z) be the second derivative of z**4/96 + 3*z**3/16 + 7*z**2/8 - 1567*z. Let r(g) = 0. What is g?
-7, -2
Let k be (-2)/3 + (-12985)/(-15). Factor -393*b - 235*b**2 + k*b - 402*b - 35*b**3.
-5*b*(b + 7)*(7*b - 2)
Solve -384/7*c**2 + 0 - 36/7*c**3 - 1/7*c**4 - 1280/7*c = 0.
-20, -8, 0
Factor -34/5*y**3 + 66/5*y + 31/5*y**2 + 1/5*y**4 + 0.
y*(y - 33)*(y - 2)*(y + 1)/5
Let a = 6 + -2. Let h(i) be the first derivative of -14*i**2 + 5*i**a - 31*i**2 + 5*i**3 - i**5 + 4*i**4 - 4*i**4 - 6. Factor h(w).
-5*w*(w - 3)**2*(w + 2)
Let x(m) = -1 + 60*m**2 + 8*m**4 - 1897*m**3 + 1 - 16*m + 1877*m**3. Let c(q) = -q**3 - q**2 + q - 1. Let p = -3 + 4. Let b(u) = p*x(u) + 16*c(u). Factor b(w).
4*(w - 2)**2*(w - 1)*(2*w + 1)
Let r = 7797 + -7797. Let k(f) be the third derivative of r*f**3 + 0*f + 0 - 1/92*f**4 - 13*f**2 - 1/690*f**5. Factor k(y).
-2*y*(y + 3)/23
Let t(h) be the second derivative of -h**7/210 - 7*h**6/75 - 7*h**5/25 + 46*h**4/15 + 64*h**3/15 - 256*h**2/5 + 322*h. Find v such that t(v) = 0.
-8, -2, 2
Let p(m) = -m**2 + 2*m + 3. Let w be p(0). Let t = -73/16 - -81/16. Factor 0 + 0*g - 1/2*g**w - t*g**2.
-g**2*(g + 1)/2
Let j be (11 - 7922/720)/((-8)/20). Let m(p) be the third derivative of -17*p**2 - j*p**4 + 0 + 1/360*p**5 + 0*p**3 + 0*p. Let m(a) = 0. What is a?
0, 1
Factor -265*k - 195*k**2 - 110 + 41038*k**4 - 26*k**3 - 41033*k**4 - 9*k**3.
5*(k - 11)*(k + 1)**2*(k + 2)
Let o be (-4)/(-20)*4*1. Let p be (-14)/(-30) - 13/(-39). Solve 1/5*d**2 - o*d + p = 0.
2
Let o(m) = -86*m - 1374. Let r be o(-16). Let s(z) be the second derivative of -3*z**4 + 0*z**r + 10*z + 1/5*z**5 + 0 + 0*z**3. Let s(i) = 0. Calculate i.
0, 9
Let a = -21 + 45. Let y be 3/a + (-310)/(-80). Let -8*o**3 + y*o**4 + 9*o**2 - 5*o**2 + 0*o**4 = 0. Calculate o.
0, 1
Let v(b) be the second derivative of b**5/20 + 10*b**4/3 + 37*b**3/6 - 39*b**2 - 2324*b. Factor v(t).
(t - 1)*(t + 2)*(t + 39)
Let z = 500016 + -500011. Suppose -7/3*u + z*u**2 + 1/3*u**4 + 0 - 3*u**3 = 0. What is u?
0, 1, 7
Let w(d) be the first derivative of -d**6/18 + 86*d**5/5 - 5543*d**4/4 - 3080*d**3/9 + 32594*d**2 + 88752*d + 7470. Determine r, given that w(r) = 0.
-2, 4, 129
Let m(n) be the second derivative of n**6/480 + n**5/80 - n**4/96 - n**3/8 + 73*n**2/2 - 50*n. Let z(s) be the first derivative of m(s). Factor z(c).
(c - 1)*(c + 1)*(c + 3)/4
Let t be (-3540)/1062*6/(-5). Let v(q) be the second derivative of 0 + 1/12*q**3 - 1/40*q**5 + 0*q**2 + 0*q**t - 26*q. Suppose v(x) = 0. What is x?
-1, 0, 1
Let m be 48/(-9)*(-18)/(-8). Let x be (35/(-21))/(1/m). Determine v, given that 15*v - 3*v**2 + x*v**3 - 3 + 38*v**2 + 3 = 0.
-1, -3/4, 0
Let v(j) = -4*j**2 + 262*j - 382. Let g be v(64). Let -1/4*n**3 - 1/4*n**g + 1/4*n**4 + 1/4*n + 0 = 0. What is n?
-1, 0, 1
Factor -1/3*c**2 - 8/3*c + 11.
-(c - 3)*(c + 11)/3
Let v be (6967/18*2)/((-17)/(-17)). Let m = 775 - v. Solve m*h**2 - 2/9*h + 0 + 10/9*h**3 = 0.
-1, 0, 1/5
Let v = -75 - -75. Suppose 6*h + 168 - 474 = v. Factor h + 1293*j + 16*j**3 - 4*j**4 - 1357*j + 13.
-4*(j - 2)**3*(j + 2)
Let n(b) be the second derivative of b**6/60 - 3*b**5/10 + 15*b**4/8 - 29*b**3/6 + 6*b**2 + 159*b - 2. Find k such that n(k) = 0.
1, 4, 6
Let t(m) = -11*m**2 + 6*m. Let w(r) = -2*r**2 - 4*r. Let a(u) = -t(u) + 6*w(u). Factor a(x).
-x*(x + 30)
Let j(r) be the first derivative of 0*r + 43 + 1/6*r**3 + 1/6*r**2. Factor j(n).
n*(3*n + 2)/6
Suppose -118 + 8*a**4 + 12*a**3 - 6*a**4 + 18 - 102*a**2 + 29 - 232*a - 49 = 0. What is a?
-10, -1, 6
Let t = -498622/7 - -71236. Factor -t + 3*s - 3/7*s**2.
-3*(s - 5)*(s - 2)/7
Let m(y) = y**3 - 5*y**2 - 14*y + 5. Let c be m(7). Suppose 0 = -c*r + 2*r + 12. Factor 2*a**4 + a**r + a**4 + 0*a**4.
4*a**4
Let b be 19 + -7 + 2 + -11. Let i(f) be the first derivative of 1/12*f**4 + f + 28 + 7/6*f**2 + 5/9*f**b. Factor i(n).
(n + 1)**2*(n + 3)/3
Let w(i) = -35*i**4 + 49*i**3 - 201*i**2 + 227*i - 72. Let r(c) = -13*c**4 + 15*c**3 - 66*c**2 + 76*c - 24. Let v(d) = 8*r(d) - 3*w(d). What is h in v(h) = 0?
1, 24
Let p(v) be the third derivative of -v**5/45 + 1789*v**4/9 - 6401042*v**3/9 + 71*v**2 - 37*v. Factor p(c).
-4*(c - 1789)**2/3
Let j = -387999383/3927 + 98803. Let u = j - -47150/51051. Suppose -10/13*z**3 + u*z**2 - 16/13 + 2/13*z**4 + 8/13*z = 0. What is z?
-1, 2
Let q(w) = 5*w**2 - 25*w - 253. Let r(c) = 2*c**2 + 5*c + 1. Let a(l) = 2*q(l) - 6*r(l). Factor a(k).
-2*(k + 8)*(k + 32)
Suppose 4*q - 2*q = 4*z - 1132, 4*q + 859 = 3*z. Let o = z - 805/3. Suppose o*d**3 + 32/3*d + 50/3*d**2 + 8/3 + 14/3*d**4 + 2/3*d**5 = 0. Calculate d.
-2, -1
Let a(f) = -f**2 + 11*f - 26. Let p be a(7). Determine v, given that 3 + 156*v**p - 154*v**2 - 24*v - 3 = 0.
0, 12
Let s(t) be the second derivative of -1/12*t**4 + 2 + 1/100*t**5 - 20*t + 24/5*t**2 - 4/15*t**3. Factor s(c).
(c - 4)**2*(c + 3)/5
Let l be (3420/(-330))/(-57) + (-62)/(-22). Let m(g) be the second derivative of -1/14*g**4 + 0*g**2 + 1/35*g**6 - 4/35*g**5 + 3 + 0*g**l - 3*g. Factor m(i).
2*i**2*(i - 3)*(3*i + 1)/7
Determine k, given that -852*k**2 - 492*k**3 - 14*k**4 + 268*k**3 - 267*k - 293*k + 98 + 16*k**3 = 0.
-7, -1, 1/7
Let c(w) = 11*w + 68. Let o be c(-6). Determine g so that -95*g**2 + 1092*g + 84*g**3 - 564 + 57 - 571*g**o - 3*g**4 = 0.
1, 13
Let f be (-12)/(-10) - (-2112)/2640. Let 8/3*o - 8/3 - 2/3*o**f = 0. What is o?
2
Suppose -319*j = -333*j + 112. Let r(y) be the second derivative of 5/4*y**4 - 2*y**3 - 3/20*y**5 + j*y + 0 + 0*y**2. Factor r(g).
-3*g*(g - 4)*(g - 1)
Let r(x) = -x**3 - x**2 - 6*x - 1. Let m(i) = 10*i**3 + 2720*i**2 + 1225872*i + 184690824. Let v(u) = -m(u) - 8*r(u). Let v(w) = 0. Calculate w.
-452
Let d be 11 + -10 - (-2 - 4 - -2). Suppose -d*l + k + 5 = -2, 2*k - 2 = 2*l. Suppose 7*a**2 - 5*a + a**4 + 0 + a - 4*a**l + 4*a**3 - 4 = 0. What is a?
-2, -1, 1
Factor 16777216/3 + 4/3*k**2 + 16384/3*k.
4*(k + 2048)**2/3
Let c(g) be 