4.
(p - 1)**2*(p + 1)*(6*p - 7)
Suppose 105699*r**2 - 5*r**5 + 140*r**4 + 1025*r**3 - 765*r - 105839*r**2 - 255*r = 0. What is r?
-6, -1, 0, 1, 34
Suppose 4*h + 14 = 34. Let m(k) = 2*k**3 - 3*k**2 + 3*k + 3. Let b be m(1). Let 2*w**4 - h*w**3 + b*w**5 - 11*w**4 + 9*w**4 = 0. Calculate w.
-1, 0, 1
Let s be 455/(-1200) - (28/(-70) + 0/2). Let r(f) be the second derivative of -1/2*f**2 + 1/6*f**3 - s*f**4 + 0 + 15*f. Factor r(n).
-(n - 2)**2/4
Let g be (4/33)/((-92)/(-506)). Let t(n) = -2*n**2 - 37*n + 24. Let v be t(-19). Find k such that k + 0*k**4 - 4/3*k**3 + 1/3*k**v - g*k**2 + 2/3 = 0.
-1, 1, 2
Solve 24769*g**3 - 429*g**2 - 24084*g**3 + 25*g**4 - 281*g**2 = 0 for g.
-142/5, 0, 1
Suppose 4801 - 1897 = 1452*f. Let s be ((-4)/(-6) - 2) + 2. Factor -s*h - 4/3 + 2/3*h**f.
2*(h - 2)*(h + 1)/3
Let d(u) be the first derivative of 2*u**3/15 - 86*u**2/5 - 2439. Factor d(o).
2*o*(o - 86)/5
Let i(c) = -9*c**3 + 475*c**2 + 730*c - 293. Let b(m) = 29*m**3 - 1440*m**2 - 2191*m + 880. Let o(z) = -3*b(z) - 10*i(z). Factor o(p).
(p - 145)*(p + 2)*(3*p - 1)
Let n(o) be the first derivative of -o**4/24 + 2*o**3/3 - 7*o**2/4 - 136*o + 130. Let x(c) be the first derivative of n(c). Determine q so that x(q) = 0.
1, 7
Let k = -3180 - -3183. Let m(p) be the second derivative of -1/27*p**k + 0 + 2/9*p**2 - 1/54*p**4 + 23*p. Factor m(b).
-2*(b - 1)*(b + 2)/9
Let r(v) = 407*v**2 - 76*v + 75. Let p be r(1). Suppose -400*q = -p*q. Factor -4/7*w**3 + 0*w - 4/7*w**2 + q.
-4*w**2*(w + 1)/7
Suppose -629/4*z**2 + 2*z**5 - 105/4*z - 207*z**4 + 0 - 627/2*z**3 = 0. What is z?
-1/2, 0, 105
Let a = -271 + 276. Factor 48*f**4 - 6*f**3 - 13*f**3 + 3*f**5 - 3*f**2 + 77*f**a + 7*f**3 + 112*f**5.
3*f**2*(4*f - 1)*(4*f + 1)**2
Let a(q) be the third derivative of -1/210*q**5 - 4/21*q**3 + 5*q + 0 + 1/21*q**4 - 10*q**2. Determine w so that a(w) = 0.
2
Determine f, given that 11/2*f**2 - 1/4*f**3 + 6 + 47/4*f = 0.
-1, 24
Let r(n) be the first derivative of 8*n**5/5 + 33*n**4 + 220*n**3 + 406*n**2 - 588*n - 1213. Suppose r(w) = 0. What is w?
-7, -3, 1/2
Let v(s) be the second derivative of s**5/10 - 7*s**4 + 113*s**3/3 + 156*s**2 - 306*s. Let v(h) = 0. What is h?
-1, 4, 39
Let p(k) = k**2 - k + 1. Suppose -6*x - 120 = -11*x. Let t(f) = -x*f**2 + f + 0*f + 25*f**2. Let h(c) = 2*p(c) - t(c). Factor h(l).
(l - 2)*(l - 1)
Let d(n) be the first derivative of -n**4/40 + 3*n**3/5 - 69*n**2/20 + 26*n/5 - 1277. Find u such that d(u) = 0.
1, 4, 13
Let m(f) be the second derivative of f**4/6 + 70*f**3 + 621*f**2 - 3202*f. Factor m(p).
2*(p + 3)*(p + 207)
Let p = 25571/4 + -434699/68. Suppose 4/17*i + 6/17 - p*i**2 = 0. Calculate i.
-1, 3
Let a(c) be the first derivative of -1/7*c**2 - 4/21*c**3 + 0*c - 1/14*c**4 - 61. Factor a(n).
-2*n*(n + 1)**2/7
Factor 703*k**2 + 102663*k + 3*k**3 + 14419 - 224233 + 413*k**2.
3*(k - 2)*(k + 187)**2
Let x = 86 + -86. Find c, given that 552*c**2 - 4*c**3 + x*c**3 + 36*c - 520*c**2 = 0.
-1, 0, 9
Let n = 11236 - 11233. Let q(b) be the second derivative of 0*b**n - b**4 + 3/5*b**5 - 18*b + 0*b**2 - 1/10*b**6 + 0. Factor q(f).
-3*f**2*(f - 2)**2
Suppose -4*j = 3*a - 74 + 12, -j + 4*a - 70 = 0. Suppose -2/3*i**j + 50/3 + 0*i = 0. Calculate i.
-5, 5
Factor 0 - 615/4*i - 2457/4*i**2 + 3*i**3.
3*i*(i - 205)*(4*i + 1)/4
Determine y, given that 18050/11 + 98/11*y**4 + 40748/11*y**2 + 52440/11*y + 3864/11*y**3 = 0.
-19, -5/7
Let x(v) be the third derivative of -2*v**7/35 + 7*v**6/60 + 9*v**5/5 - 73*v**4/12 - 10*v**3 - 2*v**2 + 407*v + 3. Determine i, given that x(i) = 0.
-3, -1/3, 2, 5/2
Let c(y) = 4*y - 2. Let h be c(1). Factor 0*b**2 + 201 - 221 - 2*b**h - 3*b**2 + 20*b.
-5*(b - 2)**2
Let o(n) = -3*n**5 - n**4 + n**3 - n**2 + 2. Let a(y) = 22*y**5 + 5*y**4 - 13*y**3 + 27*y**2 - 19*y - 8. Let q(d) = a(d) + 7*o(d). What is j in q(j) = 0?
-3, 1, 2
Let m(b) be the third derivative of b**6/480 + 77*b**5/30 + 1229*b**4/96 + 307*b**3/12 - 159*b**2 - b. Suppose m(q) = 0. Calculate q.
-614, -1
Let a(y) be the third derivative of -245/12*y**3 + 0*y - 1/24*y**5 + 35/24*y**4 - 5 + 4*y**2. Factor a(f).
-5*(f - 7)**2/2
Let c(s) be the first derivative of -s**6/720 - s**5/120 + s**4/144 + s**3/12 + s**2 + 29*s + 2. Let h(m) be the second derivative of c(m). Factor h(b).
-(b - 1)*(b + 1)*(b + 3)/6
Let x(g) be the third derivative of -g**8/3360 - g**7/1680 + g**6/720 + g**5/240 - 7*g**3/2 - g**2 + 80. Let p(n) be the first derivative of x(n). Factor p(v).
-v*(v - 1)*(v + 1)**2/2
Factor 13/6*x - 1/6*x**2 + 34/3.
-(x - 17)*(x + 4)/6
Factor -4793*a - 3385812 + 2668522 - 1287*a - 2*a**2 - 3903510.
-2*(a + 1520)**2
Let w(x) be the first derivative of 5*x**3/3 - 325*x**2/2 + 64. Factor w(c).
5*c*(c - 65)
Let c = -85407/8 - -10676. Let p(l) be the third derivative of -5/8*l**4 + 0*l + 24*l**2 - 1/12*l**5 + c*l**6 + 1/42*l**7 + 0*l**3 + 0. What is v in p(v) = 0?
-3, -1, 0, 1
Let n = -24424 - -366361/15. Let j(t) be the first derivative of t**2 + 0*t**4 - 37 - 7/9*t**3 + 0*t + n*t**5. What is z in j(z) = 0?
-3, 0, 1, 2
Let i = -3878 - -3881. Let b(j) be the first derivative of -1 + 8/35*j**5 - 1/7*j**2 - 4/21*j**i + 3/14*j**4 - 4/21*j**6 + 0*j. Find p such that b(p) = 0.
-1/2, 0, 1
Suppose 9 + 1 = 10*q. Let l be q - (112/(-22) - -5). Find o such that l - 6/11*o**2 - 14/11*o = 0.
-3, 2/3
Let w be (2/(-4))/(2/(-40)). Let l = 3426 - 3411. Factor 9*b**2 - 3 - l - 12*b + 6 + 22*b**3 - w*b**3 + 3*b**4.
3*(b - 1)*(b + 1)*(b + 2)**2
Let p(a) be the second derivative of a**4/72 - a**3/3 - 16*a**2/3 - 440*a. Find f, given that p(f) = 0.
-4, 16
Let j(r) be the first derivative of 8*r**5 + 25*r**4 - 199 + 0*r**2 + 5/6*r**6 + 0*r + 80/3*r**3. Factor j(m).
5*m**2*(m + 2)**2*(m + 4)
Suppose -15/2*q**2 - 27/2*q**3 + 0 + 69*q = 0. What is q?
-23/9, 0, 2
Let s(o) = -3*o**2 - 70*o + 309. Let x be s(-27). Let j(p) be the second derivative of -1/2*p**4 - 8/3*p**3 + 0 + 1/5*p**5 + x*p - 3*p**2. Solve j(l) = 0.
-1, -1/2, 3
Let -98*w**5 - 1457*w**3 - 613*w**4 + 425*w**3 - 222*w**3 - 353*w**4 - 3080*w**2 - 1494*w**3 - 1200*w = 0. What is w?
-6, -10/7, -1, 0
Suppose 0 = -9*m - 69 + 114. Suppose -1345 + 1345 = m*u. What is r in -12/5*r**2 + 12/5*r + 3/5*r**3 + u = 0?
0, 2
Let a(l) be the first derivative of -5*l**4/32 + 1129*l**3/12 - 1351*l**2/16 - 451*l/4 + 1012. Factor a(o).
-(o - 451)*(o - 1)*(5*o + 2)/8
Let c = 2549 + -4355. Let w = c - -9036/5. Factor -3/5*z**4 + 9/5*z**2 - w*z + 0*z**3 + 0.
-3*z*(z - 1)**2*(z + 2)/5
Let h(m) be the second derivative of m**6/60 + 4*m**5/15 + 11*m**4/12 - 20*m**3/3 - 24*m**2 + 42*m. Let c(b) be the first derivative of h(b). Factor c(w).
2*(w - 1)*(w + 4)*(w + 5)
Factor 520*w + w**5 + 51*w**2 - 45*w**3 + 1200 - 22*w**4 - 50*w**4 + 73*w**4 - 128*w**2.
(w - 5)**2*(w + 3)*(w + 4)**2
Let t be 5/(-70) - (-639)/126. Let q = -191 + 191. Factor 12*f**2 + 6*f**3 + q + 0*f - 3*f**4 - 3/2*f**t.
-3*f**2*(f - 2)*(f + 2)**2/2
Factor -98304/11 + 40960/11*k - 2/11*k**5 - 5120/11*k**2 + 0*k**3 + 40/11*k**4.
-2*(k - 8)**4*(k + 12)/11
Let v = 20 + -23. Let q be 4 - (2 + v + 3). Solve 207*h - 2*h**2 + q - 207*h = 0.
-1, 1
Let v = 320 + -320. Let p be (0 - -2) + v/(1 + 12). Factor -4/5 + 1/5*r**p - 3/5*r.
(r - 4)*(r + 1)/5
Let p(s) = 43*s + 20*s**2 - 376 - 56*s + 376 + 177*s**3. Let f = 34 + -23. Let c(u) = 886*u**3 + 100*u**2 - 65*u + 1. Let m(d) = f*p(d) - 2*c(d). Factor m(b).
(5*b + 1)**2*(7*b - 2)
Let d(c) = 17*c**2 + 183*c + 182. Let u(h) = -144*h**2 - 1463*h - 1455. Let n(a) = -17*d(a) - 2*u(a). Factor n(m).
-(m + 1)*(m + 184)
Let q(c) be the third derivative of 155*c**8/112 - 65*c**7/21 - 49*c**6/8 + 6*c**5 - 5*c**4/6 + 16*c**2 + 7. What is o in q(o) = 0?
-1, 0, 2/31, 1/3, 2
Suppose 408/11 + 24/11*o**2 - 1638/11*o = 0. Calculate o.
1/4, 68
Let o(f) be the second derivative of 9/35*f**5 + 82*f + 4/105*f**6 - 25/14*f**2 + 0 - 15/14*f**3 + 13/42*f**4. Let o(u) = 0. What is u?
-5/2, -1/2, 1
Let c(y) = -13622*y + 163488. Let o be c(12). Let o*n**2 + 4 - 70/3*n = 0. What is n?
2/9, 3/4
Let k = 4738/20349 + -24/2261. Determine y, given that 8/3*y**2 + 4/9*y**3 - 22/9*y**4 - k + 8/9*y - 4/3*y**5 = 0.
-1, 1/6, 1
Factor -1487/3*t - 33*t**2 - 10.
-(t + 15)*(99*t + 2)/3
Let d(t) be the second derivative of t**7/49 + 37*t**6/35 + 342*t**5/35 + 40*t**4 + 608*t**3/7 + 720*t**2/7 + 63*t + 39. Suppose d(p) = 0. Wha