 be the second derivative of -m**4/4 - 420*m**3 - 264600*m**2 - 577*m. Determine v so that h(v) = 0.
-420
Let b = 288 - 155. Solve -4061*d + b*d + 1808*d - 2444*d**2 - 3208*d + 144*d**3 - 2*d**4 - 2738 = 0.
-1, 37
Let c(m) be the third derivative of 5*m**7/126 - 403*m**6/72 - 9*m**5/2 - 2274*m**2. Find q such that c(q) = 0.
-2/5, 0, 81
Let p(y) be the first derivative of -y**9/756 + y**8/420 + 2*y**3/3 + 6*y - 50. Let q(b) be the third derivative of p(b). Let q(o) = 0. What is o?
0, 1
Suppose -6*q - 5*j = -90, -778*j + 774*j = q - 34. Let k(c) be the first derivative of q - 1/7*c**3 + 39/7*c**2 - 507/7*c. Determine p so that k(p) = 0.
13
Suppose 31 = b - 3*d - d, 3*d = b - 26. Let -207*s**2 + 10*s**4 - 480*s - 27*s**3 - 11*s**2 - 288 - b*s**4 = 0. Calculate s.
-12, -2, -1
Let w(z) = -3*z + 4. Let u be w(-14). Let q = 48 - u. Factor -19*o - 6084*o**2 + 6087*o**q + 7*o.
3*o*(o - 4)
Factor 36193*j + 55296 - 5124*j**2 + 3*j**4 + 3645*j**2 - 567*j**3 - 13885*j + 27405*j**2 + 59484*j.
3*(j - 96)**2*(j + 1)*(j + 2)
Let d(s) be the first derivative of -68/69*s**3 - 28/23*s**2 + 16/23*s - 35 - 9/46*s**4. Factor d(v).
-2*(v + 2)**2*(9*v - 2)/23
Let a(q) be the third derivative of -37/210*q**7 - 29/60*q**5 + q**3 - 19/40*q**6 + 0*q - 55 + 5/24*q**4 + 2*q**2 - 1/42*q**8. Factor a(y).
-(y + 1)**3*(y + 2)*(8*y - 3)
Factor -9108082176/7 + 18870336/7*d + 3/7*d**3 - 13032/7*d**2.
3*(d - 1448)**3/7
Suppose -2*g + 11 = -o, 0*g - 4*o = 2*g + 14. Solve -4*n**4 + 24*n**2 - 75*n - 28*n**g - 17 - 21*n**2 - 63*n**2 + 23*n + 1 = 0.
-4, -1
Let x(q) = -2*q**2 - 3*q + 8. Let c(g) = -15*g**2 - 704*g + 740. Let o(z) = -5*c(z) + 35*x(z). Let o(p) = 0. What is p?
-684, 1
Let l(y) = -2*y**3 - 332*y**2 - 15130*y - 28897. Let p(k) = 4*k**2 + 1. Let t(s) = -l(s) + 3*p(s). Factor t(q).
2*(q + 2)*(q + 85)**2
Let q = 7131 - 7129. Let i(r) be the first derivative of 0*r + 4/21*r**3 - 1/14*r**4 + 0*r**q - 2/35*r**5 + 36. Determine b, given that i(b) = 0.
-2, 0, 1
Let y be (-32)/(-272)*(-2652)/(-104). What is p in -4*p**y + 28*p + 22/3*p**2 + 49/3 + 1/3*p**4 = 0?
-1, 7
Let z(d) be the first derivative of -64 + 28/3*d + 13/3*d**2 - 2/9*d**3. Factor z(b).
-2*(b - 14)*(b + 1)/3
Let q(h) be the third derivative of -1/27*h**4 + 0*h**3 + 0*h + 121/540*h**6 - 58*h**2 - 1/135*h**5 + 121/1890*h**7 + 0. Determine s so that q(s) = 0.
-2, -2/11, 0, 2/11
Let x(w) = -17*w**2 + w - 11 - 13*w**2 + 29*w**2 + 10. Let i(p) = -2*p**2 + 382*p - 9214. Let d(y) = i(y) + 2*x(y). What is z in d(z) = 0?
48
Suppose 2 = 2*c - 5*h + 6*h, -5*h = 3*c - 10. Let z(j) be the third derivative of -1/72*j**4 + 0 + c*j + 14*j**2 + 2/27*j**3 - 1/540*j**5. Factor z(n).
-(n - 1)*(n + 4)/9
Suppose 0 = y + 4*f + f - 17, -2*y = f - 16. Factor 2*v + 9*v**3 + v - y*v**2 + v**2 - 6*v**3.
3*v*(v - 1)**2
Suppose 0 = 8*c - 4*t + 24, 3*c + 513*t = 517*t - 34. Factor -13/2*j - 1/2*j**c + 7.
-(j - 1)*(j + 14)/2
What is t in 8/3*t**3 - 446/3*t + 100/3 + 182/3*t**2 = 0?
-25, 1/4, 2
Let p(i) = -21*i + 136. Let h be p(6). Suppose -h*m - 7*m + 34 = 0. Factor 0 + m*b**2 - 5/4*b**3 + 1/4*b**4 - b.
b*(b - 2)**2*(b - 1)/4
Let t(d) = -3*d**2 - d - 2. Let n(v) = 8*v**2 - 76*v + 4. Let k(x) = -n(x) - 2*t(x). Find r such that k(r) = 0.
0, 39
Let p(w) be the third derivative of w**5/300 + 11*w**4/24 + 25*w**3/3 - w**2 + 77*w. Find j such that p(j) = 0.
-50, -5
Suppose 0 = -4*k + 2*b + 18, -k - 40 = -6*k - b. Find g, given that -269*g**3 + g + 270*g**3 - k*g + 5*g**2 = 0.
-6, 0, 1
Factor 0 - 3/4*j**4 - 1/2*j**2 - 9/8*j**3 + 0*j - 1/8*j**5.
-j**2*(j + 1)**2*(j + 4)/8
Solve -76*i + 230 - 5*i**4 + 115*i**3 + 6318*i**2 - 279*i - 6303*i**2 = 0 for i.
-2, 1, 23
Let b(s) = -3*s**2 - 1476*s + 272327. Let a(v) = 2*v**2 + 1476*v - 272326. Let r(g) = 5*a(g) + 4*b(g). Solve r(d) = 0.
369
What is j in -1068 - 3/2*j**2 + 537*j = 0?
2, 356
Suppose -v = 3 - 1, -4*v = 2*t + 2. Find h, given that -6 + 22 + 13*h**4 + 33*h**t - 77*h**4 - 128*h + 252*h**2 - h**3 = 0.
-2, 1/4, 2
Suppose -303*z + 904 + 134 - 129 = 0. Factor 2/13*m**2 + 0 + 4/13*m - 2/13*m**z.
-2*m*(m - 2)*(m + 1)/13
Let w(d) be the first derivative of d**3/3 + 219*d**2/4 + 109*d/2 - 1072. Find n such that w(n) = 0.
-109, -1/2
What is y in -4*y**5 + 10*y**4 - 2*y**5 + 2*y**4 - 22*y**3 + 12*y**2 + 4*y**5 = 0?
0, 1, 2, 3
Suppose -56 = -10*a + 8*a. Let f be ((-1146)/(-4))/(-4 + 119/a). Factor -1142*h**5 + 21*h**3 + 16*h**4 + 16*h**2 + 4*h + f*h**5 + 3*h**3.
4*h*(h + 1)**4
Suppose -12*f + 8*f = 232. Let i = -36 - f. Factor 2*s**2 + 27*s**3 + 8*s**2 - i*s**3 + 5*s.
5*s*(s + 1)**2
Determine l so that -674*l + 154436*l**2 - 154439*l**2 + 810 - 133*l = 0.
-270, 1
Suppose 113739*c - 1375*c**2 + 331*c**2 - 773*c**2 - 373*c**2 + 3*c**3 + 285936*c = 0. Calculate c.
0, 365
Let a(o) = o + 7*o - 1 - 4*o + 2*o. Let u be a(1). Determine q, given that -11*q**5 + 7*q**u + 6*q**5 - 2*q**4 = 0.
0, 1
Let j(f) = -f**2 - 2*f - 26. Let q be j(7). Let u = q - -92. What is w in 0 - 2/3*w - 1/3*w**2 + 1/3*w**u = 0?
-1, 0, 2
Let p(o) be the first derivative of 5*o + 21/4*o**3 + 1/20*o**5 - 35 + 23/16*o**4 + 61/8*o**2. Factor p(i).
(i + 1)**3*(i + 20)/4
Let x(c) = 2*c + 35*c**3 - 16*c**3 - 11*c**3 + 12*c**2 - 7*c**3 + 28. Let y be x(-12). Determine h, given that -7*h**2 + 48*h + 31 + 113 + 7*h**2 + y*h**2 = 0.
-6
Let z(r) be the first derivative of -r**4/10 + 216*r**3/5 - 27189*r**2/5 + 303372*r/5 - 8761. Factor z(y).
-2*(y - 159)**2*(y - 6)/5
Let b(f) be the third derivative of 0 + 56*f**2 - 1/2*f**4 + 0*f - 4/3*f**3 - 1/15*f**5. Solve b(l) = 0 for l.
-2, -1
Let b(f) be the first derivative of -74 - 11*f - 69 - 12*f - 12*f**2 - f**3 - 22*f. Suppose b(i) = 0. What is i?
-5, -3
Let q = -835 - -810. Let g be (-134)/30 + 4 - 15/q. Factor -2/15*z**2 - g*z**3 + 0 + 2/15*z + 2/15*z**4.
2*z*(z - 1)**2*(z + 1)/15
Let q = 35/114 + 25547/57. Let p = -444 + q. Let -p*r**3 - 9*r - 39/4*r**2 - 3 - 3/4*r**4 = 0. Calculate r.
-2, -1
Let v(j) be the third derivative of -1/1512*j**8 + 2*j + 1/270*j**6 + 0 - 1/108*j**4 + 7*j**2 + 1/945*j**7 + 1/27*j**3 - 1/135*j**5. What is f in v(f) = 0?
-1, 1
Suppose -5*s + s = -3*z + 22, 5*s + 28 = 4*z. Suppose 5*l - z*b = 26, -2*b = l + 1 - 11. Factor 3*i**2 + l*i - 2*i**2 - 5*i**2 - 14*i.
-4*i*(i + 2)
Let i(y) be the third derivative of y**7/1470 + 59*y**6/840 + 2*y**5/5 + 9*y**2 + 17. Factor i(k).
k**2*(k + 3)*(k + 56)/7
Let j(h) = -16*h**4 + 20*h**3 + 6*h**2 + 6*h. Let f(l) = -30*l**4 + 40*l**3 + 11*l**2 + 11*l. Let r = -398 - -392. Let n(d) = r*f(d) + 11*j(d). Factor n(s).
4*s**3*(s - 5)
Let a(v) be the first derivative of 2*v**3/15 + 57*v**2/5 + 112*v/5 - 2053. Let a(g) = 0. Calculate g.
-56, -1
Let j(n) be the third derivative of -n**8/112 + 12*n**6/5 - 128*n**5/5 + 96*n**4 - 53*n**2 + 3. Factor j(g).
-3*g*(g - 4)**3*(g + 12)
Let -616/9*c + 2/9*c**2 + 47432/9 = 0. Calculate c.
154
Let n be 23 - 16 - 14 - 390/4. Let b = n - -106. Factor 1/2*a**5 + 2*a**4 - 2*a**2 + a**3 + 0 - b*a.
a*(a - 1)*(a + 1)**2*(a + 3)/2
Suppose 0 = 23*t - 4 - 65. Solve -13*q**t - 15*q**2 - 13*q**3 + 53*q**3 - 5*q + 15 - 22*q**3 = 0.
-1, 1, 3
Let j = 79669/139335 + -7/19905. Determine l, given that -2/7*l**4 + 2*l - j - 18/7*l**2 + 10/7*l**3 = 0.
1, 2
Let m(l) be the second derivative of -l**6/120 - 33*l**5/80 - 361*l**4/48 - 481*l**3/8 - 845*l**2/4 - 1217*l. Factor m(u).
-(u + 2)*(u + 5)*(u + 13)**2/4
Let r be (-4)/52 - (-3 + (-8640)/(-3276)). Let -38/7*j - 68/7 - r*j**2 = 0. What is j?
-17, -2
Let m(z) be the second derivative of z**6/40 + 7*z**5/80 - 17*z**4/16 - 7*z**3/24 + 6*z**2 + 631*z - 1. Suppose m(y) = 0. What is y?
-16/3, -1, 1, 3
Let j be 72/(0 - -1) - 4. Suppose -2*u + 5 = -m, -4*m + 3*m = u - 1. Factor -141*h**2 + j*h**u + 72*h**2 - 4*h - 3.
-(h + 1)*(h + 3)
Suppose u - 2 = -1. Let v be 14 + -2 + 16/(-4) + u. Factor 20*j + 0 - 16 + 5*j**2 - v.
5*(j - 1)*(j + 5)
Let a = 55/201 - -4/67. Suppose 4*i = u + 8, 4*i + 0*i - 3*u = 0. Let -5/6*t - 1/6*t**i - a - 2/3*t**2 = 0. What is t?
-2, -1
Let a = 307 + -303. Find z, given that -26*z**5 - 5*z**a + 3*z**3 + 23*z**5 + 5*z**4 = 0.
-1, 0, 1
Suppose -18/5*m**4 + 234/5*m**2 + 0*m - 2/5*m**5 - 216/5 + 2/5*m**3 = 0. Calculate m.
-6, -1, 1, 3
Let d be -1 - (4 + -4 + -1). Suppose l - 3*l + 4 = d. Determine o, given that 541*o**4 - 526*o**4 - l*o**2 - 6*o**3 + 21*o**5 + 2*o**2 = 0.
-1, 0