
Let l(z) be the first derivative of 2/45*z**5 - 2*z + 158 - 1/3*z**4 - 16/9*z**3 - 26/9*z**2. Factor l(o).
2*(o - 9)*(o + 1)**3/9
Suppose -j + 3*c = j - 2, j + 4 = 4*c. Let x = -385961/3 - -128654. Factor 0*h**2 + 0 + 2/3*h**3 + x*h**5 + 0*h + h**j.
h**3*(h + 1)*(h + 2)/3
Let o(v) = 16*v**2 + 2896*v + 2125784. Let h(z) = -3*z**2 + 4*z - 4. Let y(n) = -5*h(n) - o(n). Determine p, given that y(p) = 0.
-1458
Let z = -436 + 449. What is v in 22*v + 1 + z*v + 26 - 53*v + 3*v**2 = 0?
3
Let l(z) be the second derivative of 31*z**4/18 - 190*z**3/27 + 8*z**2/9 + 2852*z + 1. Factor l(w).
2*(w - 2)*(93*w - 4)/9
Let -216225/4 - 465/2*d - 1/4*d**2 = 0. Calculate d.
-465
Suppose 3286*m = 3217*m + 69. Let h(g) be the second derivative of 10*g - 1/18*g**4 - g**2 + 4/9*g**3 - m. Factor h(x).
-2*(x - 3)*(x - 1)/3
Let q(i) = -20*i**4 + 137*i**3 - 416*i**2 - 22*i - 11. Let m(r) = -7*r**4 + 46*r**3 - 139*r**2 - 8*r - 4. Let n(o) = 11*m(o) - 4*q(o). Factor n(h).
3*h**2*(h - 9)*(h - 5)
Let y(k) be the first derivative of 2*k**3/3 - 19*k**2 - 580*k + 4518. Solve y(g) = 0.
-10, 29
Let g(a) = -8*a**2 + 236*a + 2520. Let r(u) = -u**2 + 28*u. Let p(z) = g(z) - 4*r(z). Factor p(d).
-4*(d - 45)*(d + 14)
Let b(g) be the first derivative of 15/4*g**4 + 54 + 5/2*g**2 + g**5 + 0*g + 5*g**3. Solve b(r) = 0.
-1, 0
Let k(g) be the third derivative of -g**6/30 - 10*g**5 + 307*g**4/6 + 304*g**3 - 2*g**2 + 572. Find c, given that k(c) = 0.
-152, -1, 3
Let d(g) = 10*g - 12*g + 2*g + 5*g**2. Let w be d(1). Factor w + 6*p**2 - 6*p**3 - 6*p - 5*p**3 + 9*p**3 - 3.
-2*(p - 1)**3
Let c(i) be the second derivative of 1 - 1/12*i**4 - 94*i + 1/2*i**3 + 0*i**2. Factor c(z).
-z*(z - 3)
Let l = -1209 + 1222. Suppose 36*k - l = 95. Suppose 2/9*n**k + 0 + 10/9*n**2 + 8/9*n = 0. What is n?
-4, -1, 0
Let d(x) = x**2 - 3*x + 2. Let b(w) = -w**2 + 5*w - 5. Let u(t) = -3*b(t) - 7*d(t). Let f be u(1). Factor -27/5*r**2 - 6*r - r**f - 8/5.
-(r + 1)*(r + 4)*(5*r + 2)/5
Let k be 36/((-2530)/(-495) + 30/(-27)). Factor 3/4*q**2 + 6*q + k.
3*(q + 2)*(q + 6)/4
Let m(l) be the third derivative of -l**5/480 + 103*l**4/16 - 31827*l**3/4 - 97*l**2 + 12*l. Let m(f) = 0. What is f?
618
Find j such that -69*j**3 - 747/2*j**2 - 240 - 546*j - 3/2*j**4 = 0.
-40, -4, -1
Let l = 167627/20 - 33511/4. Find v, given that 73/5*v**2 + 52/5 - 108/5*v - l*v**3 + 1/5*v**4 = 0.
1, 2, 13
Factor 0 + 4*c**2 + 2/7*c**3 + 66/7*c.
2*c*(c + 3)*(c + 11)/7
Suppose 5*b - 21 = -3*s + 48, -4*b - 4*s + 52 = 0. Solve -22*t**3 + b*t**5 + 20*t - 3*t**3 - 10*t**5 = 0 for t.
-2, -1, 0, 1, 2
Suppose -11*f + 82 = 27. Let w be f + 9 + -5 + -2. Factor -16*i**2 + 64*i + w*i**2 - 256 + 5*i**2.
-4*(i - 8)**2
Let j(a) be the second derivative of -a**8/2520 - a**7/210 - a**6/45 - a**5/18 - a**4/12 - 9*a**3 - 8*a. Let n(s) be the second derivative of j(s). Factor n(u).
-2*(u + 1)**3*(u + 3)/3
Let m be ((-5160)/(-30))/43 + -5 + 1. Let b(h) be the first derivative of 5/4*h**4 + m*h - 10/3*h**3 + 5/2*h**2 - 3. Factor b(p).
5*p*(p - 1)**2
Let f be (2 + 144/(-70))*(-31 - 3042/(-104)). Factor -1/5 + f*k + 1/10*k**2.
(k - 1)*(k + 2)/10
Factor -3696/5*b - 853776/5 - 4/5*b**2.
-4*(b + 462)**2/5
Determine a so that -18 - 7/3*a**4 + 81*a - 69*a**2 + 65/3*a**3 = 0.
2/7, 3
Let k be 0 - 11 - (-10878)/888. Factor -23/2*m**3 - 81/2*m - 36*m**2 - 27/4 - k*m**4.
-(m + 3)**3*(5*m + 1)/4
Let s(t) be the second derivative of t**5/40 - 21*t**4/2 - t**3/12 + 63*t**2 + 2277*t. Suppose s(g) = 0. What is g?
-1, 1, 252
Let m(u) = u + 16. Let j be m(-13). Suppose 4*o + 3*t - 2 = 1, 2*t + 15 = j*o. Determine i so that -3*i**3 - 13*i**2 + i**2 - 3*i**3 - 16*i + 10*i**o = 0.
-1, 0, 4
Let y(z) be the first derivative of z**6/60 + z**5/30 - z**2 + 158*z - 171. Let c(x) be the second derivative of y(x). Factor c(g).
2*g**2*(g + 1)
Determine j so that 5067*j**2 + 11*j**3 - 36*j**3 + 2325*j + 20*j**3 + 6125 - 4872*j**2 = 0.
-5, 49
Let q(d) be the first derivative of -8*d**3 + 15/4*d**4 - 3/5*d**5 + 0*d + 6*d**2 + 14. Factor q(i).
-3*i*(i - 2)**2*(i - 1)
Let x(f) be the second derivative of f**6/6 - 21*f**5/2 + 195*f**4 - 3500*f**3/3 + 3120*f**2 + 5587*f. Find m, given that x(m) = 0.
2, 12, 26
Suppose 9*t - 37*t + 68 = 6*t. Let d(f) be the third derivative of 0*f + 0*f**3 + 0 + 1/12*f**4 + 1/120*f**6 - 23*f**t + 1/20*f**5. Find q such that d(q) = 0.
-2, -1, 0
Let g be (-27)/(-6)*((-2388)/(-1620) + 63/(-45)). Determine q, given that -35/3*q**2 - g*q**4 + 12 - 4*q + 4*q**3 = 0.
-1, 1, 6
Suppose 378*q - 382*q + 22 = 2*z, 0 = 27*q - 2*z - 40. Determine f so that 8 + 0*f**q + 1/2*f**3 - 6*f = 0.
-4, 2
Let x(s) be the first derivative of -s**4/14 - 32*s**3/21 - 55*s**2/7 + 144*s/7 + 878. Find a, given that x(a) = 0.
-9, -8, 1
Let c be 135/(-18)*(-6)/5. Factor -c*z**3 - 33*z + 0 + 5*z**3 + 3*z**3 - 36 - 10*z**2.
-(z + 3)**2*(z + 4)
Let k(s) be the first derivative of 4*s**3/3 + 72*s**2 + 140*s - 2264. Let k(q) = 0. What is q?
-35, -1
Let p(i) be the second derivative of 49*i**6/150 + 21*i**5/2 + 139*i**4/20 - 50*i**3/3 + 42*i**2/5 - 305*i. Let p(b) = 0. Calculate b.
-21, -1, 2/7
Let v(c) be the third derivative of c**6/480 + 7*c**5/60 + 191*c**4/96 + 95*c**3/6 + 32*c**2 - c - 12. What is d in v(d) = 0?
-19, -5, -4
Let d(s) be the second derivative of -s**5/70 + 19*s**4/21 + 121*s**3/21 + 82*s**2/7 - 5368*s. Factor d(a).
-2*(a - 41)*(a + 1)*(a + 2)/7
Suppose 0 = -370*b + 397*b + 7425. Let g be 150/b*55/(-20). Solve -3*t - 3/2 + 0*t**2 + g*t**4 + 3*t**3 = 0.
-1, 1
Let t be (23/1242*-9)/((-9)/2). Let x(w) be the first derivative of -1/9*w**2 - 1/9*w + 3 - t*w**3. Factor x(j).
-(j + 1)**2/9
Suppose 5*b - 42 = 9*t, 3*t - 66*b + 18 = -64*b. Factor 8/3*a**3 + 32/3*a**t + 10/3 - 38/3*a.
2*(a + 5)*(2*a - 1)**2/3
Suppose -43*v = -44*v + 75. Solve -v*h**2 - 15*h**4 + 6 + 21*h**3 - 21*h + 84*h**2 + 0*h**3 = 0.
-1, 2/5, 1
Let q(g) be the first derivative of g**6/27 - 796*g**5/45 + 11102. Suppose q(d) = 0. What is d?
0, 398
Let s = 8767 + -8743. Suppose -5*n + n + 2*m + 118 = 0, m = -n + 37. Factor 4*r**5 - s*r**3 + n*r - 173*r**2 - 5*r**4 + 189*r**2 + r**4.
4*r*(r - 2)**2*(r + 1)*(r + 2)
Determine b, given that -960*b**2 - 5*b**4 - 102772 - 21228 - 115*b**3 - 113600*b + 11250*b**2 = 0.
-62, -1, 20
Let q(f) be the second derivative of -1 + 0*f**2 + 4/15*f**4 - 4/75*f**6 + 2/105*f**7 - 3/25*f**5 + 8/15*f**3 - 22*f. Factor q(t).
4*t*(t - 2)**2*(t + 1)**2/5
Let k(a) = -4*a**3 + 9*a**2 - 951*a + 1898. Let f be k(2). Determine q, given that 0*q - 9/4*q**3 + 3/4*q**5 + 0 - 3/2*q**2 + f*q**4 = 0.
-1, 0, 2
Solve -44/17*c - 10/17*c**2 + 2/17*c**3 - 32/17 = 0.
-2, -1, 8
Let a be (-1)/(-8)*(1608 - 1592). Factor 4/7*t**a + 0 + 12/7*t.
4*t*(t + 3)/7
Let f(w) be the second derivative of -w**5/4 + 1015*w**4/2 + 5*w**3/6 - 3045*w**2 + 4521*w. Suppose f(v) = 0. Calculate v.
-1, 1, 1218
Let h(f) be the first derivative of 138 - 33*f**4 - 24*f**2 - 28/5*f**5 + 32*f - 184/3*f**3. Determine g so that h(g) = 0.
-2, -1, 2/7
Let n be 84/33 - (-174)/(-319). Let f(s) be the first derivative of 6/7*s - 3/14*s**n - 6 - 1/7*s**3. Solve f(m) = 0.
-2, 1
Factor 2/3*d**3 + 8450 + 266/3*d**2 + 9230/3*d.
2*(d + 3)*(d + 65)**2/3
Factor -747/4*j + 147 + 81/2*j**2 - 3/4*j**3.
-3*(j - 49)*(j - 4)*(j - 1)/4
Let x = 599002/7 + -84765. Let q = 808 - x. Let -3/7*y**2 - 3/7*y**5 + 3/7*y**4 + q*y**3 + 0 - 6/7*y = 0. What is y?
-1, 0, 1, 2
Let c(w) be the first derivative of -80/27*w**3 + 2/15*w**5 + 0*w**2 + 29/9*w**4 + 299 + 0*w. Factor c(y).
2*y**2*(y + 20)*(3*y - 2)/9
Let b(d) be the second derivative of 0*d**2 - 1/40*d**5 - 31*d + 1/10*d**4 + 5*d**3 + 1/600*d**6 + 0. Let w(i) be the second derivative of b(i). Factor w(v).
3*(v - 4)*(v - 1)/5
Let x(h) be the second derivative of 2 - 17/2*h**3 - 162*h - 24*h**2 + 1/10*h**6 + 51/20*h**5 + 15/4*h**4. Factor x(k).
3*(k - 1)*(k + 1)**2*(k + 16)
Let y(g) be the third derivative of -g**8/4200 - g**7/350 + g**6/900 + g**5/50 + 8*g**3 - 56*g**2. Let a(t) be the first derivative of y(t). Factor a(u).
-2*u*(u - 1)*(u + 1)*(u + 6)/5
Let b(f) be the first derivative of -f**5/20 - 15*f**4/8 + 8*f**3 + 61*f**2/2 + 94. Let n(u) be the second derivative of b(u). Factor n(t).
-3*(t - 1)*(t + 16)
Determine l so that 16 - 13*l**2 - 16*l + l**3 + 11*l - 8 + l**5 + 3*l + 5*l**4 = 0.
-4, -2, -1, 1
Suppose -9*d + 24*d - 30 