12. Let d be s(-7). Suppose -d*o - 4*o + 12 = 0. Factor -6*g**2 - 4*g + 8*g**3 + 7*g**o - 4*g**5 - g**2.
-4*g*(g - 1)**2*(g + 1)**2
Let d be ((-36)/(-8))/(-37 - 4710/(-120)). Factor 3/2 + 1/2*a**d + 2*a.
(a + 1)*(a + 3)/2
Let c(m) be the second derivative of 1/8*m**3 - 9/2*m**2 + 0 - 6*m + 1/16*m**4. Find h such that c(h) = 0.
-4, 3
Let q(h) be the second derivative of -4/21*h**4 - 16/7*h**2 - 141*h + 0 + 1/35*h**6 + 32/21*h**3 - 4/35*h**5. Determine i, given that q(i) = 0.
-2, 2/3, 2
Suppose 14*n + 13*n - 38016 = 0. Let s = 1410 - n. Find h, given that s*h**3 + 2/3*h + 2*h**2 + 2/3*h**4 + 0 = 0.
-1, 0
Suppose 30*l = 32*l - 6. Suppose -5*r + 48 = 7*r. Factor -11*q**2 + l*q**4 - 139*q**3 - 4*q**r + 2*q**2 + 133*q**3.
-q**2*(q + 3)**2
Let p(r) be the first derivative of -2*r**6/15 - 8*r**5/5 - 8*r**4 - 64*r**3/3 - 32*r**2 + 135*r - 53. Let q(d) be the first derivative of p(d). Factor q(k).
-4*(k + 2)**4
Let o be (10/(-8) - 1)*(-8)/6. Factor 6*g + 6*g - 893 + 4*g**2 - 12*g**o + 885 + 4*g**4.
4*(g - 2)*(g - 1)**2*(g + 1)
Let w(l) be the third derivative of 0 - 145/48*l**4 + 25/6*l**3 + 81*l**2 + 13/30*l**5 - 1/48*l**6 + 0*l. What is c in w(c) = 0?
2/5, 5
Let m(i) be the first derivative of -i**4/72 - 5*i**3/3 - 75*i**2 - 302*i + 195. Let w(j) be the first derivative of m(j). Suppose w(q) = 0. What is q?
-30
Let t(x) be the third derivative of -x**5/90 - x**4/6 - 5*x**3/9 + x**2 + 5. Factor t(c).
-2*(c + 1)*(c + 5)/3
Let i(x) be the second derivative of -1/77*x**7 + 3/55*x**6 + 5/22*x**4 + 0*x**2 + 27/110*x**5 + 41*x + 0 + 0*x**3. Determine m so that i(m) = 0.
-1, 0, 5
Let r(f) be the third derivative of -4*f**5/105 - 389*f**4/42 - 194*f**3/21 - 3098*f**2. Suppose r(m) = 0. What is m?
-97, -1/4
Let s = -659 - -979. Suppose -6*w**2 - s*w - 6*w**2 + 1379 + 3741 + 17*w**2 = 0. Calculate w.
32
Let f(g) be the second derivative of -g**5/10 - 250*g**4/3 + 503*g**3/3 + 1002*g**2 + 5303*g + 2. Factor f(r).
-2*(r - 2)*(r + 1)*(r + 501)
Let x(g) be the first derivative of -g**4/16 - 17*g**3/12 + 642. Suppose x(z) = 0. What is z?
-17, 0
Factor 2/11*n**2 - 194/11*n + 380/11.
2*(n - 95)*(n - 2)/11
Let r be (-31 - (-342)/12)/(1/(-2)). Let l(q) be the second derivative of -15*q - 2/9*q**3 + 1/60*q**r + 0 + 0*q**2 + 1/12*q**4. Factor l(j).
j*(j - 1)*(j + 4)/3
Let d(l) be the second derivative of 0 + 3/95*l**6 + 52*l + 17/57*l**4 + 7/19*l**3 + 5/19*l**2 + 1/399*l**7 + 13/95*l**5. Determine w, given that d(w) = 0.
-5, -1
Let c = -671 - -668. Let a be c/((-147)/(-182)) + 4. Solve 2/7*m**2 + 2/7*m**3 - a*m + 0 - 2/7*m**4 = 0.
-1, 0, 1
Let n = 1228 + -1222. Let m(z) = -3*z**3 - z**2 + 2*z - 1. Let j be m(-2). Suppose n*g**2 + 4*g**2 + j*g**5 + 13*g**3 + 40*g**4 + 22*g**3 = 0. Calculate g.
-1, -2/3, 0
Let j be ((-8)/(-14))/(4/14). Let q be (2 + (-25)/10)*(2 - j). Find u, given that 0 + 0*u**2 + q*u + 2/17*u**3 = 0.
0
Let q(g) = -4*g**2 + 10150*g - 6431304. Let l(k) = -4*k**2 + 10153*k - 6431308. Let x(f) = -2*l(f) + 3*q(f). Solve x(p) = 0.
1268
Let z(f) = -f**3 + f**2 - 24*f + 1. Let g(m) = -m**3 - 31*m**2 - 88*m - 121. Let c(p) = -g(p) - z(p). Factor c(w).
2*(w + 2)*(w + 3)*(w + 10)
Let r(c) be the first derivative of 3*c**5/5 - 69*c**4/2 - 144*c**3 - 219*c**2 - 147*c + 1707. Find i such that r(i) = 0.
-1, 49
Suppose -4*q - 5*w + 33 = 0, -2*q + 4*q - 4*w + 16 = 0. Factor -106*b + b**3 + 2*b**3 + 126*b + 20*b**q + 2*b**3.
5*b*(b + 2)**2
Let c(y) be the first derivative of 5*y**3/3 - 745*y**2/2 - 11466. Find s such that c(s) = 0.
0, 149
Suppose 0 = -34*v + 36*v - 6. Suppose d = -3*a + 2, v*a - a + 3*d = -8. Factor -6*w**2 + w**a + 10*w**3 - 10*w - 6*w**4 + 11*w**4.
5*w*(w - 1)*(w + 1)*(w + 2)
Let u be (-5552)/(-42)*(-15 - 4 - -17). Let l = -1734/7 - u. Factor -10/3*v**2 - 250/9 + l*v + 2/9*v**3.
2*(v - 5)**3/9
Let i(x) = x**3 + x**2 - x - 2. Let t(l) = 6*l**4 - 3*l - 15*l**2 - 3*l**3 + 5*l**3 + 6 - 11*l**2 - 16*l**4 + 14*l**4. Let s(p) = 3*i(p) + t(p). Factor s(y).
y*(y - 2)*(y + 3)*(4*y + 1)
Suppose 3 = 2*b - 3. Let w be (6/75)/(3/45) - 18/(-45). Factor 2/5*t**2 + 4/5*t - 1/5*t**b - w.
-(t - 2)**2*(t + 2)/5
Suppose 9916*o**4 + 9917*o**4 + 983*o + 325*o**3 + 328 - 19834*o**4 + 981*o**2 = 0. Calculate o.
-1, 328
Factor 18*y - 24 - 1/3*y**3 - 7/3*y**2.
-(y - 3)*(y - 2)*(y + 12)/3
Let k be ((-44)/6)/(51282/(-23976)). Factor k*d + 22/7 + 2/7*d**2.
2*(d + 1)*(d + 11)/7
Let u(z) = -32*z**2 + 144*z + 720. Let a(l) = 38*l**2 - 146*l - 720. Let o(f) = 5*a(f) + 6*u(f). Determine c so that o(c) = 0.
-5, 72
Let y(b) be the third derivative of -b**8/672 - b**7/420 + 11*b**6/80 - 59*b**5/120 + 7*b**4/12 + 2*b**2 + 111*b. Solve y(v) = 0.
-7, 0, 1, 4
Let l(a) be the second derivative of a**6/280 - a**5/35 + a**4/14 - 52*a**2 + 4*a - 23. Let y(w) be the first derivative of l(w). Find n such that y(n) = 0.
0, 2
Let o(m) be the first derivative of -5/4*m**4 + 0*m - 5*m**5 + 0*m**3 - 10/3*m**6 + 66 + 0*m**2. Factor o(u).
-5*u**3*(u + 1)*(4*u + 1)
Let n(j) be the second derivative of j**8/5040 - j**7/1260 - 25*j**3/6 + j + 1. Let u(v) be the second derivative of n(v). Suppose u(l) = 0. What is l?
0, 2
Factor 2/5*g**3 - 254/5 - 50*g**2 - 506/5*g.
2*(g - 127)*(g + 1)**2/5
Let t(n) be the first derivative of 7 + 25*n**2 + 4/3*n**3 + 45*n. Let s(p) = -p**2. Let r(m) = s(m) - t(m). Determine z so that r(z) = 0.
-9, -1
Let h(x) be the third derivative of x**6/120 - 13*x**5/10 - x**4/24 + 13*x**3 - x**2. Factor h(o).
(o - 78)*(o - 1)*(o + 1)
Let l(v) be the first derivative of 40*v**5/9 + 670*v**4/9 + 8138*v**3/27 - 938*v**2/3 + 98*v + 107. Determine m, given that l(m) = 0.
-7, 3/10
Let l(s) = s**3 - 5*s**2 - 2*s + 2. Let g = -172 + 173. Let k(o) be the first derivative of o**4/4 + o**2/2 + o + 2. Let x(a) = g*l(a) - 2*k(a). Solve x(t) = 0.
-4, -1, 0
Let y(c) be the first derivative of 11*c + 0*c**2 - 11 + 0*c**3 + 1/3*c**4 + 1/10*c**5. Let g(u) be the first derivative of y(u). Factor g(j).
2*j**2*(j + 2)
Let b(z) = -36*z**2 + 26 + z**3 - 5*z**3 + 9 - z + 1. Let u(p) = -6*p**3 - 54*p**2 - 2*p + 54. Let h(c) = 8*b(c) - 5*u(c). Factor h(t).
-2*(t - 1)*(t + 1)*(t + 9)
Let j = -178 + 127. Let z = j - -53. Let 0 + 4/11*h - 2/11*h**z - 2/11*h**3 = 0. Calculate h.
-2, 0, 1
Let b(d) be the third derivative of -1/1344*d**8 + 0 + 7/480*d**6 + 0*d**7 - 88*d**2 + 0*d + 1/3*d**3 - 1/8*d**4 - 1/120*d**5. Suppose b(c) = 0. Calculate c.
-2, 1, 2
Determine t, given that -176 + 1006/3*t + 2/3*t**4 - 18*t**3 - 142*t**2 = 0.
-8, 1, 33
Let o = 27730 + -27726. Let m(a) be the third derivative of 1/20*a**5 + 0*a - 1/35*a**7 + 0 + 0*a**3 + 0*a**o + 1/40*a**6 + 5*a**2. Factor m(h).
-3*h**2*(h - 1)*(2*h + 1)
Let j be 584/56 - (-67 - -77). Determine b so that 15/7*b**2 - 18/7*b - j*b**3 + 0 = 0.
0, 2, 3
Let a(z) = z**3 - 4*z**2 - 20*z + 11. Let f be a(7). Let s be (-6)/12*f/(-27). Suppose s*i**2 + 4/3*i + 1 = 0. What is i?
-3, -1
Let z(a) be the first derivative of -a**8/5040 + a**6/135 - 2*a**4/9 - a**3 + 15*a**2/2 + 100. Let f(p) be the third derivative of z(p). Factor f(u).
-(u - 2)**2*(u + 2)**2/3
Suppose 263*y - 22 = 262*y. Suppose -26*v = -15*v - y. Let 8/9*t**4 + 4/3*t**2 + 2/9*t + v*t**3 + 0 = 0. What is t?
-1, -1/4, 0
Let a(u) = 3*u**2 + 31*u - 64. Let x(n) = 16*n**2 + 155*n - 319. Let t(v) = 11*a(v) - 2*x(v). Let y be t(-33). Determine j so that -1/3*j**2 + y*j + 1/3 = 0.
-1, 1
Let t(c) be the first derivative of -c**6/21 - 74*c**5/35 + 561*c**4/14 - 2654*c**3/21 - 160*c**2/7 + 504*c + 8634. Let t(r) = 0. What is r?
-49, -1, 2, 9
Let j be -3*(-20)/72 - (33/18 + -3). Factor -14/3*k**4 - 26/3*k - 12*k**3 - 44/3*k**j - 2 - 2/3*k**5.
-2*(k + 1)**4*(k + 3)/3
Let i(t) be the first derivative of t**7/1155 + t**6/660 - t**5/165 - 26*t**2 + 96. Let b(x) be the second derivative of i(x). Factor b(w).
2*w**2*(w - 1)*(w + 2)/11
Let o be (-1)/(-1) - 1*-44. Let n be (-5)/(-3) + (-75)/o. Factor 0 + n*r + 0*r**3 + 0*r**2 - 2/11*r**4.
-2*r**4/11
Find y, given that -3/8*y + 3/8*y**3 + 108 - 108*y**2 = 0.
-1, 1, 288
Let p(m) be the first derivative of -278 - 8/3*m - 1/9*m**4 + 20/9*m**2 + 2/3*m**3. Factor p(y).
-2*(y - 6)*(y + 2)*(2*y - 1)/9
Let d(b) be the first derivative of -b**6/10 - 6*b**5/5 - 24*b**4/5 - 38*b**3/5 - 9*b**2/2 + 2853. Find t such that d(t) = 0.
-5, -3, -1, 0
Let v(a) = 2*a**2 + 583*a + 41472. Let w(y) = y**2