12. Let u be f + 1 + 6/(-2). Factor -2*g + g + 10 - 6*g**2 + 6*g + g**u.
-5*(g - 2)*(g + 1)
Let s(o) = o + 62. Let f be s(-10). Determine g, given that -9*g**5 - 4*g**4 + 15*g + 52*g**4 - 27*g - 79*g**3 + f*g**2 = 0.
0, 2/3, 1, 3
Suppose -444 = -114*l - 108*l. Factor 128/5 - 32/5*p + 2/5*p**l.
2*(p - 8)**2/5
Let c(k) be the third derivative of k**5/210 - 5*k**4/42 + 8*k**3/7 - 11*k**2 - 2*k. Factor c(s).
2*(s - 6)*(s - 4)/7
Let h(d) be the second derivative of d**6/30 - d**5/4 - 11*d**4/12 + 11*d**3/2 - 9*d**2 - 108*d. Find x, given that h(x) = 0.
-3, 1, 6
Let n(v) be the first derivative of -v**4/9 - 4*v**3/3 - 6*v**2 - 12*v - 43. Determine y, given that n(y) = 0.
-3
Let j(p) be the second derivative of 0 - 1/15*p**4 + 2/5*p**3 + 7*p - 4/5*p**2. Factor j(o).
-4*(o - 2)*(o - 1)/5
Factor -57*z**3 - 29*z + 12*z**2 + 168*z**3 - 112*z**3 + 3*z + 18 - 3*z.
-(z - 9)*(z - 2)*(z - 1)
Solve -20*l + 2*l**2 + 24*l + 92*l**3 - 94*l**3 = 0.
-1, 0, 2
Let m(h) be the first derivative of -h**5 + 25*h**4/2 - 40*h**3 - 80*h**2 + 640*h + 148. What is a in m(a) = 0?
-2, 4
Suppose 253*x + 420 - 195*x + 5*x**2 - 183*x = 0. What is x?
4, 21
Suppose 4*j - 10 = 10. Let h = 11 - 6. Find v such that -j*v**h - v**4 + 6*v**5 - 3*v**5 - v**4 = 0.
-1, 0
Let f(x) = -x**2 + 1 - 11*x + 4*x + 6*x + 0 - x**3. Let o(k) = 6*k**3 + 4*k**2 + 2*k - 4. Let q(h) = 4*f(h) + o(h). Factor q(d).
2*d*(d - 1)*(d + 1)
Let s = 1075 - 3178/3. Let u = s - 46/3. Suppose 0 - 1/3*f**2 + 0*f - u*f**3 = 0. Calculate f.
-1, 0
Factor -50/3*o + 90*o**2 - 34*o**3 + 10/3*o**4 + 0.
2*o*(o - 5)**2*(5*o - 1)/3
Let g(f) be the second derivative of 5/12*f**4 - 12*f + 0*f**3 + 0 - 10*f**2. Factor g(r).
5*(r - 2)*(r + 2)
Let 17/4*l + 0 + 1/4*l**2 = 0. Calculate l.
-17, 0
Let d(x) be the second derivative of -2*x**6/15 + 3*x**5/5 + 4*x**4/3 - 181*x. Solve d(z) = 0.
-1, 0, 4
Let t(u) = -6*u - 5. Let n(l) = l + 1. Let x(d) = 5*n(d) + t(d). Let j(o) = 4*o**2 + 5*o. Suppose 0 = -5*p + 6*p - 1. Let z(b) = p*j(b) + 3*x(b). Factor z(g).
2*g*(2*g + 1)
Let c(t) be the third derivative of t**7/2205 + t**6/1260 - t**5/63 + 2*t**4/63 + 23*t**2 - t. Suppose c(z) = 0. Calculate z.
-4, 0, 1, 2
Let w(c) = -30*c**2 + 2 - 8*c - 16*c + 28*c**2. Let v be w(-12). Factor -2*h - 12/13 - 8/13*h**v + 6/13*h**3.
2*(h - 3)*(h + 1)*(3*h + 2)/13
Let r(j) be the third derivative of -j**7/735 + 13*j**6/840 - j**5/70 - 5*j**2 - 20. Factor r(m).
-m**2*(m - 6)*(2*m - 1)/7
Suppose 12*x = -4 + 4. Let o(a) be the third derivative of -1/32*a**4 + 1/120*a**5 + x*a + 0*a**3 + 0 - 2*a**2. Factor o(j).
j*(2*j - 3)/4
Factor 2 - 1/3*o**2 - 1/3*o.
-(o - 2)*(o + 3)/3
Let i(q) = q**4 + q**3 + 1. Let j(x) = 16*x - 9*x**2 - 3*x**4 + 4*x**4 + 4 + 16*x**3 + x**4 - 15*x**2. Let y(h) = 4*i(h) - j(h). Factor y(z).
2*z*(z - 2)**3
Let b be ((-2)/(-8))/(4*(-1)/3012). Let p = b + 189. Factor 1 - 2*l + p*l**2.
(l - 2)*(3*l - 2)/4
Let c(z) be the first derivative of 1/10*z**4 - 3 + 4/15*z**3 - 4/5*z - 1/5*z**2. Factor c(q).
2*(q - 1)*(q + 1)*(q + 2)/5
Let n(f) be the second derivative of -f**4/24 - f**3/12 + f**2/2 - 5*f - 23. Factor n(l).
-(l - 1)*(l + 2)/2
Let n(l) be the third derivative of -l**7/350 + l**6/200 + 43*l**5/100 - 17*l**4/8 + 21*l**3/5 - 129*l**2 - 1. Find q, given that n(q) = 0.
-7, 1, 6
Find w, given that 1/8*w**3 - 7/4*w**2 - 31/8*w - 2 = 0.
-1, 16
Let a(c) be the third derivative of -2/21*c**3 - 5/84*c**4 + 1/70*c**5 - 11*c**2 + 0 + 0*c. Factor a(q).
2*(q - 2)*(3*q + 1)/7
Let y = 768 + -445. Let j = 977/3 - y. Factor j*w - 2/3*w**2 - 2.
-2*(w - 3)*(w - 1)/3
Let o = 277/11 - 2471/99. Suppose 2/9*h**3 - 2/3*h**2 - 2/9*h + o*h**4 + 4/9 = 0. Calculate h.
-2, -1, 1
Suppose -2*p - 19*p = -84. Let k be (-63)/(-18) + (p - 7). Factor -1/2*n**3 + 1/2*n**4 + 0*n + 0 + k*n**5 - 1/2*n**2.
n**2*(n - 1)*(n + 1)**2/2
Let y(b) be the second derivative of b**6/10 - 3*b**4/2 + 4*b**3 - 9*b**2/2 - 350*b. Solve y(o) = 0.
-3, 1
Suppose -2*d - 13 = -x + 2, 0 = -2*x - 3*d + 65. Let g = x + -23. Factor -14*j + 5*j + 6*j**2 - 6*j - j**g.
5*j*(j - 3)
Let a = 3050 - 3047. Let u(b) be the third derivative of -5/6*b**4 + 0*b + 5/3*b**a - 1/48*b**6 + 0 + 10*b**2 + 5/24*b**5. Determine y, given that u(y) = 0.
1, 2
Let k(l) = 0*l - 7*l**2 - 4*l - 7*l + l. Let h(i) = -15*i**2 - 21*i. Let y(t) = -6*h(t) + 13*k(t). Factor y(s).
-s*(s + 4)
Let n(v) be the second derivative of -3*v**5/20 - 17*v**4/10 - 12*v**3/5 + 85*v. Factor n(w).
-3*w*(w + 6)*(5*w + 4)/5
Let y(o) be the first derivative of 0*o + 1/7*o**3 - 10 + 0*o**2 - 3/28*o**4. Find c, given that y(c) = 0.
0, 1
Let m(c) = -7*c**5 + 42*c**4 - c**3 - 42*c**2 - 4. Let r(w) = 13*w**5 - 84*w**4 + w**3 + 84*w**2 + 7. Let p(h) = -7*m(h) - 4*r(h). Solve p(z) = 0 for z.
-1, 0, 1, 14
Let q(f) = 7*f**2 - 140*f - 138. Let h(t) = 34*t**2 - 700*t - 692. Let g(a) = 3*h(a) - 14*q(a). Factor g(o).
4*(o - 36)*(o + 1)
Let s(v) = 3*v + 64. Let j be s(20). Suppose -33*z**2 - 47*z**2 + j*z + 44*z + 152*z + 5*z**3 = 0. Calculate z.
0, 8
Suppose 245/6 - 35/3*j + 5/6*j**2 = 0. What is j?
7
Let w(x) be the first derivative of -x**4/2 - 16*x**3/3 + 64*x**2 + 1024*x - 486. Factor w(v).
-2*(v - 8)*(v + 8)**2
Let s(y) be the third derivative of y**7/210 - y**6/30 - 3*y**5/10 + 9*y**4/2 - 45*y**3/2 + 4*y**2. Factor s(r).
(r - 3)**3*(r + 5)
Let a(b) be the third derivative of b**6/240 - b**5/24 + b**4/16 + 3*b**3/4 + 42*b**2. Factor a(i).
(i - 3)**2*(i + 1)/2
Suppose -23 - 81 = -8*s. Suppose -s = -d - 11. Solve -2/3*g**5 - d*g**3 + 0 + 0*g + 2*g**4 + 2/3*g**2 = 0 for g.
0, 1
Let d(y) be the second derivative of y**4/4 + 7*y**3/2 + 15*y**2 + 91*y. Factor d(c).
3*(c + 2)*(c + 5)
Let a = -2/6765 + 142069/13530. Factor -6*d**5 + 3/2*d**2 + 0*d - a*d**4 - 3*d**3 + 0.
-3*d**2*(d + 1)**2*(4*d - 1)/2
Let s(v) = 7*v**5 + 23*v**4 + 38*v**3 + 16*v**2 + 2. Let l(q) = -29*q**5 - 91*q**4 - 151*q**3 - 62*q**2 - 9. Let w(r) = -2*l(r) - 9*s(r). Factor w(b).
-5*b**2*(b + 1)*(b + 2)**2
Let j(y) be the second derivative of y**4/36 + y**3/2 + 4*y**2/3 - 44*y + 2. Factor j(l).
(l + 1)*(l + 8)/3
Let z = 33/254 - 72339/2540. Let l = z - -115/4. Solve 0 + 4/5*h + l*h**2 = 0 for h.
-2, 0
Let f(l) = -43*l**2 - 474*l - 9. Let o be f(-11). Let -4/3 - 7/3*y - 2/3*y**o + 1/3*y**3 = 0. What is y?
-1, 4
Let a be 35/13 - (-10 + -40)/(-50). Determine u, given that a*u + 8/13*u**2 - 6/13 = 0.
-3, 1/4
Let l = 3009/5131 - 11/733. Factor 0*p + 16/7 - l*p**2.
-4*(p - 2)*(p + 2)/7
Suppose -t + 2*t = 13. Suppose -t - 7 = -5*f. Factor -37*l**2 + 6*l**3 - 9 + 8*l**3 + 33*l + l**3 - 2*l**f.
-(l - 3)**2*(l - 1)*(2*l - 1)
Let o(r) be the third derivative of -r**5/390 + 3*r**4/26 - 27*r**3/13 + 33*r**2. Factor o(s).
-2*(s - 9)**2/13
Let f be 7 + (-2)/(-3)*-6. Determine t, given that -t**f + 4*t**3 + t**3 + t**2 - 5*t**2 = 0.
0, 1
Factor -195 - 126 - 4*v**2 - 80*v + 65.
-4*(v + 4)*(v + 16)
Let v = -98 + 104. Let n be -2*((-98)/(-21) - v). Factor -2/3*o**3 + 0 + n*o**2 - 8/3*o.
-2*o*(o - 2)**2/3
Let o(t) = -t**3 + 5*t**2 + 17*t - 1. Let a be o(7). What is m in 3*m + a*m**2 - 2408*m**4 - 5*m**5 - 3*m + 2393*m**4 = 0?
-2, 0, 1
Let i(l) = -4*l**4 - 8*l**3 + 6*l**2 + 10*l + 4. Let x(s) = 9*s**4 + 16*s**3 - 14*s**2 - 21*s - 10. Let a(v) = -5*i(v) - 2*x(v). What is b in a(b) = 0?
-4, -1, 0, 1
Let t(g) be the first derivative of -g**3/5 - 33*g**2/10 - 87. Determine q, given that t(q) = 0.
-11, 0
Suppose -8*g = -3*g + 45. Let o = 7 + g. Let i(n) = -n**4 - n**3 + n - 1. Let m(l) = l**2 + 1. Let b(p) = o*i(p) - 2*m(p). Let b(h) = 0. Calculate h.
-1, 0, 1
Let b = 3/13 - 2/65. Let j(d) be the first derivative of -5 + 1/3*d**3 + 1/4*d**4 + 0*d - 1/2*d**2 - b*d**5. Let j(c) = 0. Calculate c.
-1, 0, 1
Let i be (-7)/(5*4/6460). Let m be 10/(-8) - i/228. Solve -m*c**3 + 0 + 8/3*c + 10/3*c**4 + 8/3*c**2 = 0 for c.
-2/5, 0, 1, 2
Let d = 7850 - 39232/5. Find g such that 3*g + d - 3/5*g**2 = 0.
-1, 6
Determine k, given that 392/5*k + 1484/5*k**2 + 0 + 28/5*k**4 + 80*k**3 = 0.
-7, -2/7, 0
Let s be (495/(-105))/(-3) - -3. Factor s*z**5 + 48/7*z**4 + 0 + 0*z + 18/7*z**3 + 2/7*z**2.
2*z**2*(z + 1)*(4*z + 1)**2/7
Let h = 14 + -11. Factor -2*o + 2*o**h - 5 - 2*o**2 - 10 + 17.
2*(o - 1)**2*(o + 1)
Let g = 80 + -35. Factor 25*n**3 + 48*n**2 + 24*n**3 - g*n**3.
4*n**2*(n + 12)
Let b be (17836/(-315))/(-14) - 4. Let d(w) be the third deriv