(v). Find g such that i(g) = 0.
-1, -1/2, 0
Suppose -5*l + 5413*o - 5412*o = -13, -5*l - 2*o = -4. Let 3/4 + 1/4*v**l - v = 0. Calculate v.
1, 3
Let k be (-2)/(-4) - 30/(-4). Let w = k + -5. Determine h so that 5 - 8 + 3*h**2 + w*h**3 + 3 = 0.
-1, 0
Let q(c) be the first derivative of -16 - 3/4*c**4 - 9*c + 6*c**2 + 3/4*c**3. Factor q(w).
-3*(w - 2)*(w + 2)*(4*w - 3)/4
Let c = 1097/6 + -182. Let u(a) be the second derivative of 0 + 4/15*a**6 + a**3 + a**2 - 3/10*a**5 - 3*a - c*a**4. Let u(o) = 0. What is o?
-1, -1/4, 1
Solve -3/5*q**3 + 564/5*q - 132/5*q**2 - 576/5 = 0.
-48, 2
Let f(y) be the second derivative of 5*y**7/42 + 5*y**6/6 + 7*y**5/4 - 5*y**4/12 - 20*y**3/3 - 10*y**2 - 108*y. Suppose f(t) = 0. What is t?
-2, -1, 1
Suppose -176*u + 565*u + 4*u**2 + 58564 + 579*u = 0. What is u?
-121
Suppose 296/11*n + 18/11*n**4 - 6/11*n**3 - 96/11 - 232/11*n**2 = 0. Calculate n.
-4, 2/3, 3
Let j(g) be the second derivative of g**6/105 + g**5/7 + 4*g**4/7 + 22*g**3/21 + g**2 + 27*g. Factor j(m).
2*(m + 1)**3*(m + 7)/7
Suppose 5*l + 2*q = 4*q - 5, 4*q - 20 = 0. Let p be (1 - l)/(3 + (0 - 5)). Find b such that -3/5*b**5 + 6/5*b**4 + 0 + 3/5*b - 6/5*b**2 + p*b**3 = 0.
-1, 0, 1
Let x = -68/329 + 1531/2632. Factor 9/4 + x*c**2 + 21/8*c.
3*(c + 1)*(c + 6)/8
Let i(n) = -n**3 - 20*n**2 + 8*n + 48. Let c be i(-20). Let q be 50/(-3)*42/c. Find r, given that 1/4*r**2 + q + 5/2*r = 0.
-5
Let y(j) = j**3 + 8*j**2 + j + 9. Let t be y(-8). Let o be (t/(-3))/((-7)/42). Factor 0*z**2 + o*z - 2*z**3 - 4*z**2 - 4*z.
-2*z*(z + 1)**2
Let z(w) = 18*w + 308. Let n be z(-17). Factor -3 - 3/2*h**n - 9/2*h.
-3*(h + 1)*(h + 2)/2
Let d be ((-1169)/4)/(-7)*4. Let x be d/13 - (-4)/26. Let s + 1 + x*s**2 + 6*s + 1 - 8*s**2 = 0. Calculate s.
-1, -2/5
Let q(r) = -6*r - 18. Let d be q(-6). Let g be (3/(-21))/((-3)/d). Suppose -12/7*n**2 - g - 15/7*n - 3/7*n**3 = 0. Calculate n.
-2, -1
Let z(w) be the second derivative of -w**8/67200 + w**6/2400 + w**5/600 + w**4/6 - 18*w. Let n(b) be the third derivative of z(b). What is q in n(q) = 0?
-1, 2
Let k(u) be the first derivative of 2*u**5/5 + 5*u**4/2 + 14*u**3/3 + 3*u**2 + 362. Factor k(x).
2*x*(x + 1)**2*(x + 3)
Let b(j) be the first derivative of j - j**2 + 1/3*j**4 + 7/6*j**3 - 13. Let u(w) be the first derivative of b(w). Factor u(v).
(v + 2)*(4*v - 1)
Suppose -2*z - 2*p + 8 = 0, 5*p - 12 = -2. Let d be 2/(15/(-20) - (-10)/8). Find b such that 26/3*b**z + 4*b**3 + 8*b + 8/3 + 2/3*b**d = 0.
-2, -1
Let z be (4/6 - (-26)/(-3))*(-155)/372. Determine t, given that 14/3*t**2 - 4/3 + z*t = 0.
-1, 2/7
Let 6*s + 324*s**4 - 135*s**2 - 18*s + 9*s**5 - 143*s**3 + 87*s**5 - 130*s**3 = 0. What is s?
-4, -1/4, -1/8, 0, 1
Let y(u) be the first derivative of -3 + 3*u - 3/2*u**3 - 1/2*u**4 - 3/2*u**2. Let p(o) be the first derivative of y(o). Find g such that p(g) = 0.
-1, -1/2
Let i(n) be the second derivative of 2*n**6/105 - 11*n**5/35 - 25*n**4/21 - 26*n**3/21 - 64*n. Factor i(b).
4*b*(b - 13)*(b + 1)**2/7
Suppose 0 = 2*i - 1 - 27. Suppose -6 - i = -4*x. Factor 4*f**2 + f**x - 2*f**3 + f - 4*f**2.
f*(f - 1)**2*(f + 1)**2
Let t be (36/(-544) + (17/8 - 2))*8. What is m in -6/17 - 2/17*m**2 + t*m = 0?
1, 3
Suppose 9*a + 4*s = 4*a + 45, a + 3*s - 20 = 0. Let o(p) be the second derivative of 0*p**3 - a*p - 1/48*p**4 + 0 + 0*p**2. Solve o(v) = 0.
0
Suppose 5*t = 10*a - 7*a + 27, -5*t + 5*a = -35. Suppose -5*c + 2*n = 8, t*c + 3*n = -c + 12. Find x, given that 0 + 1/5*x**4 + c*x - 1/5*x**2 + 0*x**3 = 0.
-1, 0, 1
Factor 1 - 3*b**4 - 720*b**2 - 528*b - 348*b**3 - 31*b**4 - 23*b**4 - 49.
-3*(b + 2)**3*(19*b + 2)
Let i = 5/627 - -1/19. Let s(r) be the second derivative of -i*r**4 + 0 - 6*r + 0*r**2 + 1/110*r**5 + 4/33*r**3. Let s(o) = 0. Calculate o.
0, 2
Let z(l) = -l**3 - 2*l**2 + 59*l + 120. Let u be z(-2). Let 3/7*d**3 + 0 + 15/7*d + 18/7*d**u = 0. What is d?
-5, -1, 0
Factor l + 1059*l**2 - 2*l - 1067*l**2 - l.
-2*l*(4*l + 1)
Let g = -5 - -14. Factor -1 - x**2 - g*x**2 + 5*x + 6*x**2.
-(x - 1)*(4*x - 1)
Let z(y) = -3*y**4 - 53*y**3 + 438*y**2 - 387*y. Let p(i) = i**4 + 27*i**3 - 220*i**2 + 194*i. Let d(a) = 5*p(a) + 2*z(a). Determine u so that d(u) = 0.
0, 1, 14
Let a be 374/231*7 - (0 - -11). Factor -4/9*y**3 + 2/9*y - a*y**4 + 0 + 5/9*y**2.
-y*(y - 1)*(y + 2)*(3*y + 1)/9
Let o(l) be the third derivative of l**8/448 + l**7/70 + l**6/160 - l**5/8 - l**4/8 + l**3 - 41*l**2. Determine t so that o(t) = 0.
-2, 1
Let k(p) = 7*p - 4. Let w be k(4). Factor 15 + 6*r + 71*r**2 - 33*r**2 - w*r - 35*r**2.
3*(r - 5)*(r - 1)
Let p(z) be the second derivative of -z**2 + 20*z + 2/3*z**3 + 0 + 5/24*z**4. Factor p(w).
(w + 2)*(5*w - 2)/2
Let s(r) be the third derivative of -r**8/840 + r**7/525 + 17*r**6/60 + 11*r**5/6 - 6*r**2 + 8*r. Factor s(f).
-2*f**2*(f - 11)*(f + 5)**2/5
Let k(c) = 8*c**2 + 10*c + 140. Let p(z) = -6*z**2 - 7*z - 140. Let r(q) = 5*k(q) + 6*p(q). Suppose r(a) = 0. What is a?
-7, 5
Factor 4*f**4 - 72*f**3 + 716*f**2 - 8855*f + 578 - 2*f**4 + 7631*f.
2*(f - 17)**2*(f - 1)**2
Let t(b) be the second derivative of b**6/240 - b**5/30 + 5*b**4/48 - b**3/6 + 11*b**2 + 13*b. Let d(u) be the first derivative of t(u). Solve d(z) = 0 for z.
1, 2
Find k, given that -2/5*k**4 - 2/5*k**3 - 2/15*k**5 - 2/15*k**2 + 0 + 0*k = 0.
-1, 0
Suppose 9*c - 3/5*c**2 - 42/5 = 0. Calculate c.
1, 14
Let u be (-338)/(-1040) + (3 - 4)/8. Let 0 - 2/5*a**4 + 0*a + u*a**3 + 1/5*a**5 + 0*a**2 = 0. What is a?
0, 1
Suppose -75 = -4*v - 31. Let b = 78/7 - v. Factor -1/7 - 1/7*g**4 + 2/7*g**2 - 1/7*g + 2/7*g**3 - b*g**5.
-(g - 1)**2*(g + 1)**3/7
Let z(u) = u**2 + 3*u + 2. Let i be z(4). Let y = i + -26. Find w, given that 2 - w**2 - 3*w + y + 3*w**3 - 5*w**2 = 0.
-1, 1, 2
Let m(p) be the first derivative of -3/5*p**5 + 3/2*p**2 - 3*p - 3/2*p**4 + 1/2*p**6 + 2*p**3 + 12. Solve m(g) = 0.
-1, 1
Let m(k) be the third derivative of k**2 - 1/30*k**5 + 0 - 1/5*k**3 - 1/300*k**6 + 0*k - 7/60*k**4. What is x in m(x) = 0?
-3, -1
Suppose -73 = -4*p - 5*w, -4*p - 5*w = -5*p - 13. Suppose 4*u + p = -5*m, -3*u = 2*m - 1 + 3. Suppose 4*r + 3*r**u + 8*r**2 + 3*r**2 - 12*r**2 = 0. Calculate r.
-2, 0
Let u(q) be the third derivative of q**7/840 + q**6/72 + q**5/40 + q**4/4 + 34*q**2. Let j(k) be the second derivative of u(k). Solve j(r) = 0 for r.
-3, -1/3
Let b(s) = 9*s**2 + 17*s - 65. Let a be b(2). Factor 5/2*y**3 + 0*y + 54 - 45/2*y**2 - 1/2*y**a + 5/2*y**4.
-(y - 3)**3*(y + 2)**2/2
Factor -60*f**2 + 640*f + 20480 + 118*f**2 - 53*f**2.
5*(f + 64)**2
Factor -68*o**5 + 2*o**4 + 0*o**2 + 71*o**5 - 3*o**3 - 3*o**2 + o**4.
3*o**2*(o - 1)*(o + 1)**2
Let j(m) = -13*m**2 - 31*m - 18. Let z(p) = -29*p**2 - 60*p - 36. Let k(q) = 13*j(q) - 6*z(q). Find h such that k(h) = 0.
-2/5, 9
Let s(l) = -9*l**3 + 3*l**4 - 6 + 11 + 3*l - 8. Let u(m) = -6*m**4 + 19*m**3 + m**2 - 7*m + 7. Let h(y) = 7*s(y) + 3*u(y). Let h(n) = 0. What is n?
0, 1
Let l(c) be the third derivative of c**7/504 + 13*c**6/72 + 169*c**5/24 + c**4/8 - c**3/6 + 15*c**2 - 2. Let n(d) be the second derivative of l(d). Factor n(a).
5*(a + 13)**2
Let q(t) be the first derivative of t**4 + 12*t**3 + 16*t**2 + 361. Determine u so that q(u) = 0.
-8, -1, 0
Let r be (-188)/2*2/(-4). Factor -3*x**3 + 3*x**2 - 3*x**4 - r*x**5 + 96*x**5 - 46*x**5.
3*x**2*(x - 1)**2*(x + 1)
Let v = 29 + -26. Let 0*s**v + 2*s**3 - s**5 - s + 0*s**3 = 0. Calculate s.
-1, 0, 1
Let h(y) be the second derivative of 17*y + 2/15*y**4 + 1/35*y**7 - 2/15*y**6 + 7/50*y**5 - 4/15*y**3 + 0*y**2 + 0. Solve h(p) = 0 for p.
-2/3, 0, 1, 2
Let m(h) be the third derivative of -h**7/630 + h**6/360 + h**5/90 + 2*h**2 - 13. Let m(p) = 0. Calculate p.
-1, 0, 2
Factor -3/5*j**4 - 27/5 - 12/5*j**3 + 36/5*j + 6/5*j**2.
-3*(j - 1)**2*(j + 3)**2/5
Factor -30*h**3 - 12*h**4 - 24*h + 8*h**4 + h**4 - 51*h**2.
-3*h*(h + 1)**2*(h + 8)
Let d(s) = -7 + s - 2*s - s. Let o be d(-5). Factor -2*p**2 + 6*p + 3*p - o*p.
-2*p*(p - 3)
Suppose -5*x + x = -40. Suppose -2*k = -0*k - x. Factor -2*i**2 - 4 - 2*i + k*i - 4*i + 7*i.
-2*(i - 2)*(i - 1)
Let d = -2274 + 2277. Let l(v) = -v**2 + 7*v - 6. Let z be l(5). Factor 0 + 1/2*m - 1/2*m**d - 1/4*m**2 + 1/4*m**z.
m*(m - 2)*(m - 1)*(m + 1)/4
Let u = 53815/3 + -17938. Factor -2/9 + 0*r**2 + 1/9*r**3 - u*r.
(r - 2)*(r + 1)**2/9
Let w(n) = -9*n**3 + 14*n**2 + 15*n + 10. Let s(k)