- 11. Let g(v) be the first derivative of h(v). Solve g(a) = 0 for a.
-1, 0, 2
Factor 5*i**4 - 10*i + 10*i + 74*i**3 + 125*i**2 + 56*i**3.
5*i**2*(i + 1)*(i + 25)
Suppose 0 = -3*n - 3*i + i + 28, 0 = -4*n + i + 30. Let g be (-3)/(-2) - (n + -3 - 4). Factor 1/4*a + 0 + 1/2*a**4 + 0*a**3 - g*a**2 - 1/4*a**5.
-a*(a - 1)**3*(a + 1)/4
Factor -3/4*y**2 + 18 + 3/2*y.
-3*(y - 6)*(y + 4)/4
Let n(i) = -5*i + 2*i + 1 + 5*i. Let c be n(3). Find s, given that -6*s**2 + 2*s**3 - 2 - c*s + s - 4*s**3 + 0*s**2 = 0.
-1
Let x = -29/657 + 2087/2628. Suppose 1/4*r**3 + 7/4*r**2 - x*r**4 + 0*r - 1/4*r**5 - 1 = 0. Calculate r.
-2, -1, 1
Let n(c) = -20*c**2 + 180*c + 224. Let m(k) = -7*k**2 + 59*k + 75. Let g(d) = -8*m(d) + 3*n(d). Factor g(x).
-4*(x - 18)*(x + 1)
Let i = -138 - -150. Let x be (7/14)/(2/i). Let 1/2*p**x + 0*p + 0 + p**2 = 0. What is p?
-2, 0
Let x be (168/8)/(-7)*(6 + (-288)/42). Factor 0 + 24/7*q**2 + x*q - 4/7*q**3 + 2/7*q**5 - 8/7*q**4.
2*q*(q - 3)**2*(q + 1)**2/7
Suppose -36 = -169*c + 305*c - 154*c. What is p in -2/9*p**4 - 50/3*p**c + 10/3*p**3 + 250/9*p + 0 = 0?
0, 5
Let y be -15 + (-37)/(1998/(-900)). Factor -q**2 - 1/3*q**3 + 1/3*q**4 - 2/3 + y*q.
(q - 1)**3*(q + 2)/3
Let d(h) be the second derivative of -h**5/10 + h**3 + 2*h**2 - 78*h. Factor d(o).
-2*(o - 2)*(o + 1)**2
Let -9*n**5 - 12*n + 25*n**2 + 33*n**3 + 5 + 2*n**2 + 0*n**2 - 3*n**4 - 11 - 6 = 0. Calculate n.
-1, 2/3, 2
Suppose 3*y = 4*v + 39, y + y + 4*v - 6 = 0. Suppose 28 = 4*a - 4*r, -y*r + 4*r = -10. Determine q so that a*q**5 + 2*q**3 - 6*q**5 - 5*q**5 = 0.
-1, 0, 1
Let h be 45/180 + (-2)/(-8)*-1. Factor -1/5*g**2 + h - 7/5*g**3 + 0*g - 6/5*g**4.
-g**2*(g + 1)*(6*g + 1)/5
Let u(f) be the first derivative of -5*f**6/6 - 5*f**5 - 15*f**4/4 + 15*f**3 + 256. Factor u(c).
-5*c**2*(c - 1)*(c + 3)**2
Suppose 2*b + a = -0*b - 14, -4*b + 5*a - 56 = 0. Let m = 11 + b. Find c, given that -4*c - 3 + 2 + 4 + c**m = 0.
1, 3
Let u = 286 + -286. Let z(t) be the first derivative of 45/4*t**4 + 10/3*t**3 + 3*t**5 + 0*t - 2 - 10/3*t**6 + u*t**2. Let z(o) = 0. What is o?
-1, -1/4, 0, 2
Suppose -6 - 2*r**2 - 292*r - 3*r**2 + 297*r + 6 = 0. Calculate r.
0, 1
Suppose 2 - 102 = -50*t. Let g(z) be the first derivative of -t*z**2 + 9 - 2/3*z**3 - 2*z. Factor g(i).
-2*(i + 1)**2
Let m(h) = 145*h**3 - 300*h**2 - 995*h + 790. Let w(o) = -12*o**3 + 25*o**2 + 83*o - 66. Let q(k) = -3*m(k) - 35*w(k). Find c such that q(c) = 0.
-2, 2/3, 3
Let p(v) be the second derivative of v**4/28 - 9*v**3/14 - v - 25. Factor p(b).
3*b*(b - 9)/7
Find a, given that 8*a + 15*a**4 - 135*a**3 - 12*a**2 + 117*a**3 + 16*a - 3*a**5 = 0.
-1, 0, 2
Let a(y) = -5*y**4 + 22*y**3 - 40*y**2 - 2*y - 2. Let w(m) = 110*m**4 - 480*m**3 + 880*m**2 + 45*m + 45. Let s(c) = -45*a(c) - 2*w(c). Factor s(z).
5*z**2*(z - 4)*(z - 2)
Factor -24*d**4 - d**5 + 0*d**5 + 6*d**3 - 150*d**3 + 0*d**5.
-d**3*(d + 12)**2
Determine c so that 4*c**2 - 51*c**3 - 26*c + 14*c + 67*c**3 = 0.
-1, 0, 3/4
Let i(z) be the third derivative of -5*z**8/84 + z**7/2 + 19*z**6/24 - z**5/2 + 62*z**2 - z. Suppose i(f) = 0. What is f?
-1, 0, 1/4, 6
Let l(w) be the third derivative of w**5/30 + w**4/4 - 10*w**3/3 - 21*w**2 - 2. Factor l(c).
2*(c - 2)*(c + 5)
Find z, given that -89*z - 3*z**2 + 5290 + 217*z + z**2 - 7338 = 0.
32
Let i(z) = z**2 - 12*z + 2. Let u = -99 - -111. Let c be i(u). Factor -1/2*w + 0 + 3/4*w**c - 1/4*w**3.
-w*(w - 2)*(w - 1)/4
Let l be 0 + 2 - (-3 + 0). Suppose -l*f + 13 = -2. Suppose -p + f*p**3 + p**4 - p**3 + 2 + p**2 - p**5 - 1 - 3*p**2 = 0. Calculate p.
-1, 1
Let s be 10/(-4)*18/(-15). Suppose -4*r + s*i - i = -56, 20 = r - 2*i. Find l, given that 18*l + l**2 - 6*l + 2*l**2 - r*l**3 + l**2 - 8 + 4*l**4 = 0.
-1, 1, 2
Let d = 22 - 20. Factor 8 + 20*t**d + 18*t**2 - 37*t**2 - 8*t + 8.
(t - 4)**2
Let h = -36077/5 + 4185407/580. Let n = h + -2/29. Factor -1/4*x**3 + 1/2 + 5/4*x - 1/4*x**4 + n*x**2.
-(x - 2)*(x + 1)**3/4
Let v = 68 - 67. Let c be -2 + 7 + (-5)/v. Factor 2/13*i**2 + c + 0*i - 4/13*i**3.
-2*i**2*(2*i - 1)/13
Let q = 573 + -571. Let s(y) be the second derivative of -2*y**3 + 0 + q*y - 1/3*y**4 + 0*y**2. Determine z, given that s(z) = 0.
-3, 0
Let h(v) be the first derivative of v**4/24 + v**3 + 47*v**2/12 + 5*v + 917. Factor h(o).
(o + 1)*(o + 2)*(o + 15)/6
Let g(m) be the second derivative of m**4/72 - 13*m**3/18 + 23*m**2/4 + 4*m + 78. Let g(l) = 0. What is l?
3, 23
Let s be 496/(-120) + 4 + 8/42. Let n(r) be the first derivative of -1/7*r**4 + 2 + 0*r**2 + 0*r - s*r**5 - 2/21*r**3. Find g such that n(g) = 0.
-1, 0
Let m(c) be the first derivative of -12/13*c**2 - 18/13*c - 16 - 8/39*c**3. Factor m(r).
-2*(2*r + 3)**2/13
Let l(z) be the second derivative of 3*z**4/20 - 44*z**3/15 - 2*z**2 + 199*z. Find c, given that l(c) = 0.
-2/9, 10
Let y = -357 + 359. Let h(f) be the third derivative of 1/18*f**3 + 5/144*f**4 + 0*f - 6*f**y + 0 + 1/90*f**5 + 1/720*f**6. Factor h(b).
(b + 1)**2*(b + 2)/6
Let l(q) be the second derivative of q**8/12600 - q**6/2700 - 7*q**3/6 - q. Let s(r) be the second derivative of l(r). Factor s(a).
2*a**2*(a - 1)*(a + 1)/15
Let u(j) be the second derivative of -19*j**6/60 - j**5/20 + j + 41. Let u(y) = 0. Calculate y.
-2/19, 0
Let t = 4385 + -21923/5. Factor 0 + t*w**2 - 8/5*w.
2*w*(w - 4)/5
Let o be 0 - ((-8)/2 + 1). What is n in -3*n**5 - 6*n**4 + 4*n**5 + 511*n**3 - 502*n**o - 4*n**2 = 0?
0, 1, 4
What is y in -354/5*y**2 + 177/5*y**3 + 57/5*y + 18 + 6*y**4 = 0?
-15/2, -2/5, 1
Factor -3/4*z**2 - 1/2*z + 0 + 0*z**3 + 1/4*z**4.
z*(z - 2)*(z + 1)**2/4
Let r(i) be the third derivative of i**6/108 - 17*i**5/270 + i**4/18 - 34*i**2 + 3*i. Find p such that r(p) = 0.
0, 2/5, 3
Let g = 172993/27 + -6408. Let j = -5/27 - g. Factor 0 - j*w**2 + 2/3*w.
-2*w*(w - 1)/3
Let u(a) be the third derivative of -500*a**3 + 0 + 8*a**2 - 75/2*a**4 - 1/40*a**6 - 3/2*a**5 + 0*a. Determine w, given that u(w) = 0.
-10
Let a(g) be the third derivative of g**6/288 - g**5/32 - 9*g**3/2 - 20*g**2. Let c(v) be the first derivative of a(v). Find x such that c(x) = 0.
0, 3
Factor -48/7*i**3 + 765/7*i - 96/7 - 216*i**2.
-3*(i + 32)*(4*i - 1)**2/7
Let c(w) be the third derivative of -w**8/36960 - w**7/6930 - w**6/3960 - 13*w**4/24 - 15*w**2. Let i(u) be the second derivative of c(u). Factor i(r).
-2*r*(r + 1)**2/11
Let f(c) = 4*c**3 - 4*c**2 - 3*c + 7. Let i be f(3). Let t = i - 208/3. Factor -2/9*x**2 + 4/9*x + t.
-2*(x - 3)*(x + 1)/9
Let 16 + 16*v - 5*v**4 - 34406*v**2 + 56*v**3 - 7*v**4 + 34330*v**2 = 0. What is v?
-1/3, 1, 2
Factor 5/3*i - 1/3*i**2 + 22.
-(i - 11)*(i + 6)/3
Let k(n) = -7*n**2 + n - 5. Let b(z) = -8*z**2 - 6. Let h = -25 - -31. Let u(j) = h*k(j) - 5*b(j). Factor u(f).
-2*f*(f - 3)
Suppose 0 = -v - 4, -m - 10 = -v + 5*v. Suppose -3*b = -5*q - 5, -5*b = -4*q - m + 2. Find z such that -2/7*z - 2/7*z**4 + b - 6/7*z**3 - 6/7*z**2 = 0.
-1, 0
Factor 1/5*o**2 - 1/5*o**4 + 0 + 24/5*o**3 - 24/5*o.
-o*(o - 24)*(o - 1)*(o + 1)/5
Let l be (-1)/(-12) + -10 + (-3650)/(-360). Factor l*y**2 + 0 - 4/9*y.
2*y*(y - 2)/9
Let b(q) be the third derivative of q**5/4 + q**4/2 - q**3 + 23*q**2. Let n(x) = -x**2 + x - 1. Let c(o) = b(o) - 6*n(o). What is k in c(k) = 0?
-2/7, 0
Let j(l) = -2*l**2 + 94*l - 1101. Let t be j(24). What is o in 0 - 10/7*o - 8/7*o**2 + 2/7*o**t = 0?
-1, 0, 5
Let s be (-4)/16 + (12932448/896 - -31). Find q such that -s - 2700/7*q**2 - 2/7*q**4 - 27000/7*q - 120/7*q**3 = 0.
-15
Let m(c) be the second derivative of c**5/200 + 11*c**4/40 - 53*c**3/30 + 18*c**2/5 - 2*c - 95. Determine u, given that m(u) = 0.
-36, 1, 2
Let q be 25/(-675) + 10945/270. Determine t so that -81/2 - 27/2*t**2 + q*t + 3/2*t**3 = 0.
3
Suppose 4*l = 5*l + 8. Let n(y) = 2*y**4 - y**3 + 3*y - 3. Let i(k) = -6*k**4 + 4*k**3 - 8*k + 8. Let z(d) = l*n(d) - 3*i(d). Factor z(p).
2*p**3*(p - 2)
What is t in 1/6*t - 2/3*t**2 + 2/3*t**4 - 1/6*t**3 + 0 = 0?
-1, 0, 1/4, 1
Let x = -5515/4 + 1380. Let d(f) be the first derivative of -x*f + 5/4*f**2 - 5/12*f**3 + 12. Find y such that d(y) = 0.
1
Let d(z) be the first derivative of -1/12*z**4 + 11/2*z**2 + 0*z + 1/60*z**6 - z**3 + 1/10*z**5 - 8. Let q(c) be the second derivative of d(c). Factor q(g).
2*(g - 1)*(g + 1)*(g + 3)
Let o = 305/264 - 1/33. Let x(l) be the second derivative of l + o*l**2 - 13/8*l**3 + 0 + 1/4*l**4. Fi