9. What is v in h(v) = 0?
-2/67, 1
Let x(j) be the second derivative of j**4/36 - 7*j**3/3 - 43*j**2/6 + 2*j + 21. Factor x(n).
(n - 43)*(n + 1)/3
Let -6712/7*j**2 - 5184/7*j - 360/7*j**3 - 1024/7 + 50/7*j**4 = 0. Calculate j.
-8, -2/5, 16
Let x = -1108 - -749. Let p = 3965/11 + x. Factor -162/11*b**3 + 36*b**2 - 152/11*b + p.
-2*(b - 2)*(9*b - 2)**2/11
Let r = -63 + 61. Let v be (r + 3)*(-1 - -3). Determine w so that 9*w**4 - 25*w**4 - 8*w**3 + 0*w + 11*w**v + 5*w**2 - 4*w + 12*w**5 = 0.
-1, 0, 1/3, 1
Let v(n) be the first derivative of -n**3/12 + 27*n**2/8 - 55*n/2 - 2736. Find b, given that v(b) = 0.
5, 22
Let a(b) be the third derivative of 2809/70*b**5 + 0*b + 7890481/42*b**3 + 1 - 148877/42*b**4 - 53/210*b**6 - 27*b**2 + 1/1470*b**7. Factor a(q).
(q - 53)**4/7
Let b = 9091 - 9089. Let d(l) be the first derivative of 7 - 2*l**3 + 9/2*l**b - 3/4*l**4 + 0*l. Find q, given that d(q) = 0.
-3, 0, 1
Let u be (157125/12)/5 - (-8)/(-16). Let j = 2619 - u. Suppose 0 + j*g**2 + 21/4*g = 0. What is g?
-7, 0
Let p be (-90)/13500*(-10)/8. Let k(f) be the second derivative of -1/72*f**4 + 0*f**3 + 0*f**2 + 21*f + 0 + p*f**5. Factor k(w).
w**2*(w - 1)/6
Let n(p) be the first derivative of -37 + 0*p + 1/7*p**2 + 2/21*p**3 - 2/35*p**5 - 1/14*p**4. Find v such that n(v) = 0.
-1, 0, 1
Determine z, given that 5/4*z**2 + 520 - 105/2*z = 0.
16, 26
Let y(n) be the first derivative of n**6/660 - n**5/66 + 2*n**4/33 - 4*n**3/33 + 28*n**2 - 7. Let c(h) be the second derivative of y(h). Factor c(k).
2*(k - 2)**2*(k - 1)/11
Let x(c) be the second derivative of c**5/10 + 521*c**4/3 + 90132*c**3 - 544968*c**2 + 9317*c. Solve x(l) = 0.
-522, 2
Let n(y) be the second derivative of -4/3*y**4 + 2*y + 0*y**2 - 37 - 38/9*y**6 + 64/15*y**5 + 50/63*y**7 + 0*y**3. Factor n(p).
4*p**2*(p - 3)*(5*p - 2)**2/3
Factor 0*d**2 - 2*d**3 - d**3 - 264*d + 261*d - 4*d**2 + 10*d**2.
-3*d*(d - 1)**2
Let p(b) be the second derivative of 59*b**4/6 - 36*b**3 - 20*b**2 - 4205*b. Factor p(f).
2*(f - 2)*(59*f + 10)
Factor 205*m + 3285 + 20*m**2 - 3285.
5*m*(4*m + 41)
Let l be (14/(-9))/(-7)*9. Suppose 0 = 4*b + q - 36, b + 2*q + l = -q. Determine u so that 30*u + 132*u**3 - 88*u**2 + 14*u**5 - 74*u**4 - b*u - 4*u = 0.
0, 2/7, 1, 2
Factor -8*t**4 - 42*t - 673/2*t**2 - 676*t**3 + 0.
-t*(t + 84)*(4*t + 1)**2/2
Suppose 41*f - 430 = 36*f. Factor 13*r**4 - 8*r**5 - 54*r**3 + 10*r**5 + 8*r**4 - 39*r - 20*r**2 + 9 - 5*r**5 + f*r**2.
-3*(r - 3)*(r - 1)**4
Suppose -26 = -7*t - 5. Determine v, given that 15*v**t + 21*v**4 + 15*v**4 - 11*v**4 - 3*v**2 - 7*v**2 = 0.
-1, 0, 2/5
Let l be (2/20)/((-1)/(-12)). Let p be (2/50)/(-42*19/(-23940)). Factor -2/5*a**3 - l*a + 2/5 + p*a**2.
-2*(a - 1)**3/5
Let a(j) be the first derivative of -90 + 1/4*j**6 + 0*j + 9/5*j**5 + 0*j**2 - 3*j**3 - 3/8*j**4. Let a(s) = 0. Calculate s.
-6, -1, 0, 1
Let o(w) be the third derivative of -w**8/448 - 3*w**7/40 - 143*w**6/160 - 403*w**5/80 - 57*w**4/4 - 22*w**3 - 70*w**2 + 3*w. Solve o(r) = 0.
-11, -4, -1
Let m(l) = 15*l + 2. Let k be m(1). Let t = 19 - k. Factor 4 + 420*x**t + 152*x - 153*x**4 + 98*x**3 + 5 - 533*x**4 + 7.
-2*(x - 1)*(7*x + 2)**3
Let t be 71 + 7 + -68 + 3/9*-26. Factor -t*y**2 + 2/3*y**3 + 0 - 2*y.
2*y*(y - 3)*(y + 1)/3
Determine t, given that 4/5*t**4 + 69316/5*t + 8124/5*t**2 + 61504/5 + 316/5*t**3 = 0.
-31, -16, -1
Suppose -c = c - 2. Let n be 2/5 + 1 + 165/25. Suppose 15*m**3 + 1 + n*m - c - 5*m**4 - 28*m = 0. What is m?
-1, 0, 2
Let x(n) be the third derivative of n**5/270 - 83*n**4/27 - 37*n**3/3 + 132*n**2 + 20*n. Factor x(d).
2*(d - 333)*(d + 1)/9
Determine c so that 87/2 - 23/4*c - 1/4*c**2 = 0.
-29, 6
Let m(u) = -49*u**2 + 3804*u + 3617624. Let p(z) = -54*z**2 + 3804*z + 3617626. Let f(s) = -22*m(s) + 20*p(s). Suppose f(w) = 0. Calculate w.
-1902
Find a such that -2715/2*a - 1/2*a**3 + 1357/2 + 1359/2*a**2 = 0.
1, 1357
Determine f, given that 0 - 795/2*f**2 + 3/2*f**3 + 0*f = 0.
0, 265
Suppose -3*n + 5*a = -214, 4*a = 15 + 1. Suppose 2*q - 5*b = 48, n = 5*q - b - b. Factor -2*s**2 - 2*s**3 - q*s - 4*s**2 + 16*s**2 + 6.
-2*(s - 3)*(s - 1)**2
Factor -4*n - 2/5*n**2 - 32/5.
-2*(n + 2)*(n + 8)/5
Let r be ((-20)/(-6) - 0) + (-1456)/1092. Suppose 12*a**3 - a**4 + 3*a**3 + 72 - 24*a + 6*a**r + 4*a**4 - 72 = 0. What is a?
-4, -2, 0, 1
Let h(s) be the second derivative of 10/3*s**4 + 0 - 4/3*s**3 + 1/5*s**2 - 51*s. Let h(g) = 0. Calculate g.
1/10
Let k(g) be the third derivative of -g**8/1680 + 2*g**7/175 - 47*g**6/600 + g**5/5 - 6*g**2 + 7*g - 2. Let k(i) = 0. Calculate i.
0, 3, 4, 5
Let g be ((-6)/20)/(7/364*-39). Find y such that 0 - 2/5*y**3 - g*y + 4/5*y**2 = 0.
0, 1
Let x(l) be the second derivative of 0 + 0*l**3 + 1/30*l**6 - 1/210*l**7 - 83*l + 0*l**2 - 2/25*l**5 + 1/15*l**4. Factor x(i).
-i**2*(i - 2)**2*(i - 1)/5
Let g(m) be the third derivative of 1/15*m**5 - 14 + 0*m - 8/3*m**3 + 0*m**4 - 8*m**2. Find o, given that g(o) = 0.
-2, 2
Let q(a) = 2*a + 41. Let r be q(-19). Determine x so that -13*x**2 + 132*x**4 + 1002*x**r - 28*x**5 + 61*x**2 - 794*x**3 = 0.
-1, -2/7, 0, 6
Let w = 629 + -633. Let x(h) = -h**3 - 5*h**2 - 7*h - 9. Let j be x(w). Determine r, given that 1/5 - 2/5*r**j + 2/5*r - 1/5*r**2 = 0.
-1, -1/2, 1
Let v(m) be the first derivative of -m**5 + 85*m**4/4 - 340*m**3/3 + 250*m**2 - 240*m - 1768. Determine s, given that v(s) = 0.
1, 2, 12
Suppose -40*i = -24 - 176. Let -548*d**3 + 1088*d**3 + 59*d**2 - i*d**4 - 500*d**3 - 139*d**2 = 0. What is d?
0, 4
Suppose 215*c**2 - 174*c - 142*c**2 - 70*c**2 = 0. Calculate c.
0, 58
Let p be (323/(-34) - -10)*0. Let x(z) be the second derivative of 1/30*z**6 + 1/2*z**3 + 1/5*z**2 - 11*z + p + 29/60*z**4 + 21/100*z**5. Factor x(d).
(d + 1)**2*(d + 2)*(5*d + 1)/5
Suppose 19*r**2 + 68760*r**3 - 271 + 5759 - 68716*r**3 - 11*r**2 - 2156*r + 76*r**2 - 4*r**4 = 0. Calculate r.
-7, 4, 7
Let p(o) be the first derivative of o**8/840 - o**7/105 - o**6/60 + o**5/6 + 2*o**4/3 - 28*o**3 + 95. Let l(d) be the third derivative of p(d). Factor l(a).
2*(a - 4)*(a - 2)*(a + 1)**2
Find d such that 697/3*d**2 - 19/3*d**4 + 302/3*d**3 + 12 + 412/3*d = 0.
-1, -2/19, 18
Suppose 2*b - 6 = 2*h, 0 = 3*b - b + 4*h + 6. Let t be (-296)/(-16) - b/2. Factor 20*s - 4*s**3 + 3*s**3 - t*s + s**2.
-s*(s - 2)*(s + 1)
Let b(p) = -p**3 + 66*p**2 - 101*p - 1726. Let a be b(64). Let -2/3*g**5 - 2/3*g**4 + 0*g + 10/3*g**3 + 0 - a*g**2 = 0. What is g?
-3, 0, 1
Suppose 47*b - 809 = 413. Let w(p) be the first derivative of 5/2*p + b + 5/18*p**3 + 5/3*p**2. Factor w(i).
5*(i + 1)*(i + 3)/6
Let h(u) = -u**2 - 2*u + 5. Let k be (2/8)/((-7)/(-28)). Let d be (7/2)/7*(-2)/k. Let z(v) = -1. Let f(o) = d*h(o) - 6*z(o). Factor f(q).
(q + 1)**2
Suppose -5 = -4*x + 3*w - 6, 18 = 3*x + 4*w. Factor -8*q**3 + 4*q - 2*q**2 + 4*q**3 + 4*q**x - 4 + 2*q**2 + 0*q.
-4*(q - 1)**2*(q + 1)
Suppose -3*x - 206 = -71. Let j = 47 + x. Factor 0*y**2 - 3*y**4 + 6*y**3 - 7*y**4 + 18*y**j + 49*y**5 - 47*y**5.
2*y**2*(y - 3)**2*(y + 1)
Suppose 312*q = 306*q + 12. Let v(x) be the second derivative of 4*x + 0*x**q + 1/15*x**3 + 0 - 1/30*x**4. Factor v(z).
-2*z*(z - 1)/5
Let w be ((-1744)/3924)/(8/(-3)). Solve 0 - 1/6*c**3 - w*c**2 + 0*c = 0 for c.
-1, 0
Find x, given that -3403*x**2 + 2*x**4 + 5048*x**2 + 1901250 - 56*x**3 + 54600*x - 5153*x**2 = 0.
-25, 39
Let s(r) be the third derivative of 0*r**4 + 0*r + 1/200*r**6 - 54/5*r**3 + 89*r**2 + 0 + 9/100*r**5. What is q in s(q) = 0?
-6, 3
Factor 29 - 72*k**2 + 71*k**2 + 4 + 10*k - 2*k.
-(k - 11)*(k + 3)
Let i(u) be the first derivative of 4*u**3/3 - 576*u**2 + 1148*u + 1886. Factor i(n).
4*(n - 287)*(n - 1)
Let z(s) be the third derivative of s**8/42 + 11*s**7/105 + 3*s**6/20 + s**5/30 - s**4/12 - 1674*s**2. Factor z(u).
2*u*(u + 1)**3*(4*u - 1)
Let k(q) = 5*q**5 + 40*q**4 + 89*q**3 - 142*q**2. Let h(f) = 16*f**5 + 119*f**4 + 269*f**3 - 430*f**2. Let l(b) = -4*h(b) + 13*k(b). Solve l(o) = 0.
-42, -3, 0, 1
Let y = -3305 + 247876/75. Let q(x) be the second derivative of -y*x**6 + 0*x**3 + 1/25*x**5 - 1/30*x**4 + 0 + 0*x**2 + 7*x. Factor q(l).
-2*l**2*(l - 1)**2/5
Let g(m) be the first derivative of m**3/6 - 7*m**2/4 - 4*m + 218. Find h, given that g(h) = 0.
-1, 8
Let r(z) be the first derivative of 0*z**2 - 1/4*z**4 + 0*z - 19 - 1/9*z**3 - 1/5*z**5 - 1/18*z**6. Factor r(t).
-t**2*(t