a(j) = 0?
-2, -1, 0, 1
Let j = -4/1925 + 1941/7700. Let t(l) be the second derivative of 3/16*l**2 + 0 - 3/40*l**5 + j*l**4 - 9*l - 5/16*l**3. Factor t(w).
-3*(w - 1)*(2*w - 1)**2/8
Let t = -1229 - -1236. Let g be (-30)/(-140)*t*2. Determine j, given that 2/7*j**5 + 6/7 + 4/7*j**2 + 12/7*j**g - 10/7*j**4 - 2*j = 0.
-1, 1, 3
Let l = 568 - 550. Let o(g) be the third derivative of 1/138*g**5 + 0 + 1/92*g**4 - l*g**2 + 0*g + 1/1380*g**6 - 3/23*g**3. Factor o(n).
2*(n - 1)*(n + 3)**2/23
Suppose -4*a = 12*h - 17*h + 5, -15 = -a - 2*h. Suppose 5*q = -3*s + 9*q + 26, -q - a = 0. Factor -2/17*b + 0 + 2/17*b**s.
2*b*(b - 1)/17
Let o(r) be the first derivative of -r**5/15 - r**4/2 + 5*r**3 + 25*r**2/3 + 2091. Factor o(y).
-y*(y - 5)*(y + 1)*(y + 10)/3
Let c(m) = -7*m**3 - 4*m - 3. Let i be c(-1). What is s in -5*s**3 - 4*s**2 - 8*s**3 + 5*s - 6*s**2 + 10 + i*s**3 = 0?
-2, -1, 1
Let t(z) be the first derivative of 14*z**3/3 - 450*z**2 + 256*z - 659. Factor t(v).
2*(v - 64)*(7*v - 2)
Determine r so that -288/7*r**2 + 20/7*r**5 - 28*r**3 + 144/7*r + 32/7*r**4 + 0 = 0.
-3, -2, 0, 2/5, 3
Factor -5 - 77026*n**2 + n - n + 77027*n**2 - 4*n.
(n - 5)*(n + 1)
Let h(a) be the first derivative of a**4/14 - 34*a**3/21 - 20*a**2/7 + 72*a/7 - 1646. Determine b, given that h(b) = 0.
-2, 1, 18
Solve 2*l**2 + 3*l - 251 - 33*l + 51 + 0 = 0.
-5, 20
Let j(f) be the second derivative of -4*f - 5*f**3 + 14*f**2 + 1/6*f**4 - 4. What is p in j(p) = 0?
1, 14
Let d(r) be the first derivative of -53*r**2 + 14*r**2 + 17 - 778*r + 271*r - r**3. Suppose d(m) = 0. What is m?
-13
Let g be 3531/1605*70/99. Factor -16/3 - g*j**2 - 92/9*j.
-2*(j + 6)*(7*j + 4)/9
Let k(n) be the third derivative of -n**7/1260 + 7*n**6/720 + n**5/120 - 55*n**4/144 - 25*n**3/18 - 673*n**2. Find w, given that k(w) = 0.
-2, -1, 5
Determine o so that 2/3*o**2 - 168*o + 0 = 0.
0, 252
Find i such that 34*i**2 + 404 - 22*i**2 + 20*i - 17*i**2 - 19 = 0.
-7, 11
Let g(c) = 159*c + 26553. Let f be g(-167). What is o in 0 - 5/3*o**5 + 0*o**4 + 10/3*o**2 + 5*o**3 + f*o = 0?
-1, 0, 2
Let l(v) be the first derivative of -28 + v**3 + 3/5*v**2 + 2/5*v**4 - 1/5*v. Determine b, given that l(b) = 0.
-1, 1/8
Let n(o) = o**3 + o + 1. Let q(j) = -3*j**3 + 12*j**2 - 9*j - 9. Let u(g) = 2*n(g) + q(g). Let m be u(11). Factor -m*s**4 + s**2 + 40*s**4 + 5*s**2 - 9*s**3.
3*s**2*(s - 2)*(s - 1)
Let r(t) = 41*t**2 + 5. Let x be r(2). Suppose 5*f - 356 - x = 0. Determine w so that -90*w**3 - 35*w**4 - 5*w**5 + 9*w + 5*w**2 - f*w**2 - 49*w = 0.
-2, -1, 0
Let f = 166762 - 166760. Solve 216/7*s - 6/7*s**f - 1944/7 = 0 for s.
18
Let h(q) be the third derivative of 11*q**4/12 - q**3 + 4*q**2. Let u be h(3). Factor -36 - u*j - 3*j**3 - j**3 + 0*j**3 - 28*j**2.
-4*(j + 1)*(j + 3)**2
Let l(i) be the first derivative of -80*i**2 - 140*i + 36 - 55/3*i**3 - 5/4*i**4. Find q, given that l(q) = 0.
-7, -2
Suppose g + 7*g + 72 = 0. Let x be (-2 - 15/g) + (-7)/(-3). What is c in -159*c**3 + 15*c - 3 + 9 + 144*c**3 - 6*c**x = 0?
-1, -2/5, 1
Let i(t) = t**2 + 13*t + 7. Let d(y) = -y**2 - 12*y - 6. Let o(c) = -c**2 + 5*c - 7. Let g be o(5). Let n(x) = g*d(x) - 6*i(x). Solve n(q) = 0 for q.
-6, 0
Let v be 3*6*(-15 + 3/(-36)*-184). Let a(q) be the third derivative of 1/24*q**5 + 0 - 22*q**2 - 1/240*q**v + 0*q - 7/48*q**4 + 1/4*q**3. Solve a(o) = 0.
1, 3
Let k(f) be the first derivative of -2*f**5/5 + 4*f**4 + 22*f**3/3 - 18*f**2 - 1166. Suppose k(i) = 0. What is i?
-2, 0, 1, 9
Let f(z) be the first derivative of -z**4/4 - 3*z**3 - z**2/2 - 6*z + 19. Let k be f(-9). What is q in 384 - 3*q - k*q**2 - 384 = 0?
-1, 0
Solve -106/5*u + 94/3*u**2 + 56/15*u**3 - 36/5 = 0 for u.
-9, -1/4, 6/7
Let c(r) = 119*r**3 - 8*r**2 - 6*r + 1. Let y be c(-1). Let s be 48/y - 66/(-40). Factor 0 + 5/2*i - 5/4*i**2 - s*i**3.
-5*i*(i - 1)*(i + 2)/4
Let c = 328 + -326. Factor 58*w**4 - 11*w**3 + 4*w**c - 62*w**4 - 24*w + 35*w**3.
-4*w*(w - 6)*(w - 1)*(w + 1)
Let f be (0/(4 - 0))/(0 + -2). Let v(r) be the third derivative of f*r - 1/240*r**6 + 0*r**5 + 0*r**4 + 0*r**3 + 0 - 9*r**2. Factor v(i).
-i**3/2
Let -28/3 - 26/9*u - 2/9*u**2 = 0. What is u?
-7, -6
Let x(i) be the second derivative of 5*i**4/24 - 215*i**3/12 - 1995*i**2/2 - 3789*i. Solve x(o) = 0.
-14, 57
Let b(u) be the first derivative of -135 - 45/4*u**4 + 0*u + u**5 + 10*u**3 + 40*u**2. Factor b(z).
5*z*(z - 8)*(z - 2)*(z + 1)
Let v(h) be the third derivative of 1/30*h**5 + 0*h - 13/12*h**4 + 4*h**3 - h**2 + 0. Factor v(m).
2*(m - 12)*(m - 1)
Let z(i) be the third derivative of -i**7/210 - 11*i**6/360 + 7*i**5/90 + 5*i**4/9 - 573*i**2. Suppose z(k) = 0. What is k?
-4, -5/3, 0, 2
Find i, given that -2/3*i**3 - 108808*i + 1612/3*i**2 + 215472 = 0.
2, 402
Let p(h) be the second derivative of 5*h**4/4 + 85*h**3/6 + 10*h**2 - 34*h. Let r(f) = -f**2 + f - 2. Let m(t) = p(t) + 10*r(t). Factor m(j).
5*j*(j + 19)
Let s(j) be the third derivative of -j**6/60 - j**5 - 75*j**4/4 + 2*j**2 + 89*j. Determine n so that s(n) = 0.
-15, 0
Let s = 20 + 69. Let p = s - 79. Factor -2*u - 2*u**3 - 8*u**2 + 3*u**2 + 3*u**2 + p*u + 8.
-2*(u - 2)*(u + 1)*(u + 2)
Let q(m) be the third derivative of -m**6/60 - 7*m**5/12 + 7*m**4/3 - 19*m**3/6 - 411*m**2. Factor q(y).
-(y - 1)*(y + 19)*(2*y - 1)
Suppose 52 = 37*f - 11*f. Factor 6*h**3 - 40*h + 2*h**3 + 76*h**2 - 40*h**3 - f*h**4 - 2*h**4.
-4*h*(h - 1)**2*(h + 10)
Solve -108/5 - 2/3*a**4 - 194/15*a**3 - 1066/15*a**2 - 402/5*a = 0 for a.
-9, -1, -2/5
Suppose 0 = -12*b + 48 + 72. Determine j so that 20*j + 20*j + 6*j**2 - 3*j**2 + b*j - 8*j = 0.
-14, 0
Let q(m) be the first derivative of 104*m + 4/3*m**3 - 175 - 30*m**2. Determine l, given that q(l) = 0.
2, 13
Find x such that 527*x**2 + 1132*x - 197*x - 15*x**3 - 1199*x**2 + 547*x**2 + 325 = 0.
-13, -1/3, 5
Let g(h) be the first derivative of h**4/4 - 1482*h**3 + 3294486*h**2 - 3254952168*h + 3625. Factor g(a).
(a - 1482)**3
Suppose 142476289 + 721154*f + f**3 - 25446995 + 4994642 + 1488*f**2 + 16894*f = 0. Calculate f.
-496
Let h = 198310 + -991544/5. Factor 2/5*a**4 + 2/5*a + 4/5 - 2/5*a**3 - h*a**2.
2*(a - 2)*(a - 1)*(a + 1)**2/5
Let 2/7*n - n**2 + 120/7 = 0. What is n?
-4, 30/7
Let j(r) = r**2 - 37*r + 117. Let o be j(34). Let g be 2/8 + o + -14. Let g*y**5 - 5/2 - 20*y**2 + 35/2*y**3 + 45/4*y - 15/2*y**4 = 0. Calculate y.
1, 2
Let h(a) be the first derivative of -a**5 - 125*a**4/2 + 1060*a**3/3 - 540*a**2 + 4200. What is u in h(u) = 0?
-54, 0, 2
Let u = -3001 - -6005/2. Let h(n) be the first derivative of -1/3*n**3 + 0*n + u*n**2 + 4. Factor h(k).
-k*(k - 3)
Let s(u) be the second derivative of 7*u**6/10 + 129*u**5/10 - 81*u**4/4 - 106*u**3 - 78*u**2 - 766*u. Let s(p) = 0. What is p?
-13, -1, -2/7, 2
Let i(o) be the first derivative of -o**3/3 + 66*o**2 - 131*o + 2160. Factor i(a).
-(a - 131)*(a - 1)
Suppose 14230 = 5*q + 14215. Let o(w) be the second derivative of -6*w - 3/7*w**2 + 1/42*w**4 + 0 - 2/21*w**q. Determine n, given that o(n) = 0.
-1, 3
Suppose -32 = -48*t + 40*t. Solve -13467*h + 194*h**2 + 7*h**2 - t*h**3 - h**3 + 4*h**3 + 300763 = 0 for h.
67
Let u be (-4)/26 + 1575/(-325) + (-4860)/(-140). What is s in -61/7*s + 136/7*s**4 - 39*s**3 + u*s**2 - 16/7*s**5 + 6/7 = 0?
1/4, 1, 6
Let n(b) be the first derivative of 1/4*b**4 - 6*b - 7/2*b**2 + 45 + 0*b**3. Suppose n(m) = 0. What is m?
-2, -1, 3
Factor 14/11*w**2 - 40/11*w - 150/11.
2*(w - 5)*(7*w + 15)/11
Let d(t) be the second derivative of -t**7/700 - t**6/200 - t**5/200 + t**3/6 - 63*t**2 - 239*t. Let j(s) be the second derivative of d(s). Factor j(u).
-3*u*(u + 1)*(2*u + 1)/5
Let p(h) be the first derivative of 3*h**4/2 - 47*h**3/3 + 44*h**2 + 16*h - 2526. Determine l, given that p(l) = 0.
-1/6, 4
Find n such that -36/7 - 208/7*n**2 + 142/7*n + 132/7*n**3 - 2/7*n**5 - 4*n**4 = 0.
-18, 1
Let l be (828/(-270) - 8)*(-115)/(-1). Let o = l - -1276. Solve o*y**2 + 5/6*y**3 - 25/6*y + 0 = 0.
-5, 0, 1
Suppose 0 = -10*c + 15*c - 55. Factor -c*d - 8*d - d**2 + 8 - 13*d + 34*d.
-(d - 4)*(d + 2)
Let c(p) be the second derivative of 2*p**7/21 + 12*p**6/5 + 91*p**5/5 + 54*p**4 + 176*p**3/3 + 2524*p. What is a in c(a) = 0?
-11, -4, -2, -1, 0
Find i, given that -2 + 2718*i**2 + 2 - 5383*i**2 + 2749*i**2 + 152*i + 4*i**3 = 0.
-19, -2, 0
Let r(l) be the second derivative of l**4/3 - 106*l**3 - 972*l**2 