- 2)*(n + 1)*(n + 11)
Let j be 110/25 + (-8)/20. Determine v so that 160*v**j + 4860*v**2 + 5*v**5 + 33*v**4 + 1350*v**3 + 3645*v - 53*v**4 = 0.
-9, -1, 0
Let z(b) be the first derivative of -b**3/6 + 83*b**2/4 - 455*b - 5623. Suppose z(a) = 0. What is a?
13, 70
Let s be 80/(-45) - (-7 - (1 - 6)). Factor -s*h**2 + 40/3*h - 200.
-2*(h - 30)**2/9
Let b be 8/(-28)*(-1)/(112/196). Determine c so that b*c**2 - 19/2 - 9*c = 0.
-1, 19
Let k = -34 - -38. Suppose -5*z + 1 = -d, -k*d = z - 2*d + 2. Factor z*i**2 - 6*i**3 + 24*i - 12 + 3*i**4 + 0 - 9*i**2.
3*(i - 2)*(i - 1)**2*(i + 2)
Let d(h) be the third derivative of -h**6/40 - 1773*h**5/20 - 1047843*h**4/8 - 206425071*h**3/2 - 1745*h**2. Factor d(p).
-3*(p + 591)**3
Let k(i) be the second derivative of i**4/60 + 59*i**3/30 - 93*i**2/5 - 162*i - 1. Factor k(p).
(p - 3)*(p + 62)/5
Let n(g) be the first derivative of 5*g + 1/5*g**3 - 29 - 1/10*g**4 + 0*g**2. Let m(t) be the first derivative of n(t). Factor m(c).
-6*c*(c - 1)/5
Let i be ((-16)/(-14))/(34/119). Suppose 5*n = 5*b + 5, n - b = i*n - 11. What is z in -z**4 - 23*z**3 + 25*z**3 + n*z**4 = 0?
-1, 0
Suppose -1547*t + 3*t**2 + 361*t - 3584*t + 1896075 = 0. What is t?
795
Let f(z) = 3*z**3 - 15*z**2 - 2*z + 20. Let k(p) = 18*p**2 - 576 + 12*p**2 + 536 - 5*p**3 + 5*p. Let x(r) = -5*f(r) - 2*k(r). Suppose x(g) = 0. What is g?
-1, 2
Let g be ((-100)/80)/((-1)/2). Let i(x) be the first derivative of -5/3*x**3 + 0*x + g*x**2 - 12. Determine f so that i(f) = 0.
0, 1
Let r(l) be the first derivative of 8*l - 2*l**3 - 2/5*l**5 + 2*l**4 + 8 - 4*l**2. Factor r(c).
-2*(c - 2)**2*(c - 1)*(c + 1)
Suppose 82 = 52*b - 74. Let n = 12/19 + 9/76. Find y such that 0 + 0*y - 3/4*y**b - n*y**2 + 3/4*y**5 + 3/4*y**4 = 0.
-1, 0, 1
Let h be (-15)/(-35) + 7/((-98)/(-120)). Suppose -11*r = -h*r. Suppose -8*c - 5*c**2 + r*c**2 - 22*c - 40 = 0. What is c?
-4, -2
Let m(z) be the first derivative of z**6/165 - z**5/110 - z**4/66 + z**3/33 - 31*z + 52. Let u(y) be the first derivative of m(y). Factor u(v).
2*v*(v - 1)**2*(v + 1)/11
Let w(k) be the first derivative of -12/5*k**2 + 2/5*k**3 + 0*k + 35. Factor w(o).
6*o*(o - 4)/5
Let z(m) = 34102*m + 102308. Let y be z(-3). Factor 8/9*f**y + 2/9*f - 2/3.
2*(f + 1)*(4*f - 3)/9
Let l(c) be the first derivative of -1/36*c**6 - 46 - 1/18*c**3 + 0*c + 0*c**2 + 1/30*c**5 + 1/24*c**4. Suppose l(t) = 0. What is t?
-1, 0, 1
Let m be (-4)/(1/((-5)/2)). Let o be (-6)/18*-1*12. Factor 10*r - 3*r**2 + 5*r**2 - 4*r**2 - m*r**3 + 4*r**o - 2*r**4.
2*r*(r - 5)*(r - 1)*(r + 1)
Let l(u) be the second derivative of 2/9*u**6 - 19*u - 1/63*u**7 - 37/30*u**5 - 4*u**3 + 10/3*u**4 - 3 + 0*u**2. Suppose l(d) = 0. What is d?
0, 2, 3
Let c(r) be the first derivative of -3*r**5/5 + 39*r**4 - 132*r**3 - 21216*r**2 - 221952*r + 348. Determine g, given that c(g) = 0.
-8, 34
Let y(b) = 4*b**2 - 736*b - 740. Let v be y(185). Let h(c) be the first derivative of 27 + c**2 + 0*c**3 + v*c - 1/2*c**4. Factor h(x).
-2*x*(x - 1)*(x + 1)
Suppose 3*z = 4*m - 2*m + 7, 5*m - 10 = 2*z. Suppose -h - 10 = -5*b, 5*h - 12 - 18 = z*b. Factor 94 - h*r + 69 - 50*r + 5*r**2 + 17.
5*(r - 6)**2
Find n, given that 3956120/13*n**2 + 0 + 2/13*n**5 + 1980050/13*n + 1972092/13*n**3 - 3976/13*n**4 = 0.
-1, 0, 995
Let i(j) = 35*j**3 + 15*j**2 - 105*j + 25. Let v(x) = -x**3 - 2*x**2 + 2*x. Let z(r) = -r**2. Let q(g) = -v(g) + 2*z(g). Let o(t) = i(t) - 30*q(t). Factor o(b).
5*(b - 1)**2*(b + 5)
Let z(j) be the first derivative of 3*j**2 + 17 - 9/4*j**4 - 34*j - 7/2*j**3. Let s(f) be the first derivative of z(f). Find p, given that s(p) = 0.
-1, 2/9
Let j(f) = -18*f**2 + 19*f + 54. Let g(h) = -8*h**2 + 9*h + 26. Let r(l) = -7*g(l) + 3*j(l). Factor r(d).
2*(d - 5)*(d + 2)
Let d(v) = -2956*v + 11827. Let c be d(4). Suppose -14/19*n**2 - 2/19*n**c + 2/19*n + 14/19 = 0. Calculate n.
-7, -1, 1
Let w(b) = -b**2 - 9*b - 18. Let l be w(-6). Let q(y) be the second derivative of 0*y**2 + l + 5/18*y**3 + 1/36*y**4 + 2*y. What is h in q(h) = 0?
-5, 0
Let u(o) be the second derivative of 19773*o**7/70 + 18252*o**6/25 - 4446*o**5/25 + 232*o**4/15 - 8*o**3/15 + 2*o - 259. Suppose u(b) = 0. What is b?
-2, 0, 2/39
Let g(v) be the third derivative of -v**7/105 + 43*v**6/20 - 64*v**5/15 + 317*v**2. Factor g(l).
-2*l**2*(l - 128)*(l - 1)
Let g = 7713/8 + -965. Let h = 53/40 - g. Find f such that -h*f + 0 + 1/5*f**2 = 0.
0, 11
Let v(s) = -s**2 - 41*s - 123. Let d be v(-39). Let r be (-1 - -1)/((-15)/(d/(-12))). Factor 0*j**2 + 2/7*j**3 + r - 2/7*j.
2*j*(j - 1)*(j + 1)/7
Let d(n) be the third derivative of 4/9*n**4 + 16/9*n**3 + 0*n - 1/40*n**6 - 1/30*n**5 - 178*n**2 + 0. Factor d(c).
-(c - 2)*(3*c + 4)**2/3
What is x in 290107737/5 + 3/5*x**3 + 4131/5*x**2 + 1896129/5*x = 0?
-459
Let g(j) be the second derivative of 2*j**7/21 + 4*j**6/3 - 276*j**5/5 + 1390*j**4/3 - 2650*j**3/3 - 6000*j**2 + 8280*j. Factor g(x).
4*(x - 5)**3*(x + 1)*(x + 24)
Suppose 1/3*a**5 + 100/3*a**2 + 0 - 4/3*a**4 - 100/3*a - 7*a**3 = 0. What is a?
-5, 0, 2, 5
Suppose 7*p = -133 + 147. Factor -9*q**p - 11*q**2 - 12*q**2 - 11*q**2 + 78*q - 148 + 41*q**2.
-2*(q - 37)*(q - 2)
Let p be 14*(208/(-28) + 4)/1. Let s = 145/3 + p. Factor -5/3 + s*x**2 + 4/3*x.
(x - 1)*(x + 5)/3
Let p(g) be the first derivative of 5*g**4/4 - 260*g**3/3 + 255*g**2/2 + 3411. Factor p(h).
5*h*(h - 51)*(h - 1)
Let c = 3/3050 - -758/4575. Let g(q) be the second derivative of 1/3*q**2 + 0 - c*q**3 + 18*q + 1/60*q**5 + 0*q**4. Solve g(h) = 0.
-2, 1
Suppose 0 = -2*z + 2*n, z + 202*n - 200*n - 12 = 0. Let s(h) = 3*h**2 + h - 2. Let v be s(-2). Factor 95*f**z - 4*f - 32*f**2 + 55*f**3 + v*f - 59*f**4.
f*(f + 2)*(4*f - 1)*(9*f - 2)
Let x be (608/133)/(25/(875/60)). Suppose -4/3*m**5 + 0 - 12*m**3 - x*m - 28/3*m**2 - 20/3*m**4 = 0. Calculate m.
-2, -1, 0
Let w be (-51)/(-63) + (6/(-4))/(162/(-36)). Factor w - 12/7*s**3 - 16/7*s**2 + 4/7*s.
-4*(s + 1)**2*(3*s - 2)/7
Suppose 0 = -4*w - 3*b + 27, -w - 30 = -5*b - 8. Find f, given that -20*f + 5*f + 11 - 15*f**w - 21 + 0*f**2 + 40*f**2 = 0.
-1/3, 1, 2
Let p(y) be the third derivative of -y**7/735 + 17*y**6/420 + 2*y**5/7 + y**4/21 - 80*y**3/21 - 1229*y**2 - 2. Suppose p(i) = 0. What is i?
-2, 1, 20
Let u = 741919/5070 + -3/1690. Let l = u + -146. Factor l*m**2 + 1/3*m + 0 - 2/3*m**3.
-m*(m - 1)*(2*m + 1)/3
Suppose 0 = -y - b + 6, -y - 12*b + 10 = -15*b. Suppose -y*q + 20*q = 117. Suppose 32/7*h + 4/7 + q*h**2 = 0. Calculate h.
-2/7, -2/9
What is x in 0 - 3/4*x**4 + 255/4*x**2 - 12*x**3 + 75*x = 0?
-20, -1, 0, 5
Let t(k) = k**2 - 70*k + 904. Let s be t(53). Let q(p) be the first derivative of -2/3*p**3 + 4*p**2 - 8*p + s. Factor q(l).
-2*(l - 2)**2
Suppose 382/9*u**2 + 30 + 4/9*u**4 - 238/3*u - 70/9*u**3 = 0. Calculate u.
1/2, 3, 5, 9
Let k be (-1200)/(-180)*18/(-10) - -14. Let w(d) be the second derivative of -1/10*d**5 + 0*d**k + 0 + 1/6*d**4 + 2/3*d**3 - 6*d. Find f, given that w(f) = 0.
-1, 0, 2
Let p(q) be the second derivative of -129*q**4/28 - 383*q**3/42 + 2*q**2/7 + 1557*q + 3. Find l such that p(l) = 0.
-1, 4/387
Let f(m) be the first derivative of -14*m**5/45 - 17*m**4/6 + 56*m**3/27 + 172*m**2/3 + 32*m - 1196. Suppose f(r) = 0. What is r?
-6, -4, -2/7, 3
Let r(j) = 2*j**3 + j**2 - 2. Let c(s) = 21*s**3 + 7*s**2 - 13*s - 12. Suppose -4*d + 3*d = -2*f + 3, -18 = -4*f - 2*d. Let m(u) = f*r(u) - c(u). Factor m(y).
-(y - 1)*(3*y + 2)*(5*y + 3)
Let d(h) = 7*h**4 + 130*h**3 + 332*h**2 + 109*h + 13. Let k(f) = 3*f**4 + 65*f**3 + 166*f**2 + 54*f + 6. Let i(a) = 6*d(a) - 13*k(a). Find o such that i(o) = 0.
-2, -1/3, 0, 24
Let h = 41/3583 - -3255/28664. Factor 529/2 + 23/2*l + h*l**2.
(l + 46)**2/8
Suppose 0 = -16*j + 4*j + 24. Factor -8*w + 7*w**j - 6026*w**3 + 6046*w**3 + 5*w**2.
4*w*(w + 1)*(5*w - 2)
Let b = -28770 + 28770. Let o(y) be the third derivative of b*y + 0 + 1/270*y**5 - 39*y**2 + 0*y**3 + 1/54*y**4. Factor o(u).
2*u*(u + 2)/9
Let t = 164 + -161. Suppose 11*r + 57*r + 34*r - 867 - t*r**2 = 0. Calculate r.
17
Let m(a) = 13*a**3 + 69*a**2 + 1591*a + 12167. Suppose 7*k = -3 - 25. Let n(l) = 36*l**3 + 207*l**2 + 4772*l + 36501. Let c(p) = k*n(p) + 11*m(p). Factor c(g).
-(g + 23)**3
Let z = 1984453/5 - 396890. Find w, given that 0 + 3/5*w**5 - 9/5*w**3 + 3/5*w**2 + 6/5*w - z*w**4 = 0.
-1, 0, 1, 2
Let h(a) be the third deriv