l?
-1/3, 2/5
Let w = 159 + -34. Let z = w - 54. Factor -4*k**3 - z*k**4 - 75*k**4 + 0*k**5 - 4*k**5 + 138*k**4.
-4*k**3*(k + 1)**2
Let k(y) be the third derivative of -y**6/5 - 126*y**5/5 + y**4/16 + 63*y**3/4 + 2*y**2 + 1232*y. Find b, given that k(b) = 0.
-63, -1/4, 1/4
Let -2/11*x**4 - 1406080/11 - 322/11*x**3 - 362336/11*x - 17784/11*x**2 = 0. What is x?
-52, -5
Let o be 392/2940 - (2/(-5)*1)/(-12). Let b(x) be the third derivative of -1/2*x**3 - 1/8*x**4 - 3*x**2 + 0*x + o*x**5 + 0. What is w in b(w) = 0?
-1/2, 1
Let o be (-5)/((-10)/18)*281/12645. Factor -o*i**3 + 3*i**2 - 14/5*i + 0.
-i*(i - 14)*(i - 1)/5
Let j = -1612 + 16123/10. Let b(m) be the second derivative of j*m**5 + 0*m**2 + 0 + 1/4*m**4 + 0*m**3 - 13*m. Suppose b(r) = 0. What is r?
-1/2, 0
Suppose 0 = -6*o + 4 + 8. Factor -o*u - 6*u + 92395*u**4 - 12*u**2 - 92391*u**4.
4*u*(u - 2)*(u + 1)**2
Suppose -6*r - 13 = -37. Let -31*t**3 + 18*t**r + 77*t - 2 + 71*t + 6*t**2 - 139*t = 0. What is t?
-1/2, 2/9, 1
Factor 10 - 62/9*b - 26/9*b**2 - 2/9*b**3.
-2*(b - 1)*(b + 5)*(b + 9)/9
Let o = -42/50423 - -252199/100846. Determine u so that 6 - 1/2*u**5 - 3/2*u**3 - o*u**4 + 14*u + 17/2*u**2 = 0.
-3, -2, -1, 2
Let l(w) = 88*w**3 + w**2 - 18*w + 35. Let k be l(2). Let d = k + -703. Factor 0*u**3 + 12/7*u**d + 0*u - 16/7*u**2 + 4/7*u**5 + 0.
4*u**2*(u - 1)*(u + 2)**2/7
Suppose -3138*m + 6509 = -2905. Solve 0 + 1/3*p**m + 8/3*p**2 + 0*p = 0 for p.
-8, 0
Let z = -1040/707 - -172052/3535. Solve 476/5*h + z + 8/5*h**2 = 0 for h.
-59, -1/2
Let y(p) be the second derivative of 36*p**2 + 1/4*p**4 + 0 + 74*p - 11/2*p**3. Factor y(v).
3*(v - 8)*(v - 3)
Let p(f) be the first derivative of f**6/9 + 4*f**5/5 + 4*f**4/3 - 4*f**3/3 - 3*f**2 - 1090. What is n in p(n) = 0?
-3, -1, 0, 1
Let w(t) = -t**4 - t**2 + 2*t + 2. Let j(n) = n**4 - 76*n**3 - 933*n**2 - 3386*n + 4388. Let g(m) = -2*j(m) - 6*w(m). Determine k so that g(k) = 0.
-13, 1
Let m(s) be the first derivative of -13/20*s**5 + 1/4*s**4 + 0*s**2 + 0*s + 5/24*s**6 + 1/3*s**3 + 35. What is c in m(c) = 0?
-2/5, 0, 1, 2
Let a(y) = y**3 - 145*y**2 + 3542*y - 910. Let h be a(114). Find w, given that 0 - h*w - 1/3*w**2 + 1/3*w**3 = 0.
-2, 0, 3
Let k(f) be the first derivative of 0*f - 41/16*f**4 - 1/20*f**5 - 50*f**2 - 73 - 110/3*f**3. What is i in k(i) = 0?
-20, -1, 0
Suppose 5*g - 6 = 2*g + 2*o, 12 = -2*g - 4*o. Suppose -5*d = 4*u + 6, 4*d + 8*u - 7*u - 4 = g. Solve 240*k + 184*k**d + 12 + 15 + 216*k**2 + 9 = 0 for k.
-3/10
Factor 480 + 835*i**2 + 32990*i**4 + 185*i**3 - 32985*i**4 - 237*i + 1372*i.
5*(i + 1)**2*(i + 3)*(i + 32)
Let l = -235 - -237. Determine b so that 2*b - 3*b**l + 2*b**2 - 12*b - 3*b = 0.
-13, 0
Let t(j) be the second derivative of -j**4/4 - 25*j**3/2 - 99*j**2 - 949*j. Factor t(h).
-3*(h + 3)*(h + 22)
Suppose -45*o + 27 = -36*o. Let l(d) be the first derivative of 0*d**2 + 0*d + 14 - 3/4*d**4 + 0*d**o. Determine w so that l(w) = 0.
0
Determine c so that 2*c**3 - c**3 - 1096 - 337*c + 302*c - 24757*c**2 - 1057*c + 24487*c**2 = 0.
-2, 274
Let w(c) be the second derivative of 0*c**2 + 38*c + 0 - 1/72*c**4 - 7*c**3 + 0*c**5 + 1/1080*c**6. Let x(f) be the second derivative of w(f). Factor x(t).
(t - 1)*(t + 1)/3
Let z(c) be the second derivative of -c**7/147 + 37*c**6/105 - 43*c**5/7 + 611*c**4/21 + 3887*c**3/21 + 2197*c**2/7 + 8*c + 18. Suppose z(n) = 0. Calculate n.
-1, 13
Let q be (1/(-4)*(59 - 57))/(50/(-180)). Factor -3*p**2 - q*p**4 + 3/5*p + 0 + 21/5*p**3.
-3*p*(p - 1)**2*(3*p - 1)/5
Let t(a) = -2*a + 12. Let r be t(3). Suppose 24 = 5*z - 3*l, -3*z + 0*z + 2*l + 15 = 0. Factor -3*p**z - r*p**2 + 2*p**2 - 9*p + 7*p**3 + p.
4*p*(p - 2)*(p + 1)
Let t(b) be the first derivative of 10/3*b**3 - 1/2*b**4 + 0*b + 1/3*b**6 - 2*b**5 + 0*b**2 - 169. Find z, given that t(z) = 0.
-1, 0, 1, 5
Let y(j) = -16*j**2 - 1029*j + 4792. Let p(q) = -3*q**2 - 201*q + 958. Let u(k) = -11*p(k) + 2*y(k). Suppose u(h) = 0. What is h?
-159, 6
Let o(y) = y**3 - 16*y**2 - 17*y + 3. Let w be o(17). What is c in -4*c**w + 15*c**2 + 3*c + 13*c - 6*c**2 + 3*c**2 = 0?
-1, 0, 4
Let b(q) be the third derivative of q**5/20 + 71*q**4/8 + 69*q**3 - 2425*q**2. Find n, given that b(n) = 0.
-69, -2
Let 36*r**3 - 280 - 5*r**5 - 248*r**2 + 60*r**4 - 372*r**2 - 765*r - 45*r**3 - 61*r**3 = 0. What is r?
-1, 7, 8
Let h be (-2)/6 - (-9 + (-140)/(-21)). Let 52*p**h - 4035*p + 4083*p + 0*p**4 + 4*p**4 + 24*p**3 + 16 = 0. What is p?
-2, -1
Let k be (14/(-2814))/((-1)/(-45)). Let z = 142/335 + k. Factor 0*x - 1/5*x**5 - z*x**2 + 0 - 3/5*x**3 - 3/5*x**4.
-x**2*(x + 1)**3/5
Let o(l) = -7*l + 1. Let d(a) = -2*a + 1. Let w(s) = -22*d(s) + 6*o(s). Let g be w(9). Let 1/4*x - 13/8*x**3 + 0 - 9/4*x**4 + 7/8*x**g = 0. What is x?
-1, -2/9, 0, 1/2
Let z be (42*9/54 - (8 + -1))/(-2). Let d(f) be the third derivative of 0*f**3 + 0 - 22*f**2 + 1/3*f**4 - 1/15*f**6 + 7/15*f**5 + z*f - 2/15*f**7. Factor d(b).
-4*b*(b - 1)*(b + 1)*(7*b + 2)
Let r = -418/3 + 141. Let s be (-28)/(-9)*((-2526)/42 + 61). Solve 4/3 + r*c**2 - 1/3*c**3 - s*c = 0 for c.
1, 2
Let 1/10*t**5 - 534/5 - 184/5*t + 19/2*t**4 + 543/10*t**3 + 797/10*t**2 = 0. What is t?
-89, -3, -2, 1
Let q(l) be the first derivative of l**4/32 - 23*l**3/8 - 71*l**2/8 + 207. Factor q(y).
y*(y - 71)*(y + 2)/8
Let r(y) be the second derivative of -1/3*y**3 + 2 + 1/6*y**4 + 17*y + 0*y**2. Suppose r(p) = 0. Calculate p.
0, 1
Factor -6*v**2 + 2/9*v**3 + 34/3*v - 50/9.
2*(v - 25)*(v - 1)**2/9
Let w(g) be the second derivative of g**7/4200 + g**6/225 + 13*g**5/600 + g**4/20 - 11*g**3/6 + 62*g. Let c(p) be the second derivative of w(p). Factor c(o).
(o + 1)**2*(o + 6)/5
Suppose -2*f = -3*u - 45, -4*u - u + 14661 - 14616 = 0. Factor 72 + 1/3*d**3 + f*d + 6*d**2.
(d + 6)**3/3
Factor -116*i**2 - 1560*i**2 - 64*i**2 + 2191*i - 7935 - 5*i**4 + 5462*i - 210*i**3 + 2237*i.
-5*(i - 3)*(i - 1)*(i + 23)**2
Suppose 176*w = 175*w + 3. Factor 4*r + r**2 - 4*r**w + 38*r**2 - 16 - 23*r**2.
-4*(r - 4)*(r - 1)*(r + 1)
Suppose 465*t - 470*t = -2*n + 9, -6*n + 57 = -5*t. Factor 1/9*y**5 + 0*y + 0 + 5/9*y**4 + 4/9*y**2 + 8/9*y**t.
y**2*(y + 1)*(y + 2)**2/9
Let t(w) be the first derivative of -w**6/10 + 12*w**5/25 + 9*w**4/4 - 18*w**3/5 + 777. Let t(h) = 0. What is h?
-3, 0, 1, 6
Let d(y) = -58*y**2 - 96920*y - 117418618. Let p(t) = 12*t**2 + 19384*t + 23483724. Let f(u) = 4*d(u) + 19*p(u). Factor f(i).
-4*(i + 2423)**2
Let t be 24/(-10)*(7105/147 + -50). Determine q, given that -43/10*q**2 - 29/10*q**3 + 13/10*q**t + 3/5*q**5 - 1/10*q + 3/5 = 0.
-3, -1, -1/2, 1/3, 2
Let c be ((-9735)/3770)/((12/16)/(-1)). Let o = c + -82/29. Factor -2/13*h**4 - 6/13*h**3 + 0*h**2 + o*h + 0.
-2*h*(h - 1)*(h + 2)**2/13
Let x = -468/29 - -18749/1160. Let o(r) be the third derivative of 9/100*r**5 + 1/5*r**3 + 0*r + x*r**6 + 0 + 1/350*r**7 + 13*r**2 + 7/40*r**4. Factor o(n).
3*(n + 1)**3*(n + 2)/5
Let q(y) be the first derivative of 1/2*y**4 - 6*y**2 + 1/27*y**6 + 0*y + 47 + 14/45*y**5 - 2*y**3. Factor q(r).
2*r*(r - 2)*(r + 3)**3/9
Let b be ((-50)/8)/((-40)/64). Factor 16*o**2 + 0 + 2*o**4 + b*o**3 + 112*o - 104*o + 0.
2*o*(o + 1)*(o + 2)**2
Let p(b) be the third derivative of 5*b**8/12 - 818*b**7/105 + 103*b**6/5 - 284*b**5/15 + 20*b**4/3 - 1424*b**2. Let p(i) = 0. What is i?
0, 2/7, 2/5, 1, 10
Let t(b) be the first derivative of 1/9*b**3 + 0*b - 4 + 1/3*b**2. Factor t(i).
i*(i + 2)/3
Let t(k) be the third derivative of -k**5/270 + 193*k**4/108 + 110*k**3/3 - 8*k**2 - 299*k + 1. Find y, given that t(y) = 0.
-5, 198
Let y(x) be the third derivative of 7*x**6/24 + 2*x**5 - 305*x**4/24 - 25*x**3 - 2*x**2 + 483*x. Factor y(k).
5*(k - 2)*(k + 5)*(7*k + 3)
Let h(m) be the first derivative of -18/25*m**5 + 24/5*m**2 + 3/5*m**4 + 24/5*m**3 - 1/5*m**6 - 89 + 0*m. Solve h(p) = 0 for p.
-2, -1, 0, 2
Let h(t) be the second derivative of -t**7/42 + 53*t**6/10 - 312*t**5 - 1600*t**4/3 - 2*t - 293. Solve h(u) = 0 for u.
-1, 0, 80
Let a(y) be the third derivative of 0 - 185/24*y**4 + 73/420*y**5 + 62*y**2 + 0*y - 1369/42*y**3 - 1/840*y**6. Factor a(r).
-(r - 37)**2*(r + 1)/7
Let v be -3 - (-121)/60 - (47 - 48). Let f(l) be the third derivative of -v*l**6 + 0*l - 22*l**2 + 0 + 2/3*l**3 + 1/4*l**4 + 0*l**5. Solve f(k) = 0.
-1, 2
Factor 2*y**4 - 5*y**4 - 207024*y + 5130 + 908*y**3 - 102146*y**2 - 48218 + y**4