 2)*(o + 1)*(o + 2)/2
Factor 628*u**3 + 1857*u**2 + 3*u**4 + 6*u**4 + 314*u**3 + 924*u.
3*u*(u + 1)**2*(3*u + 308)
Let z(u) be the third derivative of 19/30*u**6 + 1372/3*u**3 + 49/6*u**4 - 7*u**5 - 32*u + 0 + 2*u**2 - 2/105*u**7. Let z(i) = 0. Calculate i.
-2, 7
Let a be ((-26)/(-24))/(19422/13446). Factor a*j**4 + 6*j - 15/4*j**3 + 3/2*j**2 + 0.
3*j*(j - 4)*(j - 2)*(j + 1)/4
Let b = -568225 + 568609. Factor b + 75/4*j**3 + 3/4*j**4 + 528*j + 162*j**2.
3*(j + 1)*(j + 8)**3/4
Let h(w) = -w**3 - 14*w**2 - 3*w - 44. Let g be h(-14). Let l be 5*64/(-40)*g/4. Find v, given that 1/4*v**l + 1/4 + 3/2*v**2 + v + v**3 = 0.
-1
Let z(a) be the second derivative of a**7/252 - a**6/60 - a**5/120 + a**4/24 - 2224*a. Determine p so that z(p) = 0.
-1, 0, 1, 3
Determine c so that 40/3*c - 400/3 - 1/3*c**2 = 0.
20
Find j, given that -358 + 184383*j - 117*j**2 + 106 - 184011*j - 3*j**3 = 0.
-42, 1, 2
Let y = 43/39 + -10/13. Let o be (-2552)/(-5104)*0/3. Factor -1/6*c - 1/6*c**3 + o - y*c**2.
-c*(c + 1)**2/6
Suppose 3*z + 3*q - 60 = -q, 5*q - 63 = -3*z. Suppose -20*o + z*o = 0. Let 0*h - 6*h**3 - 3/4*h**5 + o + 3*h**2 + 15/4*h**4 = 0. What is h?
0, 1, 2
Let w(a) be the second derivative of -6*a - 3/2*a**2 + 25/12*a**3 + 0 + 3/8*a**4. Find i such that w(i) = 0.
-3, 2/9
Factor 1/2*c + 0 - 5/2*c**3 + 2*c**2.
-c*(c - 1)*(5*c + 1)/2
Let z(m) be the first derivative of -4*m**2 + m + 5/4*m**3 - 45. Factor z(s).
(s - 2)*(15*s - 2)/4
Let w = 223 - 219. Suppose 9*f - 4*f**2 - 33*f - 12 + 12*f + w = 0. Calculate f.
-2, -1
Let c(i) = -3*i**3 + i + 1. Let q be c(-1). Factor -2*f**4 - q*f**4 - 16*f**2 + 9*f**4 + 0*f**4.
4*f**2*(f - 2)*(f + 2)
Let r be (22/4015)/((-3)/6). Let z = r - -1123/2555. Suppose -z*p**4 + 3/7*p**2 - 3/7*p**3 + 0 + 3/7*p = 0. What is p?
-1, 0, 1
Let j = 1918 - 1898. Let r = 5 - 0. Let p(i) = i**4 + i**2. Let b(o) = -5*o**4 + o**2 - 4. Let x(z) = j*p(z) + r*b(z). Determine v so that x(v) = 0.
-2, -1, 1, 2
Factor -56/13*d - 48/13 - 20/13*d**2 - 2/13*d**3.
-2*(d + 2)**2*(d + 6)/13
Factor -15/7*l**3 + 1/7*l**4 + 0 + 75/7*l**2 - 125/7*l.
l*(l - 5)**3/7
Let a(c) be the third derivative of 0 - 2/105*c**7 - 4*c + 85/6*c**4 + 100*c**3 - 3/10*c**6 - 3/5*c**5 - 2*c**2. Factor a(z).
-4*(z - 3)*(z + 2)*(z + 5)**2
Let o(v) = -5*v**2 + 294*v + 903. Let b(l) = -10*l**2 + 591*l + 1807. Let x(m) = -3*b(m) + 7*o(m). Factor x(s).
-5*(s - 60)*(s + 3)
Let r(b) be the first derivative of 4*b**5/5 - b**4 - 224*b**3/3 - 124. Determine v, given that r(v) = 0.
-7, 0, 8
Let s = -16 + 22. Let a be (-42)/(-126) - 1*(-10)/s. Factor -81*r + 5*r**a + 13*r + 3*r.
5*r*(r - 13)
Let j be (10/(-4))/(((-9690)/(-136))/(-57)). Let r(w) be the third derivative of -1/24*w**4 + 0*w + 25*w**j + 1/180*w**5 + 0 + 1/9*w**3. Factor r(b).
(b - 2)*(b - 1)/3
Let a be 40/(-180) + (-83)/(-9) + 1. Factor 3*u - 4*u**4 - 11*u + 16*u**2 - 12 - a*u**3 + 18*u**3.
-4*(u - 3)*(u - 1)*(u + 1)**2
Factor 1/4*m**2 - 345/4 - 28*m.
(m - 115)*(m + 3)/4
Let i(k) be the third derivative of k**7/105 - 4*k**6/15 + 31*k**5/15 - 20*k**4/3 + 11*k**3 + 1595*k**2. Factor i(m).
2*(m - 11)*(m - 3)*(m - 1)**2
Let i be (-10299)/(-12) - (8 + -7). Let z = 864 - i. Factor 3/2 - 33/4*o**2 - z*o.
-3*(o + 1)*(11*o - 2)/4
Let c be (-65)/(-195) + (-190)/(-6). Suppose 1018 - 890 = c*m. Factor 3/5*r**3 + 0*r**2 + 3/5*r**5 + 0*r - 6/5*r**m + 0.
3*r**3*(r - 1)**2/5
Let h be (4 - 1375/340)/((-3)/5). Let x = h + 179/340. Factor 0 + 1/5*p**3 + 2/5*p + x*p**2.
p*(p + 1)*(p + 2)/5
Let i(s) be the third derivative of 2*s**2 - 1/30*s**5 + 0 + 1/2*s**4 + 7/3*s**3 + 25*s. Factor i(x).
-2*(x - 7)*(x + 1)
Let h(r) be the first derivative of r**6/12 - 11*r**4/8 + r**3 + 7*r**2 - 12*r - 1850. What is l in h(l) = 0?
-3, -2, 1, 2
Let r = 149 - 146. Find j, given that 3*j**4 - 30*j**r + 46*j**3 + 3*j**5 + 9*j**2 - 31*j**3 = 0.
-3, 0, 1
Let l be ((-13)/(-195))/(12/120). Let r(q) be the first derivative of -l*q**2 + 2/3*q + 2/9*q**3 + 10. Find s such that r(s) = 0.
1
Let h be (10/(-20))/(3/(-534)). Let i = -72 + h. Solve -40*r**4 + 48*r + 10 + 3*r**3 + i*r + 3*r**3 + 4*r**3 + 105*r**2 = 0 for r.
-1, -1/2, -1/4, 2
Let d(u) be the second derivative of 2048*u**2 + 107*u**4 - 190*u - 2176/3*u**3 + 0 - 17/5*u**5 + 1/30*u**6. Suppose d(o) = 0. Calculate o.
2, 32
Factor -14 + 38 + 18*l + 15*l**2 - 4*l**3 - 23*l**2 + 2*l.
-4*(l - 2)*(l + 1)*(l + 3)
Suppose 14*c + 60 = 10*c + 4*t, -t + 15 = 0. Find z, given that -1/7*z**2 + c - 26/7*z = 0.
-26, 0
Let o = 569692 + -569690. Determine j, given that -1/2*j**3 - 11/2*j**o + 11/2 + 1/2*j = 0.
-11, -1, 1
Let c be -7*(-36)/168*18. Let x(h) be the second derivative of -c*h + 10/39*h**3 + 25/13*h**2 + 1/78*h**4 + 0. What is f in x(f) = 0?
-5
Let k(y) = 50*y**4 + 1694*y**3 - 349494*y**2 + 693836*y - 346164. Let g(j) = -2*j**4 - j**3 + 2*j**2 + 2*j + 2. Let t(z) = 52*g(z) + 2*k(z). Factor t(o).
-4*(o - 416)**2*(o - 1)**2
Let a(o) be the third derivative of -o**7/630 + 4*o**6/45 - 16*o**4/3 + 28*o**2 - o. Let p(z) be the second derivative of a(z). Factor p(m).
-4*m*(m - 16)
Let l(a) be the first derivative of -1/32*a**4 + 12167*a - 1587/4*a**2 + 147 + 23/4*a**3. Find p, given that l(p) = 0.
46
Let r = -12 - -10. Let z be 1 + (-2 + r - (-244)/76). Solve -12/19*b**2 + z - 14/19*b + 14/19*b**3 + 8/19*b**4 = 0.
-2, -1, 1/4, 1
Factor 5439*k - 5514*k - 29 + 92 + 9*k**2 + 3*k**3.
3*(k - 3)*(k - 1)*(k + 7)
Let o(r) = r**2 + 433*r - 1614. Let n(g) = 72*g - 270. Let w(h) = -17*n(h) + 3*o(h). Factor w(b).
3*(b - 3)*(b + 28)
Let f = -2/659 + 13843/1318. What is a in f*a**3 + 51/2*a - 51/2*a**2 - 9 - 3/2*a**4 = 0?
1, 2, 3
Let d(k) = -k**2 + 41. Let z be d(-6). Let q(g) = -5*g**2 + 4*g - 3. Let u(x) = -1 + 0*x**2 + 0*x**2 + x - x**2. Let n(m) = z*q(m) - 20*u(m). Factor n(p).
-5*(p - 1)*(p + 1)
Let y(t) be the second derivative of 5*t**7/42 + 13*t**6/6 + 55*t**5/4 + 515*t**4/12 + 220*t**3/3 + 70*t**2 + 3376*t. Let y(f) = 0. Calculate f.
-7, -2, -1
Let m(s) be the first derivative of 40*s**3/27 - 82*s**2/9 + 56*s/3 - 206. Let m(v) = 0. Calculate v.
2, 21/10
Let r(w) = w**2 + 4*w + 2. Let c be r(-4). Suppose 0 = 4*n - 20, -2*t + c*n + 21 = 5*n. Solve -7 + 13 + t*k**3 + 12*k**2 + 20*k - 5*k = 0 for k.
-2, -1
Let t = 7788/5 + -256973/165. Let l = t + 7/33. Factor l + 1/5*p - 1/5*p**2.
-(p - 2)*(p + 1)/5
Let v = 271423/4 + -135701/2. Factor -9/4*q**3 + v*q + 1/4*q**4 + 11/4*q**2 + 0.
q*(q - 7)*(q - 3)*(q + 1)/4
Let v(u) be the first derivative of -4/7*u**2 + 15*u + 5/21*u**3 - 1/42*u**4 + 7. Let g(k) be the first derivative of v(k). Let g(m) = 0. What is m?
1, 4
Let n(y) be the third derivative of 23*y**6/480 + y**5/40 - 23*y**4/96 - y**3/4 + 1058*y**2 + 2*y. Determine g, given that n(g) = 0.
-1, -6/23, 1
Determine l so that -2/19*l**4 - 1452/19*l**2 + 112/19*l**3 - 1682/19 - 3248/19*l = 0.
-1, 29
Factor -8*j**2 + 112/15*j + 12/5*j**3 - 2/15*j**4 + 0.
-2*j*(j - 14)*(j - 2)**2/15
Suppose 3644 = -19*r + 3644. Let a(f) be the third derivative of 3/5*f**3 + r + 7/150*f**5 + 1/4*f**4 + 1/300*f**6 - 6*f**2 + 0*f. Factor a(i).
2*(i + 1)*(i + 3)**2/5
Suppose 0 = 2*n + 10*n - 24. Determine r, given that 75*r**5 - 11*r**2 - 9*r**2 + 55*r**4 - n + 2 - 40*r**3 = 0.
-1, -2/5, 0, 2/3
Let p(o) be the first derivative of -o**6/3 + 2*o**5 + 15*o**4/2 - 10*o**3/3 - 14*o**2 - 539. Suppose p(n) = 0. What is n?
-2, -1, 0, 1, 7
Factor 2/5*i**2 - 1584/5 - 52/5*i.
2*(i - 44)*(i + 18)/5
Suppose 2*a - 294 = 16*a. Let y be (-45)/9 - a/4. Solve -z + 3/4*z**2 + y*z**3 + 0 = 0.
-4, 0, 1
What is r in 12*r**2 + 0*r - 1/5*r**4 - 17/5*r**3 + 0 = 0?
-20, 0, 3
Factor 17/2*z**2 + 1/2*z**3 + 104 - 113*z.
(z - 8)*(z - 1)*(z + 26)/2
Suppose -3*v + 753 = 4*u, -3*v + 2*v = 2*u - 253. What is q in -123*q**3 + v*q**3 - 123*q**3 + 5*q**2 = 0?
-5, 0
Let u(b) be the first derivative of -142 + 5*b**3 - 27/4*b**4 + 1/2*b**6 + 0*b**2 + 9/5*b**5 + 0*b. Suppose u(w) = 0. Calculate w.
-5, 0, 1
Let i = 32248/9 + -32246/9. Determine k so that -i*k**3 + 14/9*k**2 - 28/9*k + 16/9 = 0.
1, 2, 4
Solve -1/3*n**3 - 2660/3*n + 124/3*n**2 - 78400/3 = 0.
-16, 70
Let v be 4 + -1 + 0/(1/1). Determine g, given that -g + 20*g**2 - 12*g**v + 20*g - 11*g = 0.
-1/3, 0, 2
Factor 372*t - 1295735*t**3 - 565*t**2 + 4 + 2591630*t**3 - 1295706*t**3.
(t - 2)*(t - 1)*(189*t + 2)
Factor -8/5*k**2 + 0*k - 44402/5*k**4 + 0 - 1192/