- 1/60*q**6 - 1/3*q**3 + 38*q + q**2 + 0. Factor r(t).
-(t - 2)**2*(t - 1)*(t + 1)/2
Let h(o) = 2*o**2 - 13*o - 22. Let j = -270 + 278. Let d be h(j). Factor 1/2 + w**d + 9/4*w.
(w + 2)*(4*w + 1)/4
Let g(q) be the second derivative of 0 - q**5 + 1/2*q**6 + 6*q + 0*q**2 + 0*q**3 + 0*q**4 + 5/42*q**7. Let g(z) = 0. What is z?
-4, 0, 1
Suppose -3*g = -2*g, 2*u - 10 = 2*g. Solve -18*h**u + 21*h**5 + 107*h**4 - 104*h**4 = 0.
-1, 0
Suppose l = 4*u + 45, -4*l + 3*u + 18 = -123. Suppose -l*d**2 - 16 + 169 - 63 - 405*d + 85*d**2 - 20*d**3 + 133*d**2 = 0. Calculate d.
1/4, 3, 6
Let t(p) be the second derivative of -93*p**5/20 - 2*p**4/3 + 10540*p. Factor t(i).
-i**2*(93*i + 8)
Let a(c) be the third derivative of c**6/360 + c**5/18 + 2*c**4/9 + 110*c**2 - 4. Factor a(j).
j*(j + 2)*(j + 8)/3
Let o be (84/98)/(83/(-42) - -2). Suppose 88 = -14*g + o*g. Suppose 3/2*f**5 + 27/8*f**g - 21/4*f**3 + 15/4*f - 9/2*f**2 + 9/8 = 0. What is f?
-3, -1, -1/4, 1
Factor -110/3*u**2 - 2/3*u**3 - 36*u + 0.
-2*u*(u + 1)*(u + 54)/3
What is p in 27/5 + 1/5*p**2 + 28/5*p = 0?
-27, -1
Factor 267*b**4 - 1250*b**3 + 332313*b**2 - 266*b**4 + 58312*b**2.
b**2*(b - 625)**2
Let t(q) be the second derivative of q**5/12 - 25*q**4/8 + 35*q**3/3 + 105*q**2/2 + 4*q - 4. Let r(v) be the first derivative of t(v). Let r(x) = 0. What is x?
1, 14
Let q be (13/(104/(-240)))/(-2). Suppose 9*u = -5*w + 14*u - q, u - 13 = -4*w. Factor 10/7 - 2/7*i**w - 8/7*i.
-2*(i - 1)*(i + 5)/7
Let y(w) be the first derivative of 0*w**3 + 0*w - 4 + 5/2*w**2 + 1/24*w**5 + 0*w**4 + 1/48*w**6. Let j(d) be the second derivative of y(d). Factor j(a).
5*a**2*(a + 1)/2
Let t be (0 - -52) + 20*(-6)/(-30). Let p be 25/21 + t/588. Suppose -3/7*g**3 - 9/7*g + p*g**2 + 3/7 = 0. What is g?
1
Suppose 9*g - 3*g = -g. Suppose g = 6*m - 13 - 5. Factor -c - 7*c**2 + 30*c**3 + 24*c**m - 2*c - 59*c**3 - c**4.
-c*(c + 1)**2*(c + 3)
Let r = 333 - -161. Let x = 1522/3 - r. Factor 20/3*z**4 - 50/3*z**3 - x*z**2 - 2/3*z**5 + 128/3 + 160/3*z.
-2*(z - 4)**3*(z + 1)**2/3
Let j(x) be the first derivative of -x**3/2 + 450*x**2 - 135000*x - 13064. Factor j(w).
-3*(w - 300)**2/2
Let j(n) be the third derivative of -n**5/210 + 13*n**4/14 + 79*n**3/21 - 3621*n**2. Determine a so that j(a) = 0.
-1, 79
Let l be (2/(-4))/(-2 + (-44)/(-24)). Suppose l*h - 19 = -4. Determine z, given that 4*z**3 + 8*z**4 - 5*z**3 + h*z**3 - 4*z**4 = 0.
-1, 0
Suppose -251*j + 249*j - 2*y = -36, -2*j + 84 = 5*y. Factor l**3 + 3*l**j - 4/3*l**4 + 2/3*l + 0.
-l*(l - 2)*(l + 1)*(4*l + 1)/3
Let x be (2/36)/((-36)/(-162)) + 3/(-12). Let v(w) be the third derivative of 1/40*w**5 + 17*w**2 + 9/4*w**3 + x*w - 3/8*w**4 + 0. Factor v(c).
3*(c - 3)**2/2
What is m in 161*m**2 - 48*m**2 - 114*m**2 + 1430 + 285*m + 428*m = 0?
-2, 715
Let n = -914 + 633. Let x = -281 - n. Find a, given that -2/3*a**3 + 1/3*a**2 + 1/3*a**4 + 0 + x*a = 0.
0, 1
Let f(t) = t - 1. Let u(o) = -3*o**3 + 84*o**2 - 526*o + 958. Let l(v) = -2*f(v) + u(v). Let l(i) = 0. Calculate i.
4, 20
Suppose -5*w = -w + 48. Let i(p) = p**3 + 13*p**2 + 13*p + 16. Let h be i(w). Find s such that 7*s**2 + 3*s - 531*s**3 + 2*s**2 + 540*s**3 + 3*s**h = 0.
-1, 0
Let -36/5*f**2 + 4/5*f**3 - 304/5*f + 336/5 = 0. Calculate f.
-6, 1, 14
Let 74892/7 - 99789/7*f**3 - 15/7*f**5 - 245283/7*f**2 - 10428*f - 2409/7*f**4 = 0. Calculate f.
-79, -2, -1, 2/5
Let x be 1292/9792 - 115/(-368). Factor 2/9*j + x - 2/9*j**2.
-2*(j - 2)*(j + 1)/9
Factor -9*h**3 - 197/4*h**2 - 41 - 81*h + 1/4*h**4.
(h - 41)*(h + 1)*(h + 2)**2/4
Let r(b) = 8*b**2 - 6 - 8*b - b**3 - 4*b + 9. Let v be r(6). Suppose 24 + 79*m - 35*m - 4 + 28*m**2 + 4*m**v = 0. What is m?
-5, -1
Let q(h) be the first derivative of 20/13*h**3 + 1/39*h**6 + 0*h**2 - 17/26*h**4 - 28/65*h**5 + 0*h - 195. Determine t so that q(t) = 0.
-2, 0, 1, 15
Let o(t) be the third derivative of 5/9*t**3 + 12*t**2 - 2/45*t**6 + 0 + 6*t + 1/5*t**5 - 4/9*t**4 + 1/315*t**7. Find g, given that o(g) = 0.
1, 5
Let w(q) be the third derivative of -1/24*q**6 - 5/12*q**5 + 0*q**4 + 2*q**2 + 53 + 0*q**3 + 0*q. Determine k so that w(k) = 0.
-5, 0
Let t(g) be the first derivative of 3*g**4/4 + 212*g**3/5 + 126*g**2/5 + 1338. Suppose t(m) = 0. What is m?
-42, -2/5, 0
Let l(z) be the second derivative of -10/39*z**3 + 0*z**2 + 54*z - 1/130*z**5 - 7/78*z**4 + 0. Suppose l(k) = 0. Calculate k.
-5, -2, 0
Let k(l) be the first derivative of -l**2/2 - 2*l - 1. Let j(z) = -25*z**2 - 28*z - 5. Let h(i) = j(i) + 2*k(i). Determine t so that h(t) = 0.
-3/5
Factor 32*g**4 + 10065*g**5 + 10057*g**5 - 12*g**4 - 20118*g**5 + 24*g**3.
4*g**3*(g + 2)*(g + 3)
Let r(c) be the second derivative of c**5/5 + 27*c**4/4 + 10*c**3/3 + 35*c - 30. Solve r(w) = 0.
-20, -1/4, 0
Let g(v) be the first derivative of -3*v**4/16 - 231*v**3 - 160083*v**2/2 - 5738. Find s such that g(s) = 0.
-462, 0
Let r(v) be the third derivative of 13*v**6/48 - 67*v**5/120 + v**4/24 - 1945*v**2. Factor r(f).
f*(f - 1)*(65*f - 2)/2
Let h(r) be the third derivative of 68*r + 0 - 1/3*r**5 - 1/24*r**6 + 5/8*r**4 + 15*r**3 + 2*r**2. Determine n, given that h(n) = 0.
-3, 2
Let f(c) = -c**3 - 13*c**2 - 35*c + 11. Let t(x) = -10*x - 29. Let j be t(-2). Let o be f(j). Factor -w**o - 3/2*w - 1/2.
-(w + 1)*(2*w + 1)/2
Suppose 3*u = -2*z + 24, -z + 18 = u + 4. Let s be 4/(-12) + z/27. Factor -s*f - f**4 + 1/3*f**3 + 0 + f**2.
-f*(f - 1)*(f + 1)*(3*f - 1)/3
Let n = 59487/2 - 29733. Factor n - 3/2*s**2 - 9*s.
-3*(s - 1)*(s + 7)/2
Let x be -10*-1*6/15. Let i(w) = -w**2 + 24*w + 25. Let b(t) = -8*t - 8. Let r(a) = x*i(a) + 14*b(a). Solve r(f) = 0 for f.
-3, -1
Let r be 2/(-4) - (-13)/(-26) - 19. Let i(p) = 3*p**3 - 11*p**2 - 7*p + 3. Let o(n) = -n**3 + 2*n**2 + n - 1. Let v(j) = r*o(j) - 5*i(j). Factor v(q).
5*(q + 1)**3
Let b = -10 + 79. Suppose 6*w + 45 = b. Factor 4/3*k**5 + 0 + 20/3*k**2 - 4/3*k**w - 4*k**3 - 8/3*k.
4*k*(k - 1)**3*(k + 2)/3
Let v(w) be the first derivative of 3*w**4/4 - 255*w**3 - 387*w**2 + 1536*w + 2617. Factor v(i).
3*(i - 256)*(i - 1)*(i + 2)
Let a = -424 - -426. Let 84*l**4 + 76*l**3 + 1296*l - 172*l**4 + 90*l**4 + 768*l**2 + 24*l**a = 0. What is l?
-18, -2, 0
Let f = -52 + 55. Determine q so that -10*q**4 + q + 12*q**f + 13*q**4 - 2*q + 15*q**2 + 7*q = 0.
-2, -1, 0
Suppose -5*n**4 + 3379*n**3 - 5784*n**3 + 2410*n**2 - 515*n + 515*n = 0. What is n?
-482, 0, 1
Let i(s) be the first derivative of 0*s + 2/3*s**3 - 5/12*s**4 - 1/5*s**5 - 38 + 4/3*s**2. Factor i(l).
-l*(l + 1)*(l + 2)*(3*l - 4)/3
Let k = 205168 + -205166. Find l such that 8 + 17/2*l + 1/2*l**k = 0.
-16, -1
What is w in -467046*w - 86870556 - 837*w**2 - 1/2*w**3 = 0?
-558
Suppose 51 - 22*u**2 - 78*u**3 + 225 - 114*u**2 + 82*u**3 - 2076 - 1940*u = 0. Calculate u.
-10, -1, 45
Let v = -124312 + 124314. Factor 16/11 + 1/11*u**4 - 3/11*u**v + 8/11*u**3 - 2*u.
(u - 1)**2*(u + 2)*(u + 8)/11
Let l(q) be the first derivative of -q**5/60 + 5*q**4/36 + q**3/18 - 5*q**2/6 - 36*q - 59. Let a(o) be the first derivative of l(o). Factor a(i).
-(i - 5)*(i - 1)*(i + 1)/3
Let i(w) be the third derivative of -w**8/1008 + w**7/105 + w**6/36 - 4*w**5/45 - 11*w**4/24 - 7*w**3/9 - 3052*w**2. Factor i(o).
-(o - 7)*(o - 2)*(o + 1)**3/3
Factor -30*y + 0 + 5/4*y**3 - 115/4*y**2.
5*y*(y - 24)*(y + 1)/4
Suppose -3*b + n + 3 = 0, 2*b - 1 = -3*n + 12. Suppose 3*f - 4*f = -b. Factor 45*c - 10*c**5 - 45*c + c**3 + f*c**5 - 2*c**4.
-c**3*(2*c + 1)*(4*c - 1)
Let a = 225 + -222. Suppose -7 = -a*q - 3*y + 4*y, -2*q + 5 = -y. Factor 0*s**3 - 2/11*s**4 + 4/11*s**q - 2/11 + 0*s.
-2*(s - 1)**2*(s + 1)**2/11
What is i in 4*i**2 - 140 - 282*i**2 + 302*i + 65*i**3 - 85*i + 23*i**2 - 5*i**4 + 118*i = 0?
1, 4, 7
Let a(w) be the second derivative of 0*w**2 + 11/6*w**4 + 0 + 10/3*w**3 + 1/10*w**5 + 53*w. Solve a(j) = 0.
-10, -1, 0
Solve 10*u**2 + 11*u**2 - 6*u**2 - 4*u**2 + 200*u + 2016 - 7*u**2 = 0 for u.
-36, -14
Let x(t) be the third derivative of -t**8/448 + t**7/35 - 9*t**6/160 - 9*t**5/40 - 326*t**2. Determine i so that x(i) = 0.
-1, 0, 3, 6
Suppose 2*u - 13 = -3*w, 0 = -2*u - 2*w + 220 - 210. Factor 0*a**u + 7/3*a**4 + 2/3*a**3 + 0 + 5/3*a**5 + 0*a.
a**3*(a + 1)*(5*a + 2)/3
Let i(p) be the second derivative of p**7/14 - p**6/5 - 3*p**5/4 + 5*p**4/2 + 2*p**3 - 12*p**2 - 297*p. Solve i(o) = 0 for o.
-2, -1, 1, 2
Let k(x) = 4*x**2 + 28*