t x(t) = -17*t**2 + t + 8. Let b(o) = -11*o**2 + o + 5. Let i(k) = 8*b(k) - 5*x(k). Let i(q) = 0. What is q?
0, 1
Let f(g) be the second derivative of -5*g**6/12 - g**5/2 + 3*g**4/4 - g**3/3 - 3*g**2/2 + 9*g. Let b(j) be the first derivative of f(j). Factor b(w).
-2*(w + 1)*(5*w - 1)**2
Let u(p) be the first derivative of -1 + 8/39*p**3 + 1/26*p**4 + 5/13*p**2 + 4/13*p. Factor u(z).
2*(z + 1)**2*(z + 2)/13
Let g(n) be the third derivative of -11*n**5/20 + 43*n**4/56 - 3*n**3/7 + 36*n**2. Factor g(d).
-3*(7*d - 2)*(11*d - 3)/7
Find r, given that r - 1/2*r**2 + 0 = 0.
0, 2
Suppose v + 12 = 4*v. Let b be 0 - (16/(-3) + v). What is c in b*c**2 + 2*c**3 + 1/3*c + 4/3*c**4 + 1/3*c**5 + 0 = 0?
-1, 0
Factor 2*c**3 + 1496 - 3*c + c**3 - 18*c**2 - 1478.
3*(c - 6)*(c - 1)*(c + 1)
Suppose 1/4*c - 1/4*c**4 + 3/4*c**3 - 3/4*c**2 + 0 = 0. Calculate c.
0, 1
Let a(y) be the third derivative of 0*y - 1/48*y**5 + 11/840*y**7 + 1/224*y**8 + 0*y**3 - 2*y**2 - 1/48*y**4 + 1/240*y**6 + 0. Suppose a(q) = 0. Calculate q.
-1, -1/2, 0, 2/3
Factor 2*h + h**3 - 6*h**3 + 5*h**4 - 25*h**2 - 8*h - 9*h.
5*h*(h - 3)*(h + 1)**2
Let 158/5*c**4 + 64/5*c**3 + 0*c + 0 + 8/5*c**2 + 24*c**5 = 0. Calculate c.
-2/3, -2/5, -1/4, 0
Let m be 6 + (-9)/6*2. Let r be 3 + (0/m)/1. Find b, given that 0 + 0*b + 2/5*b**4 + 4/5*b**5 - 2/5*b**2 - 4/5*b**r = 0.
-1, -1/2, 0, 1
Let f be 3/(-3)*4*-1. Factor 1 + 4*j**2 + 1 - 4*j**2 - f*j**2 + 2*j**4.
2*(j - 1)**2*(j + 1)**2
Let t(i) be the third derivative of i**6/120 + i**5/15 - i**4/24 - i**3/3 - i**2. Let h be t(-4). Let -c**h - 1 + 2 - c**2 + c**4 = 0. Calculate c.
-1, 1
Let b(c) = -2*c**4 - 14*c**3 + 8*c**2 + 1. Let w(i) = -i**4 - i**3 + i**2 - 1. Let o(q) = b(q) - 5*w(q). Let h(x) be the first derivative of o(x). Factor h(d).
3*d*(d - 2)*(4*d - 1)
Let m = -1042 + 2087/2. Determine z so that m - 3/4*z + 3/4*z**3 - 3/2*z**2 = 0.
-1, 1, 2
Let j(a) be the second derivative of a**6/20 + 3*a**5/20 - 5*a. Determine w so that j(w) = 0.
-2, 0
Let x(b) be the first derivative of 9*b**4/20 - 4*b**3/5 + 3*b**2/10 + 13. Solve x(r) = 0 for r.
0, 1/3, 1
Suppose 4 = 3*u - 17. Let r(l) be the second derivative of -2/45*l**6 + 1/126*l**u - 1/9*l**4 + 1/10*l**5 + 0*l**2 + 1/18*l**3 + 0 + l. Factor r(q).
q*(q - 1)**4/3
Solve 8/9*g**2 + 0 + 0*g + 10/9*g**4 - 8/3*g**3 = 0 for g.
0, 2/5, 2
Let c(f) be the second derivative of -f**7/273 + f**6/39 - 3*f**5/65 - 2*f**4/39 + 8*f**3/39 + 36*f. Find z such that c(z) = 0.
-1, 0, 2
Suppose -5*j + 6 = -5*k - 29, -j - 8 = 4*k. Determine n, given that -2*n**j + 0*n**3 - 2*n**2 + 4 - 6*n + 0*n**4 + 5*n**3 + n**3 = 0.
-1, 1, 2
Let p be 0 - 2/(-6)*0. Let l(h) be the second derivative of -1/40*h**5 - 1/12*h**4 + p*h**3 + 0*h**2 + 1/60*h**6 + 0 - h. Determine b, given that l(b) = 0.
-1, 0, 2
Let m be 0/(1 - (-1 + 4)). Let f = 4 - m. Solve l**3 + 2*l**3 - l + l**f + 2*l**2 + l = 0 for l.
-2, -1, 0
Let h(w) = w**3 - w**2 - w + 1. Let l(p) = -49*p**3 - 119*p**2 - 50*p - 7. Let u(m) = -h(m) - l(m). Factor u(b).
3*(b + 2)*(4*b + 1)**2
Let i(o) be the second derivative of o**7/1080 + o**6/135 + o**5/90 - 5*o**4/12 - 3*o. Let w(c) be the third derivative of i(c). Let w(d) = 0. What is d?
-2, -2/7
Let q(c) = c - 6. Let j be q(5). Let h = j + 4. Factor -1/4*n + 1/4*n**h - 1/4*n**2 + 1/4.
(n - 1)**2*(n + 1)/4
Let l(r) be the third derivative of -r**9/6048 + r**7/560 + r**6/360 - r**3 - 6*r**2. Let a(j) be the first derivative of l(j). Factor a(b).
-b**2*(b - 2)*(b + 1)**2/2
Solve 2/3*a**3 - 1/3*a**5 - 1/3*a + 0*a**2 + 0 + 0*a**4 = 0 for a.
-1, 0, 1
Let u(h) be the third derivative of 1/84*h**6 + 0 - 2*h**2 + 1/21*h**4 - 1/735*h**7 - 4/105*h**5 + 0*h**3 + 0*h. Factor u(k).
-2*k*(k - 2)**2*(k - 1)/7
Let b = -4 + 6. Factor -3*d**5 - d**3 + 2*d**4 + 2*d + b*d**5 - 2*d.
-d**3*(d - 1)**2
Factor -3/7*n**2 - 243/7 + 54/7*n.
-3*(n - 9)**2/7
Let i(q) be the third derivative of -q**5/70 - 5*q**4/168 + q**3/42 - 6*q**2. Determine g so that i(g) = 0.
-1, 1/6
Let k be (-2)/42*(-9 + 3). Let l(i) be the first derivative of -2/3*i**3 - 5/7*i**2 + 3 - k*i - 3/14*i**4. Let l(r) = 0. What is r?
-1, -1/3
Let h(s) = -4*s**2 + 6. Let r(f) = f**2 - 7*f - 13. Let y = 0 - -9. Let x be r(y). Let o(d) = 3*d**2 - 5. Let v(p) = x*h(p) + 6*o(p). Factor v(g).
-2*g**2
Let l(w) be the first derivative of w**3/9 + w**2/2 + 2*w/3 - 13. Let l(m) = 0. What is m?
-2, -1
Let o(u) = -19*u**2 - 1 + 11*u**2 + 4*u + 7. Let f(l) = -7*l**2 + 3*l + 5. Let a(c) = 6*f(c) - 5*o(c). Suppose a(t) = 0. What is t?
-1, 0
Let y = 1991 + -5461/3. Factor -2/3*b**4 - 512/3 + 32/3*b**3 + y*b - 64*b**2.
-2*(b - 4)**4/3
Let m = -2/339 - -1370/2373. Suppose 3*o - 15 = -3*y, -4*o - 1 = -3*y - 21. Factor 2/7*u - 2/7 - m*u**3 - 2/7*u**4 + 2/7*u**o + 4/7*u**2.
2*(u - 1)**3*(u + 1)**2/7
Let g = 0 + 0. Let p = 647/3 - 213. What is b in 10*b**4 - p*b**2 - 8/3*b**3 + g*b + 0 = 0?
-2/5, 0, 2/3
Let b = -205 - -207. Factor 1/5*n**3 + 3/5*n + 1/5 + 3/5*n**b.
(n + 1)**3/5
Suppose 0 = 5*s + 3*s - 24. Determine b, given that 2/9*b**2 - 2/9*b**4 + 2/9*b**s + 0*b - 2/9*b**5 + 0 = 0.
-1, 0, 1
Let y(d) = -d**2 - 5*d + 2. Let v be y(-6). Let i = v + 11. Let 0 + n + i*n**3 - 11/2*n**2 = 0. Calculate n.
0, 2/7, 1/2
Let 1 + 6*r**2 - 2*r**4 + 7 - 5*r - 11*r + 0*r + 4*r**3 = 0. Calculate r.
-2, 1, 2
Let g(u) be the third derivative of 1/192*u**4 + 1/24*u**3 - 1/960*u**6 - 2*u**2 - 1/160*u**5 + 1/1680*u**7 + 0 + 0*u. Factor g(t).
(t - 2)*(t - 1)*(t + 1)**2/8
Let h = -6 + 11. Suppose 0 = h*n - 7 - 8. Factor 2/3*k**2 - 2/3*k**n - 2/3 + 2/3*k.
-2*(k - 1)**2*(k + 1)/3
Factor -801*l**5 - 3*l**4 + 7*l**4 + 805*l**5 - 8*l**3.
4*l**3*(l - 1)*(l + 2)
Let j(v) be the second derivative of v**7/231 - 2*v**6/55 + 7*v**5/55 - 8*v**4/33 + 3*v**3/11 - 2*v**2/11 + 6*v. Factor j(h).
2*(h - 2)*(h - 1)**4/11
Factor -4*n - 2*n**2 + 7 - 2 - 5.
-2*n*(n + 2)
Let s be ((-95)/(-45) + -3)*-3. Let w = -51 - -161/3. Let -s - 2/3*f**2 - w*f = 0. Calculate f.
-2
Let j = -284/5 - -57. Let b(p) be the first derivative of 1/2*p**4 + 0*p + 2 + 0*p**2 + j*p**5 + 1/3*p**3. Factor b(a).
a**2*(a + 1)**2
Let f(n) be the second derivative of 0 - 1/6*n**4 - 2/3*n**3 + 1/5*n**5 + 2*n - 1/2*n**2 + 1/10*n**6. Factor f(p).
(p - 1)*(p + 1)**2*(3*p + 1)
Let o = -1427/234 + 80/13. Let t(z) be the second derivative of -z - 2/3*z**2 + 0 + o*z**4 - 1/9*z**3. Factor t(d).
2*(d - 2)*(d + 1)/3
Let t(f) = -f**2 - 8*f + 1. Let r be t(-9). Let s be (3/18)/((-1)/r). Find l, given that -2/3*l**5 + 0 + s*l**4 + 0*l**3 + 2/3*l - 4/3*l**2 = 0.
-1, 0, 1
Let d be ((-6)/(-9) - 3)*-3. Suppose d = 2*n + 1. Determine a so that 10/3*a**n + 0 + 0*a - 14/3*a**4 + 4/3*a**2 = 0.
-2/7, 0, 1
Let p(c) be the third derivative of c**8/1344 - 3*c**7/280 + c**6/32 + 5*c**5/48 + 71*c**2. Suppose p(u) = 0. What is u?
-1, 0, 5
Suppose -4*v = -4*h + 568, 2*h = -2*h - 4*v + 584. Find z such that 168*z**2 + 48 + h*z - 4*z**4 + 96*z**3 - 2*z**4 + 33*z**4 + 3*z**5 = 0.
-2, -1
Let k = 61/190 - -3/38. Factor 0 - k*c**3 - 4/5*c**2 - 2/5*c.
-2*c*(c + 1)**2/5
Let o(f) = 2*f - 2. Let a be o(6). Let z = 12 - a. Determine s, given that 2/5*s**5 + 2/5*s - 8/5*s**4 + 0 - 8/5*s**z + 12/5*s**3 = 0.
0, 1
Let 1/3 - 1/3*p**3 + p**2 - p = 0. Calculate p.
1
Let t = 730 + -1459/2. Factor -1/3*h**2 - t*h + 1/6*h**5 + 1/2*h**4 + 1/3*h**3 - 1/6.
(h - 1)*(h + 1)**4/6
Suppose -r + 8*y - 3*y + 10 = 0, 4*r + 5*y - 15 = 0. Factor 22*h**5 + 3*h**4 - 41*h**5 - 3*h**2 + 3*h**3 + 16*h**r.
-3*h**2*(h - 1)**2*(h + 1)
Suppose -15*w = -13*w + 12. Let y(r) = 8*r**4 - 3*r**3 + r**2 + 6. Let s(u) = 9*u**4 - 4*u**3 + u**2 + 7. Let l(c) = w*s(c) + 7*y(c). Factor l(k).
k**2*(k + 1)*(2*k + 1)
Let n(j) be the third derivative of -2*j**2 + 1/24*j**4 + 1/60*j**5 + 0*j + 0 + 0*j**3. Determine t so that n(t) = 0.
-1, 0
Suppose k + 6 = 2*w, -3*w + 6 = -3*k - 0*k. Factor -4*u**k + 5*u**2 - u - 2*u**2.
-u*(u + 1)
Let m(b) = b**3 + 3*b**2 - 5*b - 3. Let o be m(-4). Let l be (3/(-12))/(o/(-8)). Factor 5*f**4 - f**4 + l*f**3 - 2*f**4 - f**2 - f**3.
f**2*(f + 1)*(2*f - 1)
Let m(y) be the third derivative of -1/6*y**3 - 1/48*y**4 + 1/120*y**5 + 0 + 0*y + 2*y**2. Factor m(b).
(b - 2)*(b + 1)/2
Suppose 3*z - 2*z + 65 = 2*m, z + 5 = 0. Let l = m + -14. Factor -50/3*k**4 + 0 - l*k**2 + 8/3*k + 30*k**3.
-2*k*(k - 1)*(5*k - 2)**2/3
Let r(q) = 4*q**3 - 4*q**2. Let d(t) = -t