-1). Let a(r) be the third derivative of -1/3*r**3 + 23/72*r**4 - 7/180*r**5 + 0*r + 11*r**2 + x. Factor a(p).
-(p - 3)*(7*p - 2)/3
Let x = -1293 - -1300. Let z(d) be the second derivative of 0 + 1/36*d**4 + 1/9*d**3 + x*d + 1/6*d**2. Factor z(s).
(s + 1)**2/3
Let c(g) be the third derivative of -5/6*g**3 + 5/6*g**5 + 5/14*g**7 + 3*g**2 + 0*g + 12 - 5/84*g**8 + 0*g**4 - 5/6*g**6. Find t, given that c(t) = 0.
-1/4, 1
Let j = 710 + -707. Let h(o) be the first derivative of 7/5*o**5 + o**3 + 8 + j*o**4 + 0*o - o**2. Determine c, given that h(c) = 0.
-1, 0, 2/7
Let p(i) = -i**2 + 2*i + 5. Let k be p(0). Let o = -143/2 - -73. Factor o*w**k + 0*w**2 - 9/2*w**3 + 0*w + 0 + 3*w**4.
3*w**3*(w - 1)*(w + 3)/2
Suppose -96/5*l + 12 + 39/5*l**2 - 3/5*l**3 = 0. What is l?
1, 2, 10
Let t = 20 - -15. Let h = t + -172/5. Let -9/5*q**4 - h*q**2 + 3/5*q**5 + 9/5*q**3 + 0 + 0*q = 0. Calculate q.
0, 1
Let t(u) be the second derivative of -9*u + 0*u**3 + 2/15*u**4 + 0*u**2 - 14/25*u**5 + 49/75*u**6 + 0. Let t(y) = 0. What is y?
0, 2/7
Let v(c) be the third derivative of -c**8/70560 - c**7/8820 + c**6/315 + 19*c**5/60 - 10*c**2. Let x(h) be the third derivative of v(h). What is k in x(k) = 0?
-4, 2
Let t = 704 - 24632/35. Let r = 4/5 - t. Find y, given that 0*y**2 + 0 + 0*y + 2/7*y**5 + 2/7*y**3 - r*y**4 = 0.
0, 1
Find z such that 2*z**2 + 99 - 179*z + 37*z + z**2 + 0*z**2 + 40*z = 0.
1, 33
Let y = 143 + -98. Factor -5*l**4 - 4*l + 4*l**5 - 37*l**2 + y*l**2 - 3*l**4.
4*l*(l - 1)**3*(l + 1)
Let g be (0 + 0)*7/(-21) + 2. Let m(y) be the second derivative of 0 + 0*y**g - 1/25*y**5 - 1/30*y**4 + 1/75*y**6 - 4*y + 2/15*y**3. Find u such that m(u) = 0.
-1, 0, 1, 2
Determine j so that 804*j**2 + 504 - 3/2*j**5 + 87/2*j**4 - 1032*j - 288*j**3 = 0.
2, 21
Let d(j) be the first derivative of -j**4/24 - 7*j**3/6 + 11*j**2/6 - 213. Factor d(u).
-u*(u - 1)*(u + 22)/6
Suppose o = -5*b + 22, -4*b = -23 + 7. Suppose 2*a - 2*y = -a + 17, -5*a + 31 = -4*y. Find f, given that 2*f - 3*f**3 - 2*f**2 + f - a*f**3 + 5*f**o = 0.
-1/2, 0, 1
Suppose -h + 2 = -2*y, 5*y + 8 = 4*h + 6*y. Solve -20*f + 1 + h*f**2 + 43 + 6 = 0.
5
Let t(k) = -k**3 - 5*k**2 + 3. Let s(q) = 4*q**3 + 24*q**2 - 16. Let u(o) = o**2 + 16. Let z be u(0). Let d(j) = z*t(j) + 3*s(j). Find h, given that d(h) = 0.
-2, 0
Let i(x) = x**2 + 20*x + 15. Let k(t) = -4*t**2 - 60*t - 45. Suppose -7 - 1 = -2*p. Let u(v) = p*k(v) + 11*i(v). Factor u(c).
-5*(c + 1)*(c + 3)
Let h = 1965 + -1962. Solve 3/5*n**2 + 1/5*n**h + 3/5*n + 1/5 = 0 for n.
-1
Suppose -14*n - 536 = -564. Factor -1458/23*x**n - 8/23 + 216/23*x.
-2*(27*x - 2)**2/23
Let s(r) be the second derivative of r**7/12600 + r**6/3600 + 19*r**4/12 + 27*r. Let d(g) be the third derivative of s(g). Factor d(l).
l*(l + 1)/5
Suppose 15 + 9 = 6*b. Factor -6*o - b*o**2 - 15*o**3 + 22*o - 3*o**4 - 5*o**2 + 11*o.
-3*o*(o - 1)*(o + 3)**2
Let j(w) be the second derivative of w**4/3 - 14*w**3 + 40*w**2 + 45*w. Factor j(l).
4*(l - 20)*(l - 1)
Suppose 3*n + o = 5*n - 6, -5*n + 5*o + 20 = 0. Factor 4*c**n - 6*c - 5*c**2 - 4 - c**2.
-2*(c + 1)*(c + 2)
Let f = 257/3 - 85. Suppose 74 = 24*y + 13*y. Factor -4/3 + 0*p**2 - y*p + f*p**3.
2*(p - 2)*(p + 1)**2/3
Let i(z) be the first derivative of z**7/14 - z**6/5 + z**4/2 - z**3/2 - 3*z + 10. Let m(y) be the first derivative of i(y). Find k, given that m(k) = 0.
-1, 0, 1
Let s(m) = 3*m**3 - 3*m**2 - 11*m - 19. Let o be s(3). Factor 1/5*u**o - 3/5 - 2/5*u.
(u - 3)*(u + 1)/5
Let p(j) = 11*j**2 + 7*j - 8. Let t(u) = -9*u**2 - 6*u + 7. Let h(n) = 4*p(n) + 5*t(n). Let h(q) = 0. Calculate q.
-3, 1
Suppose 25*g + 178 = 253. Determine q so that 9/5*q**4 + 9/5*q**g + 0*q + 0 - 6/5*q**5 - 6/5*q**2 = 0.
-1, 0, 1/2, 2
Let i be 0/(3/(1/((-12)/(-18)))). Let i - 8/9*d + 2/9*d**2 = 0. Calculate d.
0, 4
Suppose -13 - 78 = 265*c - 1681. Factor 4*p - 2/3*p**2 - c.
-2*(p - 3)**2/3
Let b(d) be the third derivative of 0*d + 2 + 7/20*d**5 - 1/2*d**3 + 1/4*d**4 - 2*d**2 + 1/10*d**6. Factor b(y).
3*(y + 1)**2*(4*y - 1)
Let u = -7150/9 + 35786/45. Suppose -2/5*a**4 + 0*a**3 + 6/5*a**2 - u*a + 0 = 0. What is a?
-2, 0, 1
Let c(h) be the third derivative of h**7/70 + 3*h**6/40 - h**4/2 - 168*h**2. Factor c(o).
3*o*(o - 1)*(o + 2)**2
Let c = 22 - 7. Factor -20*f + 15 - c*f**2 - 4 + 10*f**3 + 9 + 5*f**4.
5*(f - 1)**2*(f + 2)**2
Let o(h) be the third derivative of h**5/30 + h**4/2 + h**3 - 35*h**2. Let q(d) = -3*d**2 - 24*d - 11. Let a(f) = 11*o(f) + 6*q(f). Factor a(l).
4*l*(l - 3)
What is z in 15*z**2 + 12*z + 9/2*z**3 + 0 = 0?
-2, -4/3, 0
Let x(z) be the second derivative of 14*z**6/75 + 229*z**5/25 + 573*z**4/5 - 5066*z**3/15 + 1156*z**2/5 + 2*z + 23. Find d such that x(d) = 0.
-17, 2/7, 1
Let z(w) = 2*w**2 + 233*w - 479. Let b(t) = 9*t**2 + 933*t - 1923. Let m(o) = -5*b(o) + 21*z(o). Factor m(u).
-3*(u - 74)*(u - 2)
Let r(m) be the first derivative of -m**4/14 + m**3/21 - 9*m - 7. Let x(v) be the first derivative of r(v). Factor x(b).
-2*b*(3*b - 1)/7
Let x(h) be the first derivative of -1/18*h**3 + 1/72*h**6 + 0*h - 1/48*h**4 + 19 + 1/30*h**5 + 0*h**2. Suppose x(k) = 0. Calculate k.
-2, -1, 0, 1
Suppose m = 4*m - 2*x - 6, -5*m - 2*x + 26 = 0. Factor 4*a**3 - 5*a**3 - a**2 + 54*a**5 - 53*a**5 + a**m.
a**2*(a - 1)*(a + 1)**2
Let w(m) = -2*m**3 - 9*m**2 + 5*m + 3. Let z(y) = 56*y**3 - 24*y - 3 - 46*y**3 - 13 + 15*y**2 + 29*y**2. Let s(a) = -14*w(a) - 3*z(a). Solve s(l) = 0.
-3, -1, 1
Let y = 64 - 61. Determine g, given that g**y + 16*g**2 + 41 + 29 - 45 + 35*g - 5*g**2 = 0.
-5, -1
Suppose 0 = i + 5*j - 4*j - 9, 5*j - 25 = 0. Solve 4*z**4 - 3*z**2 + 8 + 145*z**3 - 13*z**2 + 4*z**i - 153*z**3 + 4*z**5 + 4*z = 0 for z.
-2, -1, 1
Let l be (29 - 29)/(1 + -3). Factor 4/5*u**2 - 2/5*u**4 + 0*u**3 + l*u - 2/5.
-2*(u - 1)**2*(u + 1)**2/5
Let f(g) = -3*g. Let m be f(-3). Let -1 + l + 4*l**2 - 11 - m*l - 20 = 0. Calculate l.
-2, 4
Factor 16/5*a - 2/5*a**2 + 18/5.
-2*(a - 9)*(a + 1)/5
Let q be (-2)/(-12) + 202/(-780). Let t = q + 162/65. Factor 24/5 - 6*c**2 - t*c - 9/5*c**3.
-3*(c + 2)**2*(3*c - 2)/5
Let l = -55 + 51. Let v be (-3)/l + 30/280. Factor 1/7*i**2 - v*i + 9/7.
(i - 3)**2/7
Let l(o) be the first derivative of -o**3 + 81*o**2/2 - 78*o - 47. Factor l(j).
-3*(j - 26)*(j - 1)
Suppose 0 = 7*g - 4*g. Let p(r) = -4*r - 4. Let i be p(-1). Find v such that 0*v + 0*v**2 + i*v**3 + g + 2/5*v**5 - 2/5*v**4 = 0.
0, 1
Let r(o) = 2*o**2 - o. Let m(w) = -11*w**2 - 88*w + 2209. Let u(t) = m(t) + 6*r(t). Suppose u(c) = 0. Calculate c.
47
Let u(c) be the first derivative of -c**7/420 - c**6/20 - 3*c**5/10 - 20*c**2 - 59. Let x(f) be the second derivative of u(f). Let x(b) = 0. Calculate b.
-6, 0
Suppose 3*q - 4*h + 458 = 0, 0 = 3*q - 4*q - 5*h - 140. Let t = 605/4 + q. Factor 4*v - 1 - t*v**2 - 7/4*v**3.
-(v - 1)*(v + 2)*(7*v - 2)/4
Let g(r) = 2*r**2 - 14*r + 5. Let c be g(7). Suppose 29 = c*q + 2*y, -4*q + 5 = -4*y - 7. Factor 5*s**4 + 4 - 4*s**3 - 4*s**2 + 4*s**q - s**4 - 4.
4*s**2*(s - 1)*(s + 1)**2
Suppose -t - 16 = -3*k + 3*t, -4 = -2*k - 4*t. Suppose -2*r - y = -6, -9*r = -11*r + 4*y - k. Determine h, given that -28/3*h**r + 0 + 4*h + 8/3*h**3 = 0.
0, 1/2, 3
Let v(c) = -6*c**2 + 3*c - 36. Let u(r) = 5*r**2 - 3*r + 22. Let x(p) = 3*u(p) + 2*v(p). Suppose x(l) = 0. Calculate l.
-1, 2
Let r(q) = -q**2 + 6*q + 13. Let u be r(7). Let k = u - 3. Determine j so that 358*j**3 + 3*j**4 - 364*j**k + 4*j**2 - j**4 = 0.
0, 1, 2
Suppose -2*k - 10 = -3*f - 4, -3*k + 2*f - 9 = 0. Let g be k/(-4)*(-1 - -2). Factor -3/4*s + 0*s**2 + g*s**3 + 0.
3*s*(s - 1)*(s + 1)/4
Let n(a) be the third derivative of 1/6*a**4 - 2/3*a**3 - 1/60*a**5 + 0*a + 0 - 12*a**2. Solve n(c) = 0.
2
Let c(t) = t**2. Let i(y) = 6*y**2 - y. Let o(b) = 15*c(b) - 3*i(b). Factor o(f).
-3*f*(f - 1)
Let b = -19 - -137/7. Let h(l) be the first derivative of -3 + 1/4*l**4 + 1/42*l**6 - 4/7*l**2 - 1/21*l**3 - b*l + 1/7*l**5. Let h(w) = 0. What is w?
-2, -1, 1
Solve -548*c + 30876*c**2 + 2221352*c**3 - 12506764*c**3 + 352275361*c**4 + 81738*c**2 + 1 = 0 for c.
1/137
Suppose 15*b = 25*b. Let b + 0*c + 2/11*c**2 - 2/11*c**4 - 6/11*c**3 + 6/11*c**5 = 0. What is c?
-1, 0, 1/3, 1
Let p(x) = x + 3. Let w be p(11). What is t in -20*t**3 - w*t**2 + 8*t**3 + t + 22*t**3 + 3*t = 0?
0, 2/5, 1
Let f be ((-48)/56)/2 + (-26)/(-28). Let c(d) be the second d