t. Factor j(r).
-3*(r - 2)*(r + 1)
Let a(n) be the third derivative of 2/21*n**3 + 0*n + 2/147*n**7 + 2/21*n**5 + 2*n**2 + 1/21*n**6 + 1/588*n**8 + 5/42*n**4 + 0. Factor a(x).
4*(x + 1)**5/7
Let r = 141 + -141. What is v in -2*v**3 + 91*v - 131*v + 32 + r*v**3 + 12*v**2 + 4*v**2 = 0?
2, 4
Let r(z) = z + 8. Let a be r(-12). Let w be (a - -3) + 4 - 1. Find f, given that -8 - f**3 - 2*f**w + 8 = 0.
-2, 0
Let t(c) = c**2 - 6*c + 5. Let l be t(6). Suppose 12 = -2*u + u + 4*q, l*u + 5*q = 40. Find y such that -9*y**2 - u + 47*y - 33*y - y**2 = 0.
2/5, 1
Suppose -10*n + 3 = 3*w, 23*w - 18*w - 5 = 5*n. Suppose n - 6/11*c**3 + 4/11*c**2 + 2/11*c**4 + 0*c = 0. What is c?
0, 1, 2
Let r(n) be the second derivative of -n**5/80 - 3*n**4/32 + 7*n**2 - 15*n. Let g(a) be the first derivative of r(a). Factor g(s).
-3*s*(s + 3)/4
Solve -8*d**2 - 4/7*d + 4/7*d**3 + 8 = 0.
-1, 1, 14
Let c = 583/2 - 291. Let y(z) = z**2 + 2*z - 3. Let v be y(2). Let 0*a + 3/2*a**3 + 1/2*a**2 + 3/2*a**4 + 0 + c*a**v = 0. What is a?
-1, 0
Let o(z) be the first derivative of -12*z**4 + 1368*z**3 + 2061*z**2/2 + 258*z - 150. Suppose o(r) = 0. Calculate r.
-1/4, 86
Suppose 27 = 1004*f - 995*f. Factor 1/7*r**f + 0 + r**4 - 1/7*r - r**2.
r*(r - 1)*(r + 1)*(7*r + 1)/7
Let z(u) be the third derivative of -u**5/480 - 5*u**4/32 + 31*u**3/48 + 281*u**2 - 2*u. What is n in z(n) = 0?
-31, 1
Let l(c) be the first derivative of c**6/90 + c**5/60 - c**4/9 - 2*c**3/9 + 13*c + 2. Let u(q) be the first derivative of l(q). Determine o so that u(o) = 0.
-2, -1, 0, 2
Let s(n) be the third derivative of 0*n + 0*n**4 + 0*n**3 - 2*n**2 + 0 - 1/120*n**5 + 0*n**6 + 1/420*n**7. Factor s(l).
l**2*(l - 1)*(l + 1)/2
Suppose -6*r + 4*r = -4. Let c be (-2)/r + 0 + 3. Solve 0*o**c - 1 + 2*o**2 + 2*o + 2 + o = 0 for o.
-1, -1/2
Let f(i) = -i**3 + 5*i**2 - 5*i. Let c be f(3). Let x(r) be the first derivative of 6*r**2 + 2/3*r**c - 1 + 18*r. Suppose x(l) = 0. Calculate l.
-3
Let b be (-1)/(-2*4/56). What is o in b*o + 10 - 3*o**2 - 5 + 2*o + 7 = 0?
-1, 4
Suppose -2*s - s + 15 = 0. Let d be 1/2 + s/50. Solve d*i**3 + 12/5*i**2 - 12/5*i**4 - 3/5*i + 0 = 0.
-1, 0, 1/4, 1
Let t(m) = -m**3 - m**2 - m + 3. Suppose 0*s + 2*w = 5*s, 4*w = -s. Let k be t(s). Suppose -2*x - 79*x**4 + 81*x**4 - 2*x**2 + 0*x + 2*x**k = 0. What is x?
-1, 0, 1
Let v = 15 - 12. Let 42*f**2 - 144*f - 53*f**3 + f**v + 4*f**4 + 150*f**2 = 0. Calculate f.
0, 1, 6
Let a(t) = -t**3 - 3*t + 2. Let b be a(2). Let y be b/(-72) - (-2)/(-12). Factor 2*f**2 + 4*f + y - 2*f - 2 - 2.
2*(f - 1)*(f + 2)
Let t(m) = 33*m + 10*m**3 - 34*m - m**2 - 5*m**5 + 9*m**4 - 5*m**2 + 5. Let s(q) = q**4 + q**2 + q. Let x(d) = 4*s(d) - t(d). Find k such that x(k) = 0.
-1, 1
Let h(w) be the second derivative of w**7/42 + w**6/12 - w**5/4 + 5*w**2 - 2*w. Let y(r) be the first derivative of h(r). Find x such that y(x) = 0.
-3, 0, 1
Let r = 1228 + -1228. Factor -x**2 - 1/2*x + r - 1/2*x**3.
-x*(x + 1)**2/2
Let g(s) = 5*s**5 + s**4 - 23*s**3 - 41*s**2 - 18*s + 2. Let v(o) = -o**5 + o**4 + o**3 + o**2 - 1. Let w(n) = g(n) + 2*v(n). Find f, given that w(f) = 0.
-2, -1, 0, 3
Let d(b) = 2*b**3 + 9*b**2 - 18*b + 3. Let o = -247 + 241. Let l be d(o). Find v, given that -4*v**2 - 16/3 + 8*v + 2/3*v**l = 0.
2
Suppose 29*j = 2 + 56. Let w(f) be the second derivative of f**j + 1/24*f**4 - 1/3*f**3 + 0 + 6*f. Solve w(h) = 0.
2
Suppose -4*z**2 - 49*z - 27*z + 8*z**2 = 0. What is z?
0, 19
Determine s so that -40*s**3 + 0*s + 100*s**4 + 16/3*s**2 + 0 - 250/3*s**5 = 0.
0, 2/5
Let w be ((-3)/5)/((-2)/10). Suppose 14 = w*t + 2*i, 0 = 2*i - 7 - 1. Factor 0*h**t - 3*h**3 + 2 + 0*h - 2*h**2 + 3*h.
-(h - 1)*(h + 1)*(3*h + 2)
Let f = 3848 + -3848. Factor -9/2*v + f + 3/4*v**2.
3*v*(v - 6)/4
Suppose 10*h - 6*h - 104 = 0. Factor h*n - 1 - 1 - 2*n**2 - 30*n.
-2*(n + 1)**2
Suppose 5*n - 91 = 9. Let c = n - 15. Factor -2 + 2*k - 2*k**4 + 2*k**c + 10*k**2 + 0*k**4 - 6*k**2 - 4*k**3.
2*(k - 1)**3*(k + 1)**2
Let 0 - 2/5*r**2 + 18/5*r = 0. Calculate r.
0, 9
Suppose -4*o = 3*d - 388, 3*o - 3*d = 2*d + 291. Determine n, given that 50*n - o - 42 - 5*n**2 + 14 = 0.
5
Let r(p) = p**3 + p**2 + 3*p. Let n(l) = -5*l**3 + 16*l**2 - 42*l + 24. Let o(g) = n(g) + 2*r(g). Factor o(i).
-3*(i - 2)**3
Let m(b) = b**3 - 5*b**2 + 5*b - 11. Let i be m(5). Let z(c) = -c**2 - 3. Let u(n) = 1. Let d(o) = i*u(o) + 2*z(o). Factor d(l).
-2*(l - 2)*(l + 2)
Suppose 38*m = 33*m + 5. Suppose -3*b + 4 = m, -u + 4*b - 2 = 0. Find x such that 1/4*x**u - 1/4*x - 1/2 = 0.
-1, 2
Let j = -206 - -211. Let o(k) be the third derivative of j*k**2 + 0*k**3 + 0*k + 0*k**4 + 1/90*k**5 + 0. Solve o(a) = 0.
0
Let u(l) = -19*l**2 + 4 + 11*l**2 + 9*l**2. Let k(c) = c**2 + c + 4. Let i(q) = q - 3. Let v be i(-2). Let f(d) = v*u(d) + 4*k(d). Factor f(w).
-(w - 2)**2
Let y(z) be the second derivative of z**7/21 - 2*z**6/3 - 11*z**5/10 + 208*z. Let y(j) = 0. Calculate j.
-1, 0, 11
Let u(h) = -6*h**4 + 193*h**3 - 192*h**2 - 5*h. Let q(c) = 15*c**4 - 483*c**3 + 480*c**2 + 12*c. Let p(n) = -5*q(n) - 12*u(n). Solve p(l) = 0.
0, 1, 32
Let v(i) = i - 596. Let n be v(0). Let x = n - -1808/3. Factor 0 + x*y**2 - 8/3*y.
4*y*(5*y - 2)/3
Let s(k) be the second derivative of -k**8/192 - 13*k**7/252 - 13*k**6/144 + k**5/4 + k**4/3 - 14*k. Let i(z) be the third derivative of s(z). Factor i(v).
-5*(v + 1)*(v + 3)*(7*v - 2)
Let n(r) = 22 - 6*r - 22 + 0*r**3 + 2*r**3. Let k(h) = -6*h**3 + 17*h. Let o(v) = -4*k(v) - 11*n(v). Let o(f) = 0. Calculate f.
-1, 0, 1
Let j = 16 - 12. Solve 60*q**3 + 41*q**2 + 5*q**5 - q**2 + 10*q**4 + 20*q**j = 0 for q.
-2, 0
Let a(y) be the first derivative of 3*y**5/10 + 3*y**4 + 3*y**3 - 6*y**2 - 21*y/2 + 183. Factor a(b).
3*(b - 1)*(b + 1)**2*(b + 7)/2
Factor 0 - 1/2*k**3 - 2*k**2 - 3/2*k.
-k*(k + 1)*(k + 3)/2
Factor -27*f**2 - 12*f**2 - 12*f + 5*f + 30*f + 18*f - 2.
-(f - 1)*(39*f - 2)
Find m such that 0 + 8/21*m + 2/7*m**2 - 2/21*m**3 = 0.
-1, 0, 4
Suppose 2 = -23*m + 71. Suppose -5*f + 6*f = -m*s + 5, 0 = 5*s + f - 9. Factor 0 - 1/3*r + 1/3*r**s.
r*(r - 1)/3
Let y(c) = 15*c**3 - 25*c**2 - 25*c. Let n(i) = -8*i**3 + 13*i**2 + 12*i. Let j(l) = -5*n(l) - 3*y(l). What is a in j(a) = 0?
-1, 0, 3
Let v = -13 - -27. Let y be 4/(-14) - (-60)/v. Factor -4*z**2 - 8 - 16*z**2 + 36*z**3 - 36*z + 30*z**4 - 2*z**y.
4*(z - 1)*(z + 1)**2*(7*z + 2)
Let h(p) = -p**2 - 10*p - 7. Let y be h(-9). Let f(s) = -s + 17. Let n be f(17). Find m, given that 0*m + n + 2/5*m**3 + 4/5*m**y = 0.
-2, 0
Let n = 8 - -2. Factor -n*j - 2*j**3 + 22*j - j**3 + 3*j**4 - 18*j**2 + 31 - 7.
3*(j - 2)**2*(j + 1)*(j + 2)
Let z = -84 + 87. Find v, given that -27*v**3 + 40*v**z - v**4 - 154*v**2 + 7*v**3 + 54*v**2 = 0.
0, 10
Let a(u) = 4*u + 8. Let q be a(-2). Factor 24*p**3 + q*p**5 - 12*p**2 + 3*p**5 + 13*p**4 - 28*p**4.
3*p**2*(p - 2)**2*(p - 1)
Let w(p) be the first derivative of 5*p**3/3 - 15*p**2 - 35*p - 137. Let w(o) = 0. What is o?
-1, 7
Suppose 5*q = -0*q + 75. Suppose -q*n + 12*n = -21. Factor n*p**2 + p**2 - 7*p**2 + 4 + 4*p.
(p + 2)**2
Let h(d) be the second derivative of -d**7/17640 + d**6/630 - 2*d**5/105 + 17*d**4/12 - 10*d. Let f(b) be the third derivative of h(b). Factor f(n).
-(n - 4)**2/7
Let p(a) be the third derivative of -1/2*a**6 + 4/35*a**7 - 7/8*a**4 + 0*a + 9/10*a**5 + 0 + 1/2*a**3 + 5*a**2. Find y, given that p(y) = 0.
1/2, 1
Let h be 6/(-2) - (-4 - 3). Let d(m) be the first derivative of -3 + 0*m**2 - 1/6*m**3 + 0*m + 1/20*m**5 + 1/16*m**h. Let d(i) = 0. Calculate i.
-2, 0, 1
Let m(t) be the second derivative of t**7/1260 + 2*t**6/45 + 16*t**5/15 + t**4/2 + 42*t. Let n(s) be the third derivative of m(s). Factor n(j).
2*(j + 8)**2
Let y(u) be the first derivative of u**4/6 + 9*u**3 - 125*u**2/6 + 14*u - 221. Find z such that y(z) = 0.
-42, 1/2, 1
Let w be (12/(-7))/((-8)/168). Let d be 6/12 + (-2)/w. Factor d*v**2 - 2/9 - 2/9*v.
2*(v - 1)*(2*v + 1)/9
Suppose 6*w = 4*w + 16. Solve w*d**2 - 8*d**2 + 3*d**5 - 3*d**4 + 3*d**3 - 3*d**4 = 0.
0, 1
Let y(w) be the third derivative of -w**6/840 + w**5/140 + w**4/42 + 19*w**2. Suppose y(n) = 0. What is n?
-1, 0, 4
Let n(w) be the third derivative of w**7/168 + 7*w**6/480 - w**5/30 - w**4/24 + 56*w**2 - 1. Factor n(i).
i*(i - 1)*(i + 2)*(5*i + 2)/4
Suppose -y = 0, -s - y = -2*y. Find d such that -1011*d + 1010*d + s*d**3 + d