r - 3)
Let o(m) be the third derivative of 2/15*m**5 - 1/6*m**3 + 6*m**2 - 67/240*m**6 + 19/105*m**7 + 0 - 1/24*m**8 + 5/48*m**4 + 0*m. Find s, given that o(s) = 0.
-2/7, 1/2, 1
Let n(g) = 5*g**3 - 9*g**2 + 4*g - 6. Let r(k) = 4*k**3 - 8*k**2 + 3*k - 5. Let f be 1/2*(-84)/(-7). Let u(m) = f*r(m) - 5*n(m). Solve u(w) = 0 for w.
-2, -1, 0
Let u(k) = 3*k**2 + 2*k - 1. Let g be u(1). Factor -2*i**2 - g + i**3 - i**2 + 6*i**2.
(i - 1)*(i + 2)**2
Let i(v) be the third derivative of -2*v**5/105 + v**4/84 + 3*v**2. Factor i(d).
-2*d*(4*d - 1)/7
Let r = -20 - -24. Factor -r*d**3 - 5*d**3 - 2 + 3*d + 8*d**3.
-(d - 1)**2*(d + 2)
Suppose 0 = 4*p + 8, x - 8 = -0*x + 3*p. Suppose x*m = -m + 6. Factor -m*h + 6*h - 2*h + 2*h**2.
2*h*(h + 1)
Find d such that -1/7*d**2 + 0 - 3/7*d**3 + 0*d - 1/7*d**5 - 3/7*d**4 = 0.
-1, 0
Let x be (-1 - 1) + 1024/176. Let a = -115/33 + x. Let -a*v**4 + 2/3*v**3 + 0*v - 1/3*v**2 + 0 = 0. Calculate v.
0, 1
Let l be (-69)/(-225) - 1/3. Let f = l + 206/225. Factor -2/9*w**2 - 8/9 + f*w.
-2*(w - 2)**2/9
Factor -2/3*u**4 + 0*u**2 + 0 + 4/3*u**3 + 0*u.
-2*u**3*(u - 2)/3
Let z(q) be the second derivative of q**5/5 + q**4/3 - 2*q**3/3 - 2*q**2 - 8*q. Factor z(t).
4*(t - 1)*(t + 1)**2
Let h(c) = -3*c**2 - 5*c + 4. Let x(r) = r**2 + r - 1. Let w(v) = h(v) + 4*x(v). What is a in w(a) = 0?
0, 1
Let y(u) be the first derivative of -1/10*u**4 - 3 + 0*u**2 + 0*u + 0*u**3. Factor y(j).
-2*j**3/5
Let s = -15/2 + 8. Let q(i) = i**2 + 3*i - 2. Let u be q(-4). Solve -3*c**u + 1/2*c + s = 0 for c.
-1/3, 1/2
Solve 4*r**2 + 0 - 2*r + 1/2*r**4 - 5/2*r**3 = 0 for r.
0, 1, 2
Let d = 1 - -3. Suppose l + 5 = 0, -d*v + 3*v - 22 = 5*l. Factor -2*h**3 + 2*h**2 - 4*h**2 + h**v.
-h**2*(h + 2)
Let r = 455041/180 - 2528. Let i(n) be the third derivative of r*n**5 - 2*n**2 + 0*n - 1/18*n**3 + 0 + 0*n**4. Factor i(l).
(l - 1)*(l + 1)/3
Let o(w) be the first derivative of 2*w + 1/3*w**3 - 2 + 3/2*w**2. Factor o(q).
(q + 1)*(q + 2)
Let a(o) be the first derivative of 3*o**5/35 + 6*o**4/7 + 3*o**3 + 27*o**2/7 + 23. Solve a(y) = 0 for y.
-3, -2, 0
Let z(i) = i**2 + i - 9. Let h be z(3). Factor 0*n - 3/2*n**4 + 3/4*n**h + 3/4*n**5 + 0*n**2 + 0.
3*n**3*(n - 1)**2/4
Let s(c) = -2*c**5 + 5*c**4 + 7*c**3 + 5*c - 5. Let o(k) = k**5 - 2*k**4 - 3*k**3 - 2*k + 2. Let b(v) = -10*o(v) - 4*s(v). Factor b(q).
-2*q**3*(q - 1)*(q + 1)
Let s = 77/48 + -15/16. Factor 0*i - 2/3 + s*i**2.
2*(i - 1)*(i + 1)/3
Let n(t) = t**2. Let c(z) = 20*z**5 - 45*z**4 + 30*z**3 - z**2. Let u(f) = c(f) - 4*n(f). Factor u(k).
5*k**2*(k - 1)**2*(4*k - 1)
Let a(f) be the first derivative of -f**7/420 + f**6/90 + f**5/60 - f**4/6 + f**3 - 4. Let q(s) be the third derivative of a(s). Determine j so that q(j) = 0.
-1, 1, 2
Let s(l) be the third derivative of l**5/210 + 5*l**4/84 - 2*l**3/7 + l**2 + 4. Factor s(h).
2*(h - 1)*(h + 6)/7
Find p, given that 32/7 + 4/7*p**5 + 16/7*p - 40/7*p**2 - 20/7*p**3 + 8/7*p**4 = 0.
-2, -1, 1, 2
Let i be -3 - (484/(-80) + 3). Let z(q) be the second derivative of -3/4*q**2 + 0*q**4 + 1/2*q**3 + i*q**6 - 3/20*q**5 + 0 - q. Factor z(s).
3*(s - 1)**3*(s + 1)/2
Let f(z) = -2*z**5 + 6*z**4 + 10*z**3 - 24*z**2 + 16*z. Let m(t) = 4*t**5 - 12*t**4 - 21*t**3 + 48*t**2 - 32*t. Let p(k) = -13*f(k) - 6*m(k). Factor p(o).
2*o*(o - 2)**2*(o - 1)*(o + 2)
Let y(s) be the first derivative of -s**6/180 - s**5/30 - 2*s**3/3 - 1. Let h(m) be the third derivative of y(m). Factor h(p).
-2*p*(p + 2)
Let s(q) = -q**3 - 6*q**2 + 40*q + 3. Let n be s(-10). Let 8/7 + 354/7*r**2 - 88*r**n - 88/7*r + 56*r**4 = 0. Calculate r.
2/7, 1/2
Let t(c) be the third derivative of 5*c**8/336 + c**7/14 - c**6/24 - 11*c**5/12 - 5*c**4/2 - 10*c**3/3 - 20*c**2. Suppose t(x) = 0. Calculate x.
-2, -1, 2
Let t(d) be the second derivative of 0*d**3 + d + 1/180*d**6 + 0 - 1/252*d**7 + 1/120*d**5 + 0*d**2 - 1/72*d**4. Factor t(q).
-q**2*(q - 1)**2*(q + 1)/6
Let z(v) be the third derivative of v**8/1344 - v**7/280 + v**6/160 - v**5/240 - 5*v**2. Factor z(y).
y**2*(y - 1)**3/4
Suppose -10 = v + 4*b, 5*b - 13 = -5*v - 3. Let m(o) be the second derivative of -1/90*o**v + o - 1/18*o**3 + 0 + 1/36*o**4 + 1/60*o**5 + 0*o**2. Factor m(l).
-l*(l - 1)**2*(l + 1)/3
Let p(l) be the first derivative of -l**7/84 - 2*l**6/45 - l**5/60 + l**4/6 + 2*l**3/3 - 2. Let n(g) be the third derivative of p(g). Factor n(k).
-2*(k + 1)**2*(5*k - 2)
Let x(k) be the first derivative of 2*k**3/11 - 4*k**2/11 + 2*k/11 - 23. Let x(g) = 0. What is g?
1/3, 1
Let q(o) = -3*o**5 - 21*o**4 - 72*o**3 - 60*o**2 - 24*o - 18. Let z(c) = -c**3 - 1. Let r(h) = -q(h) + 18*z(h). Factor r(j).
3*j*(j + 1)*(j + 2)**3
Let u be 1/(74/(-38) - -2). Let k = -10 + u. Factor -60*o**2 - 53*o**4 - 2 + 92*o**3 + k*o + 9*o + 18*o**5 - 13*o**4.
2*(o - 1)**3*(3*o - 1)**2
Let q(v) be the second derivative of 0*v**3 + 1/3*v**4 + 0 - 2/21*v**7 - 3/5*v**5 + 0*v**2 + 2/5*v**6 + 3*v. Determine d, given that q(d) = 0.
0, 1
Suppose -5*p + 20 = 5*p. Factor 1/2 + 1/4*w**p + 3/4*w.
(w + 1)*(w + 2)/4
Let n(j) be the first derivative of 4*j**5/5 - 8*j**3/3 + 4*j - 1. Factor n(s).
4*(s - 1)**2*(s + 1)**2
Let x be ((-16)/(-24))/(16/6). Suppose 0 + 1/2*i - x*i**4 + 1/4*i**2 - 1/2*i**3 = 0. Calculate i.
-2, -1, 0, 1
Let i(q) be the second derivative of q**4/4 + q**3/2 - 3*q. Factor i(n).
3*n*(n + 1)
Let p(q) be the third derivative of q**6/60 - 2*q**5/15 + q**4/4 + q**2. Find d such that p(d) = 0.
0, 1, 3
Let c(b) be the first derivative of -b**3/3 - 3*b**2/2 + b + 3. Let j be c(-2). Factor -4*l**2 - l**2 + 2 + j*l**2.
-2*(l - 1)*(l + 1)
Let l be (-8)/5*-1*5. Suppose 0*y = 4*y - l. Solve -1/2*q + 1 - 1/2*q**y = 0.
-2, 1
Let l(j) be the first derivative of j**8/3360 - j**7/420 + j**6/240 + j**5/60 - j**4/12 + 2*j**3 + 3. Let y(r) be the third derivative of l(r). Factor y(s).
(s - 2)**2*(s - 1)*(s + 1)/2
Let l(z) be the third derivative of -z**5/150 + z**4/20 + 8*z**2. Factor l(j).
-2*j*(j - 3)/5
Let d = 18 + -18. Let a = 0 + d. Determine h, given that 1/4*h**2 + 0 - 1/4*h**4 + a*h**3 + 0*h = 0.
-1, 0, 1
Let p(o) be the third derivative of -o**6/1440 - o**5/480 - o**3/6 + 4*o**2. Let f(k) be the first derivative of p(k). Factor f(q).
-q*(q + 1)/4
Let h be 2*(-2)/(-4) - (-53)/159. Solve -2/3*c**2 - 2/3 - h*c = 0 for c.
-1
Factor -2/17*t**2 - 32/17*t - 128/17.
-2*(t + 8)**2/17
Let s(r) be the second derivative of 0*r**5 + 0 + 0*r**3 - 1/120*r**6 + 0*r**4 - 2*r + 0*r**2 - 1/168*r**7. Find m, given that s(m) = 0.
-1, 0
Let m = -7 - -10. Factor -6*i**m + 8*i**4 + 0*i**2 - 4*i**2 + 2*i**2.
2*i**2*(i - 1)*(4*i + 1)
Let h be 7/((-49)/(-30)) + 4/(-1). What is s in -h*s - 2/7*s**2 + 4/7 = 0?
-2, 1
Let u(h) = h**3 + h**2 - h. Let y(a) = -16*a**4 + 44*a**3 + 20*a**2 - 24*a. Let v(r) = -24*u(r) + y(r). Factor v(j).
-4*j**2*(j - 1)*(4*j - 1)
Let k be (6 - 2)/(1 + 1). Factor -4*g - 5*g**3 - 2*g**3 - g**3 - k + 10*g.
-2*(g + 1)*(2*g - 1)**2
Let q(p) be the second derivative of -7*p**5/100 - p**4/5 - p**3/10 + p**2/5 - 8*p. Solve q(t) = 0 for t.
-1, 2/7
Let o(q) be the first derivative of 0*q**2 - 1 - 2/3*q**3 - 1/3*q**6 - 6/5*q**5 - 3/2*q**4 + 0*q. Factor o(b).
-2*b**2*(b + 1)**3
Let s(f) = -f - 3. Let q be s(-7). Factor -2*y**4 + 0*y + 0 + 2*y - 6*y + q*y**3 + 2.
-2*(y - 1)**3*(y + 1)
Let j(m) = m - 12. Let p be j(6). Let u be -1 - 3*8/p. Factor -8/5 - 6/5*t**u + 8/5*t + 2*t**2.
-2*(t - 2)*(t + 1)*(3*t - 2)/5
Let d(y) be the second derivative of 4*y**6/45 + 2*y**5/5 + 3*y**4/4 + 5*y**3/6 + 6*y. Let u(l) be the second derivative of d(l). Factor u(r).
2*(4*r + 3)**2
Let c(k) = k**3 + k**2 - k. Let w(y) = 8*y**3 + 32*y**2 + 34*y + 8. Let a(g) = 2*c(g) + w(g). Factor a(t).
2*(t + 1)*(t + 2)*(5*t + 2)
Suppose 3*b - 6 = -6*q + q, 4*b - 8 = 0. Solve q + 0*u + u**4 + 4/3*u**5 + 0*u**2 - 1/3*u**3 = 0.
-1, 0, 1/4
Let i(l) be the second derivative of -1/2*l**3 - 3*l**2 - 3*l + 0 + 1/4*l**4. What is f in i(f) = 0?
-1, 2
Factor 1/2*w**3 - 3/4*w + 1/4*w**5 - 3/4*w**4 + 1/2*w**2 + 1/4.
(w - 1)**4*(w + 1)/4
Let z = 11413/3 + -3867. Let q = z - -64. Solve -q - 6*c - 14/3*c**2 = 0 for c.
-1, -2/7
Suppose 21*u - u = 0. Factor 3*p**2 + 3/5*p**4 + 6/5*p + u + 12/5*p**3.
3*p*(p + 1)**2*(p + 2)/5
Let s = -242 - -1214/5. Factor -s*a**4 + 0 + 2/5*a - 11/5*a**3 - a**2.
-a*(a + 1)*(a + 2)*(4*a - 1)/5
Let t = 11 + -6. Suppose -3*v + 5*a = v 