**2 + 1/2 = 0.
-2, 1
Suppose 13 = 2*h + 7. Let d(a) be the first derivative of 0*a + 1 - 1/9*a**h + 0*a**2. Factor d(i).
-i**2/3
Let b = -4 + 1. Let v(i) = -i**3 - 2*i**2 - 8*i - 1. Let u(r) = 2*r**3 + 5*r**2 + 16*r + 3. Let f(l) = b*u(l) - 5*v(l). Solve f(k) = 0 for k.
-2, -1
Let x(n) be the second derivative of -n**5/5 - 25*n**4/9 + 38*n**3/9 + 6*n**2 + 25*n. Factor x(d).
-4*(d - 1)*(d + 9)*(3*d + 1)/3
Let j(x) be the third derivative of x**6/300 - x**4/20 + 2*x**3/15 + 16*x**2. Solve j(l) = 0 for l.
-2, 1
Let b(m) be the second derivative of 9/4*m**2 + 1/40*m**5 + 0 - 5/24*m**4 + 1/4*m**3 + 6*m. Suppose b(q) = 0. Calculate q.
-1, 3
Factor 4*q**3 + 3*q - 2*q**4 - 4*q**2 + 2*q**2 + 4*q**2 - 7*q.
-2*q*(q - 2)*(q - 1)*(q + 1)
Let 0 + 2/17*a**2 + 2/17*a**3 - 2/17*a**4 - 2/17*a = 0. Calculate a.
-1, 0, 1
Let x(a) be the third derivative of a**7/42 - a**6/24 - 2*a**5/3 + 5*a**4/2 - a**2. Determine j, given that x(j) = 0.
-3, 0, 2
Let o(k) be the third derivative of 0*k + 1/480*k**6 + 4*k**2 - 1/24*k**3 - 1/96*k**4 + 0 + 1/240*k**5. Let o(q) = 0. What is q?
-1, 1
Let f be (3 - 3)*-2*(-3)/12. Determine a so that 1/6*a**2 - 1/6 + f*a = 0.
-1, 1
Let m(y) = 15*y + 12. Let t(c) = c**2 + 16*c + 11. Let s(b) = -4*m(b) + 3*t(b). Determine u so that s(u) = 0.
-1, 5
Let u(f) = f**5 - f**4 - f. Let k(j) = -7*j**5 + 9*j**4 - 2*j**3 + j. Let c = 0 - -1. Let p = 6 - 5. Let s(v) = c*u(v) + p*k(v). What is a in s(a) = 0?
0, 1/3, 1
Let f(v) = v**2 + 13*v - 66. Let s be f(4). Factor 3/7*l**3 - 3/7*l - 3/7 + 3/7*l**s.
3*(l - 1)*(l + 1)**2/7
Suppose -17 = 5*s - 2. Let x(f) = 7*f**2 + 2*f + 5. Let r(a) = -4*a**2 - a - 3. Let g(c) = s*x(c) - 5*r(c). Determine u so that g(u) = 0.
-1, 0
Let f = -147 + 147. Factor -1/4*l**4 + f + 0*l - l**2 - l**3.
-l**2*(l + 2)**2/4
Find x, given that 24/5*x**2 - 8/5*x - 132/5*x**4 + 0 + 14*x**5 + 46/5*x**3 = 0.
-2/5, 0, 2/7, 1
Suppose -103 = -4*i + 57. Let p = 10 - 10. Find f such that 32*f**5 + 6*f**3 - i*f**4 + 5/2*f**2 - 1/2*f + p = 0.
-1/4, 0, 1/4, 1
Let w(m) = m**3 + m**2 + 2. Let b be w(0). Suppose 4 = -3*v - 2, b*z + 3*v = 4. Factor 0 - p + p**5 + 2*p - 6*p**4 - 2*p**3 + z*p**4 - 1 + 2*p**2.
(p - 1)**3*(p + 1)**2
Let d(a) = a**2 - 6*a - 16. Let w be d(7). Let i(y) = y**2 + 8*y - 7. Let l be i(w). Determine r, given that 1/4 - 1/4*r**l + 0*r = 0.
-1, 1
Let i be 1*6/2 - -32. Let -i*y**3 - 5*y**2 + 36*y**3 + y**2 + 4*y = 0. What is y?
0, 2
Let r(d) be the second derivative of -d**7/252 + d**6/180 + d**5/120 - d**4/72 + 8*d. Find c, given that r(c) = 0.
-1, 0, 1
Determine b, given that 8/13*b + 6/13 + 2/13*b**2 = 0.
-3, -1
Determine u so that 16/9*u + 32/9*u**2 + 2/9 = 0.
-1/4
Let t(p) be the second derivative of -p**8/5040 + p**7/2520 + p**6/1080 - p**5/360 - 2*p**3/3 - 6*p. Let i(a) be the second derivative of t(a). Factor i(m).
-m*(m - 1)**2*(m + 1)/3
Let n(y) be the first derivative of y**6/39 + 6*y**5/65 + y**4/13 + 15. What is g in n(g) = 0?
-2, -1, 0
Let u(z) = 20*z**4 + 24*z**3 + 28*z**2. Let o(y) = -y**4 - y**3 - y**2. Let b = 18 + -17. Let c(m) = b*u(m) + 24*o(m). Determine x, given that c(x) = 0.
-1, 0, 1
Let c(s) be the first derivative of 1/6*s**6 + 0*s + 1/4*s**4 - 7/15*s**5 + 1/3*s**3 + 2 - 1/3*s**2. Factor c(o).
o*(o - 1)**3*(3*o + 2)/3
Let r(b) be the first derivative of 2/3*b**3 + 0*b**5 + 1/48*b**4 - 1/720*b**6 + 0*b - 1 + 0*b**2. Let d(p) be the third derivative of r(p). Factor d(t).
-(t - 1)*(t + 1)/2
Factor 0 + 1/3*g**3 - 1/3*g**2 + 1/3*g**4 - 1/3*g.
g*(g - 1)*(g + 1)**2/3
Let l(o) be the first derivative of 3*o**4/8 + o**3 + 2. Factor l(g).
3*g**2*(g + 2)/2
Let f(a) be the first derivative of a**4 - 16*a**3 + 96*a**2 - 256*a - 5. Factor f(n).
4*(n - 4)**3
Let g(z) = 7*z**2 - 2*z + 1. Let w(x) = 11*x**2 - 3*x + 2. Let j(u) = -8*g(u) + 5*w(u). Factor j(v).
-(v - 2)*(v + 1)
Factor -3 - 29*j**2 + 27*j**2 - 2 + 10*j - 3.
-2*(j - 4)*(j - 1)
Let z(u) = 15*u**4 + 51*u**3 + 67*u**2 + 37*u + 6. Let i(d) = -15*d**4 - 51*d**3 - 68*d**2 - 38*d - 6. Let m(w) = 4*i(w) + 5*z(w). Factor m(h).
3*(h + 1)**3*(5*h + 2)
Let x(i) be the second derivative of i**6/105 + i**5/70 - 5*i**4/42 + i**3/7 - 8*i. Factor x(y).
2*y*(y - 1)**2*(y + 3)/7
Let y(v) be the first derivative of -v**9/5292 + v**7/735 - v**5/210 + 8*v**3/3 - 6. Let h(g) be the third derivative of y(g). Suppose h(m) = 0. What is m?
-1, 0, 1
Suppose 0*v - 25 = -5*v. Find n, given that -v + 2 - 2*n + 2*n**2 + 0 - 1 = 0.
-1, 2
Let g(x) be the first derivative of 0*x - 1/2*x**2 + 1/20*x**5 + 0*x**3 + 1 + 3/16*x**4. Factor g(o).
o*(o - 1)*(o + 2)**2/4
Suppose -2*n + n = 3*n. Let f(s) be the second derivative of 0*s**2 + 2*s - 1/18*s**3 + 1/36*s**4 + n. Solve f(h) = 0 for h.
0, 1
Let l be (-75)/495 + ((-2)/1)/(-6). Determine o so that 4/11*o + 0 + l*o**2 = 0.
-2, 0
Let q = -59 - -181/3. Let k = q + -2/3. Find u such that 0 + 0*u - 2/3*u**3 - k*u**2 = 0.
-1, 0
Factor 2*q + 0*q**2 + 4*q**2 + 10*q**4 - 10*q**4 - 4*q**4 - 2*q**5.
-2*q*(q - 1)*(q + 1)**3
Suppose -9/7*s + 3/7*s**3 + 0*s**2 + 6/7 = 0. What is s?
-2, 1
Let b(y) = -y**3 + 5*y**2 - 3*y + 2. Let a be b(4). Factor -8*d - 8/3 - a*d**2.
-2*(3*d + 2)**2/3
Let i(q) be the third derivative of q**7/1260 + q**6/144 + 7*q**5/360 + q**4/48 + 8*q**2. Find g such that i(g) = 0.
-3, -1, 0
Let a(l) be the first derivative of -2*l**6/9 - 8*l**5/5 - 13*l**4/3 - 16*l**3/3 - 8*l**2/3 + 14. Find g such that a(g) = 0.
-2, -1, 0
Let d(r) be the second derivative of -r**7/168 + r**6/120 + 4*r. Determine v, given that d(v) = 0.
0, 1
Let w(t) = 2*t**2 - t - 1. Let z be w(-1). Suppose z*v - 2*o - 3*o - 9 = 0, -4 = 4*o. Factor -2*n**4 - 2*n**3 + 2*n**3 + 2*n**2 + v*n**3 - 2*n**5.
-2*n**2*(n - 1)*(n + 1)**2
Let l(z) be the third derivative of -z**6/300 + 7*z**5/150 - z**4/10 - 6*z**2. Determine v so that l(v) = 0.
0, 1, 6
Let d(n) = 10*n**4 - 19*n**3 + 41*n**2 - 21*n. Let z be 55/10*-2*1. Let u(o) = -2*o**4 + 4*o**3 - 8*o**2 + 4*o. Let p(b) = z*u(b) - 2*d(b). Factor p(i).
2*i*(i - 1)**3
Let y(s) be the second derivative of -s**5/110 + s**4/11 - 3*s**3/11 - 5*s. Factor y(v).
-2*v*(v - 3)**2/11
Suppose -9*z + 7*z + 6 = 0. Let g(u) be the second derivative of -2/15*u**z + 1/60*u**4 + 0 - 2*u + 2/5*u**2. Solve g(k) = 0 for k.
2
Let q(t) be the first derivative of 0*t + 0*t**2 + 1/12*t**3 - 4. Factor q(g).
g**2/4
Let r(x) be the first derivative of x**6/180 + x**5/45 - 2*x**2 - 4. Let z(d) be the second derivative of r(d). Factor z(k).
2*k**2*(k + 2)/3
Suppose 0 = k + r + 4*r + 24, k - r - 6 = 0. Let x = k + 2. Find s, given that -2/5*s**x + 0 + 7/5*s**4 + 0*s**2 + 0*s = 0.
0, 2/7
What is r in -4/5*r - 4/5*r**2 + 8/5 = 0?
-2, 1
Suppose 0 = -b + 3*b. Let x be b/2*14/(-28). Factor -1/4*o**3 + x + 1/4*o**2 + 0*o.
-o**2*(o - 1)/4
Let s(u) be the first derivative of 0*u + 0*u**2 - 6/5*u**5 + 11 + 1/2*u**6 + 0*u**3 + 3/4*u**4. Solve s(w) = 0 for w.
0, 1
Let m(x) be the first derivative of x**6/21 - x**4/7 + x**2/7 - 9. Factor m(i).
2*i*(i - 1)**2*(i + 1)**2/7
Let s(w) = 6*w**3 - 12*w**2 - 23*w. Let i(z) = -3*z**3 + 6*z**2 + 12*z. Let q(v) = -5*i(v) - 3*s(v). Find l such that q(l) = 0.
-1, 0, 3
Let w(v) be the third derivative of v**8/1008 + v**7/210 + v**6/180 - v**5/90 - v**4/24 - v**3/18 - 11*v**2. Factor w(z).
(z - 1)*(z + 1)**4/3
Let p(y) be the third derivative of y**6/60 + 13*y**5/150 + y**4/15 - 4*y**3/15 - 4*y**2. Factor p(v).
2*(v + 1)*(v + 2)*(5*v - 2)/5
Let c be 2 - 9/12 - (-6)/8. Factor -7/4*u + 5/4*u**c + 1/2.
(u - 1)*(5*u - 2)/4
Let b(o) = -6*o**2 + 3*o - 3. Let i(g) = 7*g**2 - 3*g + 4. Let x(z) = 4*b(z) + 3*i(z). Factor x(k).
-3*k*(k - 1)
Let t = -6 - -8. Let y(v) = 2*v**2 + 3*v - 2. Let k be y(-2). Factor -1/4*s + k - 1/4*s**t.
-s*(s + 1)/4
Let p be -20*3/2*25/(-135). Determine u, given that 0 - 20/9*u**2 + p*u**3 + 2/9*u = 0.
0, 1/5
Let u(b) be the second derivative of b**8/840 - b**7/105 + b**6/45 + b**3/2 + 3*b. Let o(m) be the second derivative of u(m). Factor o(c).
2*c**2*(c - 2)**2
Let y be (-1 - -1)*6/(-12). Let d(r) be the second derivative of 1/15*r**6 + 0 + y*r**4 - 1/20*r**5 + 0*r**2 + 0*r**3 - 2*r + 1/14*r**7. What is o in d(o) = 0?
-1, 0, 1/3
Factor 12*o**2 - 41*o + 53*o + 0*o**3 + 3*o**3.
3*o*(o + 2)**2
Let m(w) be the second derivative of w**7/294 + w**6/70 + w**5/140 - w**4/28 - w**3/21 + 8*w. Find o such that m(o) = 0.
-2,