*2 - 6*w - 4. Let p(s) = s**2 - 1. Let z(g) = p(g) - x(g). Factor z(t).
3*(t + 1)**2
Let g(l) = 4*l + 18. Let b be g(-15). Let v be (28/b)/(4/(-3)). Factor v*a**2 - a + 1/2.
(a - 1)**2/2
Suppose 2*u = 8, -5*u = 5*l - 2*u - 2. Let j be 6/27 + l/9. Factor j*k**2 + 3 - k**2 - 2.
-(k - 1)*(k + 1)
Solve 6*c - 3/2*c**3 - 6 + 3/2*c**2 = 0 for c.
-2, 1, 2
Let v(r) be the second derivative of r**5/50 - r**4/10 + 2*r**3/15 - 15*r. Factor v(w).
2*w*(w - 2)*(w - 1)/5
Let j be (2 - 3)*-4 + 1. Suppose -5*u = -2*u + 2*d, 3*d = -5*u. Find t, given that 0*t - t**j - t**4 + u*t = 0.
-1, 0
Let i(h) be the second derivative of -1/2*h**3 + 2*h**4 - 12/5*h**5 + 0*h**2 + 0 - h. Factor i(n).
-3*n*(4*n - 1)**2
Let k(o) be the first derivative of o**4/16 + o**3/3 + 5*o**2/8 + o/2 + 5. Suppose k(m) = 0. Calculate m.
-2, -1
Let j be (-210)/8*(-30)/(-375). Let a = j + 5/2. Find s, given that -2/5*s**2 + a*s**4 + 0 + 0*s + 0*s**3 = 0.
-1, 0, 1
Determine j so that 52/5*j**2 - 22/5*j - 36/5 + 6/5*j**3 = 0.
-9, -2/3, 1
Let w(g) be the second derivative of 0*g**3 + g**2 - 1/6*g**4 - g + 0. Let w(q) = 0. Calculate q.
-1, 1
What is c in 3*c**3 - 26*c**2 - 81 - 21*c + 24*c - c**2 + 78*c = 0?
3
Let o(t) be the third derivative of -1/420*t**6 + 0*t**3 + 0*t - 1/735*t**7 + 1/210*t**5 + 4*t**2 + 0 + 1/84*t**4. Factor o(f).
-2*f*(f - 1)*(f + 1)**2/7
Let z(b) be the first derivative of 14/15*b**3 - 2 + 2/5*b**2 + 0*b. Factor z(h).
2*h*(7*h + 2)/5
Solve -14 - 10*r + 65 + r**2 - 26 = 0.
5
Let h(v) = -2*v. Let i be h(-5). Let y be ((-9)/6)/((-5)/i). Determine w, given that 2/3*w**y + 0 - 2/3*w**4 + 0*w + 0*w**2 = 0.
0, 1
Let u = 4 - 1. Let r(a) = -2*a**3 + a**2 + 3*a. Let n(t) = -5*t**3 + 2*t**2 + 8*t. Let v(b) = u*n(b) - 8*r(b). Factor v(x).
x**2*(x - 2)
Let h be ((-24)/1080)/((-1)/6). Factor 14/15*p**4 - h*p - 4/15*p**5 + 2/3*p**2 + 0 - 6/5*p**3.
-2*p*(p - 1)**3*(2*p - 1)/15
Let z = -72 - -74. Factor -1/5*w**5 + 4/5*w**z + 0 - 3/5*w**4 + 0*w + 0*w**3.
-w**2*(w - 1)*(w + 2)**2/5
Suppose 0 = -5*n - 2*x + 391, 0 = -5*x + 17 - 2. Suppose -36*k**2 - 144*k - 3*k**3 + 40 - n - 72 - 83 = 0. What is k?
-4
Let w(t) be the first derivative of t**4/16 + t**3/2 + 9*t**2/8 + 12. Suppose w(r) = 0. Calculate r.
-3, 0
Let u be (4/12)/(1/3). Let y be u/(-1) + 6/2. Let 0*k**4 + k**4 - 2*k**3 + k + k**3 - k**y = 0. What is k?
-1, 0, 1
Let q(x) be the third derivative of -x**8/840 + x**6/300 - 3*x**2. Solve q(d) = 0 for d.
-1, 0, 1
Let v be (-1)/(9/6 + -1). Let n be ((-5)/(-35))/(v/(-48)). Suppose 18/7*y**4 - 8/7*y + 2/7 - 4/7*y**2 + n*y**3 = 0. What is y?
-1, 1/3
Let y(b) be the second derivative of 0 - 1/105*b**7 + 0*b**4 - 1/75*b**6 + 0*b**2 + 0*b**3 + 0*b**5 - 3*b. Factor y(u).
-2*u**4*(u + 1)/5
Let z(s) be the third derivative of -s**6/300 + s**4/60 + 9*s**2. What is v in z(v) = 0?
-1, 0, 1
Suppose 5*p + 20 = -h, 0 = -0*p + 2*p + 8. Let s = h - -3. What is g in -2/3*g**4 + 0*g + 2/3*g**2 - 2/3*g**5 + 0 + 2/3*g**s = 0?
-1, 0, 1
Let l be (4 + 1)*(-3 - (-18)/5). Find c, given that 0*c - 2/11*c**l - 6/11*c**2 + 8/11 = 0.
-2, 1
Let t(b) be the second derivative of -b**7/420 - b**6/90 + b**3/2 - 3*b. Let y(c) be the second derivative of t(c). Solve y(z) = 0.
-2, 0
Suppose -t = -0 - 2. Suppose 6 = -s + 5*x, -s - 2*x = -t*s. Factor -14*o**4 + 0*o**s - 20*o**3 - 4*o**2 + 2*o**3.
-2*o**2*(o + 1)*(7*o + 2)
Let w(a) be the second derivative of a**6/30 + a**5/20 - a**4/12 - a**3/6 - 27*a. Solve w(p) = 0.
-1, 0, 1
Let b(t) = t**2 - 4*t. Let p(i) = 2*i + 1. Let x(z) = -3*b(z) - 12*p(z). Let x(y) = 0. What is y?
-2
Let r(d) be the second derivative of d**6/10 - 3*d**4/2 - 4*d**3 - 9*d**2/2 - 9*d. Determine f, given that r(f) = 0.
-1, 3
Let h be (30/3)/2 - -1. Suppose -4*u - h = 2*r, 2*u - 6 = -3*r + u. Factor 0 + 4*f**r - f**5 - 2*f + 0 - f**5.
-2*f*(f - 1)**2*(f + 1)**2
Determine l, given that 137*l - 37*l + 1810*l**3 + 750*l**2 + 5 + 242*l**3 + 3125*l**4 + 448*l**3 = 0.
-1/5
Let i(b) = b**3 - 10*b**2 - 6*b + 63. Let p be i(10). Factor -21/4*w**3 + p + 12*w + 15/4*w**2.
-3*(w - 2)*(w + 1)*(7*w + 2)/4
Let i(p) be the third derivative of 0*p - 7*p**2 + 0*p**5 + 0 + 1/60*p**6 + 0*p**3 + 1/105*p**7 + 1/672*p**8 + 0*p**4. Let i(j) = 0. What is j?
-2, 0
Let b(p) = -p**3 + 4*p**2 + 9*p. Let o(t) = -t**3 + 7*t**2 + 18*t. Let k(h) = 5*b(h) - 2*o(h). What is y in k(y) = 0?
-1, 0, 3
Let z(x) = -15*x**3 + 27*x**2 + 12*x + 12. Let o(k) = -6*k**3 + 11*k**2 + 5*k + 5. Let l(w) = 12*o(w) - 5*z(w). Find i, given that l(i) = 0.
0, 1
Suppose -3*s + 2*u = -8, s + 5*u = 2*s - 7. Suppose 2/13*y**s + 0 + 0*y = 0. Calculate y.
0
Suppose 4*a = 8 - 0. Let x(r) be the first derivative of -2*r**2 + r**4 + 10/3*r**3 + a - 2*r**5 + 0*r. Determine f so that x(f) = 0.
-1, 0, 2/5, 1
Let u(g) = g**2 - 4*g - 188. Let l be u(-12). Solve -9/2*c**l - 3/2*c**5 + 0*c - 9/2*c**3 + 0 - 3/2*c**2 = 0 for c.
-1, 0
Let p be -4*13*(-1)/32. Let a(s) be the first derivative of -7/20*s**5 + p*s**4 - 9/4*s**3 - 2 + 1/2*s**2 + s. What is b in a(b) = 0?
-2/7, 1, 2
Let i(v) = 2*v**2 - 3*v + 6. Let p(t) = -t**2 + 2*t - 6. Let h(d) = -5*i(d) - 4*p(d). Let n(l) = -3*l**2 + 4*l - 3. Let q(g) = 2*h(g) - 5*n(g). Factor q(w).
3*(w - 1)**2
Let 4/3*n + 0*n**2 + 0 + 1/3*n**5 - 5/3*n**3 + 0*n**4 = 0. What is n?
-2, -1, 0, 1, 2
Solve -1/11*w**2 - 7/11*w + 0 = 0.
-7, 0
Let b(n) be the third derivative of -n**5/15 + 5*n**4/6 - 4*n**3 - n**2. Factor b(r).
-4*(r - 3)*(r - 2)
Factor 1/4 - 1/2*r + 1/4*r**2.
(r - 1)**2/4
Factor 6*f + 5*f**4 + f - 4*f**3 + 13*f - 20*f**2 - f**3.
5*f*(f - 2)*(f - 1)*(f + 2)
Factor 0 - 5/2*g + 1/2*g**5 + 2*g**3 + 3*g**2 - 3*g**4.
g*(g - 5)*(g - 1)**2*(g + 1)/2
Let m(p) be the second derivative of 0*p**3 + 0 + 1/420*p**6 - 1/84*p**4 + 0*p**5 - 2*p + 1/2*p**2. Let i(o) be the first derivative of m(o). Factor i(w).
2*w*(w - 1)*(w + 1)/7
Suppose -3*v - 4*z = -8, -3*z + 11 - 2 = 3*v. Let d(q) be the first derivative of 2 + 7/2*q**2 - q - v*q**3. Factor d(i).
-(3*i - 1)*(4*i - 1)
Let d(u) be the first derivative of -u**5/40 - u**4/12 - u**3/12 + 3*u + 2. Let n(g) be the first derivative of d(g). Factor n(k).
-k*(k + 1)**2/2
Let l(i) be the first derivative of 2 - 1/24*i**4 + 1/36*i**6 + 0*i + 1/18*i**3 - 1/30*i**5 + 0*i**2. Factor l(o).
o**2*(o - 1)**2*(o + 1)/6
Let q(c) be the first derivative of -3*c**4/20 + 2*c**3/5 - 3*c**2/10 - 2. Factor q(o).
-3*o*(o - 1)**2/5
Let y(m) = -m + 3. Let h be y(6). Let z be (-35)/(-30) + 2/h. Suppose 1/2*v**2 - 1/2*v**3 + z*v - 1/2 = 0. What is v?
-1, 1
Let u(g) be the third derivative of g**6/180 - 2*g**5/45 + g**4/9 - 9*g**2. Factor u(q).
2*q*(q - 2)**2/3
Let t(z) = 3*z**3 - 21*z**2 + 3*z. Let l(f) = -2*f**3 + 10*f**2 - 2*f. Let w(o) = 5*l(o) + 2*t(o). Factor w(p).
-4*p*(p - 1)**2
Let x(l) = 8*l**4 + 58*l**3 + 34*l**2 - 10*l. Let q(y) = -25*y**4 - 173*y**3 - 103*y**2 + 31*y. Let r(m) = 6*q(m) + 17*x(m). Factor r(d).
-2*d*(d + 2)**2*(7*d - 2)
Let p be ((-1)/(-5))/((-21)/(-140)). Let s = 9/10 + -17/30. Factor -j**3 + j - 5/3*j**2 + s + p*j**4.
(j - 1)**2*(j + 1)*(4*j + 1)/3
Suppose -2*o + 4 = -2*z, 3*z - 34 = -7*o + 2*o. Suppose -l = z*l - 12. Solve -90*i**4 + 148*i**l - 38*i**2 + 20*i**4 + 8 - 2*i**2 - 8*i - 38*i**2 = 0.
-2/7, 2/5, 1
Let q(x) be the first derivative of -2*x**3/3 - 2*x**2 - 26. Factor q(p).
-2*p*(p + 2)
Suppose -10*c + 12 = -4*c. Solve -2/5*d**c - 4/5*d - 2/5 = 0.
-1
Let g be (-15457)/85800 - (-4)/22. Let o(k) be the third derivative of 0 - 1/120*k**4 + g*k**6 - k**2 - 1/300*k**5 + 1/30*k**3 + 0*k. Solve o(p) = 0 for p.
-1, 1
Let j = 0 + -4. Let w be 0*(2 + 6/j). Find q, given that w - 2/9*q + 4/3*q**3 + 2/3*q**5 + 0*q**2 - 16/9*q**4 = 0.
-1/3, 0, 1
Let f(j) be the third derivative of 5*j**9/10584 - j**8/490 + 3*j**7/980 - j**6/630 - j**3 - 7*j**2. Let v(c) be the first derivative of f(c). Factor v(w).
2*w**2*(w - 1)**2*(5*w - 2)/7
Let x(y) be the second derivative of 8*y**6/15 + 14*y**5/5 - 13*y**4/4 - 29*y**3/6 - 2*y**2 - 22*y. Suppose x(i) = 0. What is i?
-4, -1/4, 1
Let p(k) = -3*k**2 - 3. Let m(y) = y**3 - 4*y**2 + y - 2. Let g(a) = 3*m(a) - 2*p(a). Factor g(q).
3*q*(q - 1)**2
Suppose 9*s - 5*s - 16 = 0. Let r(y) be the second derivative of -y**2 + 0 - 4*y + 5/3*y**3 - 2/3*y**s. Factor r(a).
-2*(a - 1)*(4*a - 1)
Suppose 4*m = -2 + 14. Find i, given that -3*i**4 + 6/5*i**m + 0 - 6/5*i + 3*i**2 = 0.
-1, 0