). Suppose -2*g + 4*g = 8. Factor v**2 + 6*v**g + v**l - 7*v**3 + v**3 - 2*v**5.
-2*v**2*(v - 1)**3
Let v(g) = -12*g**3 - 15*g**2 + 15*g + 12. Let f(q) = 145*q**3 + 180*q**2 - 180*q - 145. Let t(h) = 2*f(h) + 25*v(h). Suppose t(n) = 0. Calculate n.
-2, -1/2, 1
Let x be 2/(-2) + -1 + -10. Let j = 20 + x. Factor -18*s**2 - 10*s - 1 - 1 - 2*s - j*s**3.
-2*(s + 1)**2*(4*s + 1)
Let k be (3/25)/((-24)/(-20)). Let z(v) be the second derivative of 0 + 0*v**2 - 3/50*v**5 - 1/15*v**3 - 1/75*v**6 - k*v**4 + 3*v. Let z(d) = 0. Calculate d.
-1, 0
Let q(w) be the second derivative of w**5/4 + 5*w**4/4 - 10*w**3/3 + 26*w. Factor q(i).
5*i*(i - 1)*(i + 4)
Let j(o) = 40*o**4 - 55*o**3 + 25*o**2 + 25. Let x(y) = -5*y**4 + 7*y**3 - 3*y**2 - 3. Let q(p) = -3*j(p) - 25*x(p). Solve q(r) = 0.
0, 2
Factor 10*b**3 + 13*b**3 - 4*b**2 - 21*b**3 - 2*b + 4.
2*(b - 2)*(b - 1)*(b + 1)
Let y(p) be the third derivative of -p**6/1200 - p**5/120 + p**4/240 + p**3/12 + 35*p**2. Determine g, given that y(g) = 0.
-5, -1, 1
Let p(a) be the third derivative of a**5/30 + a**4/12 - 14*a**2. What is n in p(n) = 0?
-1, 0
Factor -1/4 + 1/4*d**2 - 1/8*d + 1/8*d**3.
(d - 1)*(d + 1)*(d + 2)/8
Suppose 16 = 4*m, 13 = -5*d - m - 13. Let x be (-3)/(-6) + d/(-4). Factor -2*z**x - z + 0*z**2 + 3*z.
-2*z*(z - 1)
Let l(o) be the first derivative of -o**4/4 + 7*o**3/3 + 2*o - 2. Let g be l(7). What is x in x**g + 3*x - x - 3*x**2 = 0?
0, 1
Let a(q) be the second derivative of -7*q - 1/42*q**7 + 0*q**2 + 0*q**3 + 0 + 1/12*q**4 + 1/10*q**6 - 3/20*q**5. Find o, given that a(o) = 0.
0, 1
Solve 18/11*w**3 + 0 + 14/11*w**2 + 4/11*w + 10/11*w**4 + 2/11*w**5 = 0 for w.
-2, -1, 0
Let j = -21 + 23. Suppose -u**5 + u**4 - u**2 + 1 + 3*u**2 - 6*u**2 + 2*u**3 + 2*u**j - u = 0. Calculate u.
-1, 1
Let w(q) be the first derivative of 1/13*q**2 + 2/39*q**3 + 4 + 0*q. Determine r so that w(r) = 0.
-1, 0
Let w(j) = -j - 1. Let r be w(-4). Suppose -3*v = 4*a - 3 - r, 0 = -a + v - 2. Factor a*z**2 + 2/7*z**3 + 0 + 2/7*z**4 + 0*z.
2*z**3*(z + 1)/7
Let v(x) be the first derivative of -3*x**5/5 + 3*x**4 - 5*x**3 + 3*x**2 + 4. Let v(t) = 0. What is t?
0, 1, 2
Let j(c) = -c**3 + 0*c**2 + 1 + 2*c**2 - 2*c - 4*c**2 + 3*c**3. Let k be j(2). Solve -3*v**3 + 1/2 - v**2 + 3/2*v**k + 3/2*v + 1/2*v**4 = 0.
-1, -1/3, 1
Let 30/7*q**3 + 15/7*q + 3/7 + 15/7*q**4 + 3/7*q**5 + 30/7*q**2 = 0. Calculate q.
-1
Suppose -3*s**2 + 1 - 1/2*s = 0. What is s?
-2/3, 1/2
Let r(h) be the third derivative of -h**5/300 + h**4/15 - 8*h**3/15 + 6*h**2. Factor r(m).
-(m - 4)**2/5
Let r(c) = c**2 + 11*c + 26. Let j be r(-8). Suppose -1/4*n**j + 0 + 1/4*n = 0. What is n?
0, 1
Suppose -4*d - 4*r = 8, 0*d - 4*r + 16 = -4*d. Let y be (8 + d)*4/25. Solve 6/5*o - y - 2/5*o**2 = 0 for o.
1, 2
Let s(y) be the third derivative of -y**6/660 - y**5/330 + y**4/132 + y**3/33 - 16*y**2. Suppose s(h) = 0. What is h?
-1, 1
Let c(q) = -q + 3. Let u be c(4). Let o be u/(-2 - 1)*0. Factor -1/3*l**3 - l**5 + 0 + o*l - 4/3*l**4 + 0*l**2.
-l**3*(l + 1)*(3*l + 1)/3
Let z(w) be the second derivative of 0*w**2 + 6*w - 1/21*w**4 - 2/21*w**3 + 0. Let z(q) = 0. What is q?
-1, 0
Let c(v) be the third derivative of v**8/1008 + v**7/210 - v**6/360 - 11*v**5/180 - v**4/6 - 2*v**3/9 + 11*v**2. Factor c(t).
(t - 2)*(t + 1)**3*(t + 2)/3
Let q(r) be the first derivative of r**3/12 - 3*r**2/8 - 11. Factor q(m).
m*(m - 3)/4
Let j(y) = -21*y**4 + 48*y**3 - 81*y**2 + 39*y - 12. Let c(q) = 5*q**4 - 12*q**3 + 20*q**2 - 10*q + 3. Let g(l) = 9*c(l) + 2*j(l). Find z, given that g(z) = 0.
1
Let p(k) be the second derivative of -1/60*k**5 - k**2 + k - 2/3*k**3 - 1/6*k**4 + 0. Let i(z) be the first derivative of p(z). Find s, given that i(s) = 0.
-2
Let z(n) be the first derivative of n**7/14 + 2*n**6/5 + 9*n**5/20 - n**4 - 2*n**3 - 4*n - 1. Let b(s) be the first derivative of z(s). Factor b(j).
3*j*(j - 1)*(j + 1)*(j + 2)**2
Let y(w) = -w**2 - 11*w - 8. Let s be y(-10). Factor u**2 + 2*u**2 + 3*u**s - 3*u**2.
3*u**2
Suppose n + 29 = z, 15 = 3*z - 5*n - 68. Let u = -31 + z. Factor -2/7*f**3 + u*f + 2/7*f**4 + 0 - 2/7*f**2 + 2/7*f**5.
2*f**2*(f - 1)*(f + 1)**2/7
Let o(d) be the first derivative of -d**7/3360 + d**6/1440 - d**3 + 1. Let p(q) be the third derivative of o(q). Suppose p(f) = 0. Calculate f.
0, 1
Let i(a) be the first derivative of a**4/4 - 5*a**3/3 - 18. Let i(f) = 0. What is f?
0, 5
Find r, given that 17*r**3 - r**2 - 13*r - 13*r**3 + 97*r - 31*r**2 - 72 = 0.
2, 3
Let a(d) = 2*d**2 - 6*d - 8. Let l(z) = 3*z**2 - 5*z - 8. Let m(c) = -5*a(c) + 4*l(c). Determine h, given that m(h) = 0.
-4, -1
Let p = 4 - 4. Determine r so that -2/3*r**3 + 1/3*r**2 + p + 0*r + 1/3*r**4 = 0.
0, 1
Find t, given that 4/9*t - 1/9*t**4 + 0 + 2/3*t**3 - t**2 = 0.
0, 1, 4
Solve 20*u**2 + 40/3*u**4 - 16/3 - 32/3*u + 116/3*u**3 = 0 for u.
-2, -1, -2/5, 1/2
Let d(i) = -i**3 + 4*i**2 - i. Let z be d(2). Let b = z + -4. Let 4*v**2 - v**3 - b*v**2 - 3*v + 2*v = 0. What is v?
0, 1
Suppose 5*r - 10 - 5 = 0. Let -6/5*o**2 + 4/5*o - 2/5*o**5 + 0 - 2/5*o**r + 6/5*o**4 = 0. Calculate o.
-1, 0, 1, 2
Let v(c) be the third derivative of -5*c**6/24 - c**5/3 + 25*c**4/24 + 10*c**3/3 + 32*c**2. Factor v(s).
-5*(s - 1)*(s + 1)*(5*s + 4)
Factor 8/3 + 1250/3*c**2 - 200/3*c.
2*(25*c - 2)**2/3
Let z(f) = -8*f**4 + 13*f**3 - 12*f**2 + 11*f. Let b(i) = i**4 - i**3 + i**2 - i. Let d(s) = 22*b(s) + 2*z(s). Factor d(o).
2*o**2*(o + 1)*(3*o - 1)
Let x(h) be the third derivative of h**9/22680 - h**8/5040 - h**7/3780 + h**6/540 + h**4/8 + 2*h**2. Let j(t) be the second derivative of x(t). Factor j(c).
2*c*(c - 2)*(c - 1)*(c + 1)/3
Suppose 5*h - 3*h = 2, 2*p + 13 = 5*h. Let o be (-45)/(-12) - (-3)/p. Factor 0*w**2 - 1/4*w**o + 0*w + 0 + 1/2*w**4 - 1/4*w**5.
-w**3*(w - 1)**2/4
Let p(v) be the first derivative of -v**7/5040 + v**6/720 - v**5/240 + v**4/144 - 5*v**3/3 + 1. Let g(c) be the third derivative of p(c). Factor g(f).
-(f - 1)**3/6
Let r be (-28)/(-42) + -2 + (-4)/(-2). Solve 1/3*u**2 + r*u + 0 = 0 for u.
-2, 0
Let z(i) be the third derivative of i**5/6 + 5*i**4/8 - 5*i**3/3 - i**2. Factor z(f).
5*(f + 2)*(2*f - 1)
Let z + 12*z - 5*z - 8 - 4*z**2 + 4*z = 0. What is z?
1, 2
Let r(i) = 3*i**2 + i + 2. Let x be r(-2). Let w = -1 + x. Factor w*a - 5*a**2 - 2*a**2 - 3*a + 2*a**3 - a**2.
2*a*(a - 2)**2
Let i(x) be the third derivative of 1/56*x**4 + 0*x - 1/280*x**6 - 4*x**2 - 1/70*x**5 + 0 + 1/7*x**3. What is d in i(d) = 0?
-2, -1, 1
Let u be ((-2)/(-370))/((-9)/(-15)). Let c = 25/37 - u. Suppose 0 + 0*y**2 + 0*y**4 + c*y + 2/3*y**5 - 4/3*y**3 = 0. Calculate y.
-1, 0, 1
Let r(l) be the third derivative of 0*l**3 - 1/108*l**4 + 0*l**5 + 0*l - 1/1512*l**8 + 0*l**7 + 0 + 2*l**2 + 1/270*l**6. Factor r(c).
-2*c*(c - 1)**2*(c + 1)**2/9
Let l(k) be the second derivative of k**9/1008 - 3*k**8/560 + k**7/140 - k**3/2 + 7*k. Let n(a) be the second derivative of l(a). Let n(h) = 0. Calculate h.
0, 1, 2
Factor 1/3*v - 1/3*v**3 - 2/3*v**2 + 2/3.
-(v - 1)*(v + 1)*(v + 2)/3
Let p(j) be the first derivative of 1/2*j**5 + 1/4*j**2 - j - 13/8*j**4 + 3/2*j**3 - 5. Factor p(v).
(v - 1)**3*(5*v + 2)/2
Let x(k) be the third derivative of 0*k - 1/210*k**5 + 0 - 1/84*k**4 + 3*k**2 + 0*k**3. Find t such that x(t) = 0.
-1, 0
Let r(l) be the third derivative of -l**9/756 + l**7/210 + l**3 + 9*l**2. Let a(h) be the first derivative of r(h). Factor a(g).
-4*g**3*(g - 1)*(g + 1)
Let q(o) be the third derivative of o**9/15120 - o**8/4200 + o**7/12600 + o**6/1800 - o**4/8 - 2*o**2. Let v(b) be the second derivative of q(b). Factor v(m).
m*(m - 1)**2*(5*m + 2)/5
Let r(l) = 18*l**3 + 11*l**2 - 7*l. Let s(t) = 54*t**3 + 32*t**2 - 21*t + 1. Let x = -3 - 4. Let q(i) = x*r(i) + 2*s(i). Suppose q(z) = 0. Calculate z.
-1, -2/9, 1/2
Let j be (252/(-15))/(5/(-1)). Let d = j - -6/25. What is s in 4/5 + 24/5*s**2 - d*s - 2*s**3 = 0?
2/5, 1
Let v(q) = -4*q**2 + 5*q - 14. Let m(l) = -3*l**2 + 5*l - 14. Let y(k) = 5*m(k) - 4*v(k). Factor y(h).
(h - 2)*(h + 7)
Suppose -7 = u - 2, 3*b + 2*u + 22 = 0. Let d = b + 6. Determine n so that -2 + 3*n**2 + 4 + 4*n + n**2 - d*n**2 = 0.
-1
Suppose -6*n + 0*n = -5*n. Determine y, given that n*y - 3/2*y**4 + 0*y**3 + 0 + 3/2*y**2 = 0.
-1, 0, 1
Let m(z) = -z - 23. Let t be m(-13). Let a be -2 - (34/t + 1). Let 6/5*c**3 + 4/5*c + 2*c**2 - 2/5*c**5 + 0 - a