g(x) = -4*x**5 - 8*x**4 - 16*x**3 - 8*x**2 + 4*x. Let p(j) = y*c(j) - g(j). Factor p(m).
4*m*(m - 1)*(m + 1)**3
Let l(a) = 6*a**4 - 38*a**3 + 42*a**2 - 22*a + 8. Let n(k) = k**4 + k**3 - 1. Let q = 1 + -2. Let h(b) = q*l(b) - 4*n(b). Factor h(g).
-2*(g - 1)**3*(5*g - 2)
Suppose 3*x = 3*s + 69, 4*s - x = -50 - 48. Let n = -25 - s. Factor -2*b**4 - 2/3*b**2 - 2*b**3 + 0 - 2/3*b**5 + n*b.
-2*b**2*(b + 1)**3/3
Let d be 3 - (-10 - (2 - 3)). Suppose q - d = -1. Factor 2*l + 2*l**2 + 4 + l - q*l + 2.
2*(l - 3)*(l - 1)
Let k(s) be the first derivative of -s**5/20 + 3*s**4/32 + s**3/8 - 11*s**2/2 - 1. Let l(h) be the second derivative of k(h). Factor l(q).
-3*(q - 1)*(4*q + 1)/4
Let s = -157/2 - -83. Solve 3/4*l**2 - s*l + 27/4 = 0 for l.
3
Let y(s) be the second derivative of s**5/100 - s**4/20 + s**3/15 - 8*s. Find v such that y(v) = 0.
0, 1, 2
Let t be -18*2/(-6) + 128/(-28). Factor 8/7*k**2 + t*k + 4/7 + 2/7*k**3.
2*(k + 1)**2*(k + 2)/7
Let n be 5/((-20)/(-12)) - -1. Suppose n = -5*z + 24. Suppose 0*r**2 + 0*r**z + 1/4*r - 1/2*r**3 + 0 + 1/4*r**5 = 0. Calculate r.
-1, 0, 1
Suppose -9*y + 5 = 5. Determine n so that 1/3*n - 1/3*n**3 - 1/3*n**2 + y + 1/3*n**4 = 0.
-1, 0, 1
Let f(k) = 3*k**3 - 3*k - 4. Let o(b) = 3*b**3 - 3*b - 5. Let m(d) = 5*f(d) - 4*o(d). Suppose m(r) = 0. Calculate r.
-1, 0, 1
Let p(i) be the third derivative of i**5/300 - i**4/120 - i**3/15 - 3*i**2. Factor p(w).
(w - 2)*(w + 1)/5
Let x(h) be the second derivative of -h**4/84 - h**3/21 - 17*h. Factor x(m).
-m*(m + 2)/7
Let j = 21 - 19. Let q(g) be the first derivative of -4/3*g + 3 + 49/24*g**4 - 7*g**3 + 5*g**j. Factor q(k).
(k - 2)*(7*k - 2)**2/6
Let o be 13 - 0*(0 + 1). Let c(i) = 15*i**3 - 17*i**2 - 11*i - 13. Let s(h) = 7*h**3 - 8*h**2 - 5*h - 6. Let y(l) = o*s(l) - 6*c(l). Let y(r) = 0. Calculate r.
0, 1
Let r = -196 + 986/5. Factor r*z**2 + 0 + 4/5*z.
2*z*(3*z + 2)/5
Determine b, given that -1/4*b**4 + 0 - 1/4*b**5 + 0*b + 1/4*b**2 + 1/4*b**3 = 0.
-1, 0, 1
Let r = -23 - -26. Let q(y) be the first derivative of -3/2*y**2 + y**r - 1/4*y**4 + 3 + y. Suppose q(x) = 0. Calculate x.
1
Let b(k) be the first derivative of -1/2*k**2 - 1/60*k**5 - 3 + 0*k**3 + 0*k - 1/24*k**4. Let p(d) be the second derivative of b(d). Factor p(n).
-n*(n + 1)
Let o(s) be the third derivative of 1/120*s**5 + 0 + 0*s**3 + 2*s**2 + 0*s - 1/48*s**4. Suppose o(a) = 0. Calculate a.
0, 1
Let m be 6/27 + (-2)/9. Let y(p) be the first derivative of m*p - 1/10*p**2 + 1 + 1/15*p**3. Solve y(j) = 0 for j.
0, 1
Let q(d) be the third derivative of -d**7/490 + d**6/280 + d**5/140 - d**4/56 - 2*d**2 + 4. Factor q(h).
-3*h*(h - 1)**2*(h + 1)/7
Let p(k) = k**4 + 27*k**3 + 27*k**2 + 9*k + 8. Let y(v) = v**4 + 18*v**3 + 18*v**2 + 6*v + 5. Let l(g) = 5*p(g) - 8*y(g). Find u, given that l(u) = 0.
-1, 0
Let v(w) be the first derivative of -1/5*w**5 - 7/4*w**4 + 7/4*w**2 - w + 7/12*w**6 - 3 + 2/3*w**3. Determine t, given that v(t) = 0.
-1, 2/7, 1
Let v(h) be the second derivative of h**6/300 - h**5/150 - 5*h**2/2 + 2*h. Let r(y) be the first derivative of v(y). What is d in r(d) = 0?
0, 1
Let d be ((-26)/(-169))/(3/13). What is z in 8/3*z - d*z**2 - 8/3 = 0?
2
Let h = -33 - -36. Let l(p) be the second derivative of -1/70*p**5 + 0 + 1/21*p**h + 0*p**4 + 0*p**2 - 2*p. Factor l(b).
-2*b*(b - 1)*(b + 1)/7
Factor 0*s**4 + 0 + 0*s + 0*s**2 - 1/4*s**5 + 1/4*s**3.
-s**3*(s - 1)*(s + 1)/4
Let b(f) be the second derivative of -1/12*f**4 - f**2 - f - 1/30*f**5 + 0*f**3 + 0. Let z(s) be the first derivative of b(s). Factor z(d).
-2*d*(d + 1)
Let q(s) = s**3. Let p(d) = -32*d**3 - 95*d**2 - 40*d + 20. Let m(x) = p(x) - 3*q(x). Factor m(w).
-5*(w + 1)*(w + 2)*(7*w - 2)
Let p(b) be the third derivative of -b**8/20160 + b**7/3780 + b**4/6 + 4*b**2. Let q(m) be the second derivative of p(m). Factor q(d).
-d**2*(d - 2)/3
Let h(v) be the third derivative of -2*v**2 - 1/3*v**4 - 7/300*v**6 - 23/150*v**5 + 0 - 4/15*v**3 + 0*v. Suppose h(g) = 0. What is g?
-2, -1, -2/7
Let y(f) = f**3 + 4*f**2 - 5*f + 4. Let l be y(-5). Let p = 21 - 19. Factor -a - p - 3*a**3 + 0*a + 2*a**2 + l*a**3.
(a - 1)*(a + 1)*(a + 2)
Let o(k) be the third derivative of k**7/315 + k**6/45 + k**5/18 + k**4/18 - 3*k**2. Determine m, given that o(m) = 0.
-2, -1, 0
Suppose -5*p + 3*f + 16 = 0, 4*f + 6 = 4*p + 5*f. Let -4/3 + 2/3*h**p + 2/3*h = 0. Calculate h.
-2, 1
Suppose z - 6 + 1 = 0. Suppose 3*y = z*y. Find g such that 2/5*g + y + 1/5*g**2 = 0.
-2, 0
Let h(p) be the third derivative of p**8/1008 - p**7/315 - p**6/180 - p**5/12 - 5*p**2. Let l(z) be the third derivative of h(z). Factor l(i).
4*(i - 1)*(5*i + 1)
Suppose 0 = -5*o - f + 19, -4*o + 5*f = -o + 11. Determine v, given that -4*v + 1 - 5*v**4 + 2*v**4 + 5*v**3 - v**o + 2*v**2 = 0.
-1, 1/3, 1
Let i(w) = w**3 - 11*w**2 - 27*w + 16. Let g be i(13). Solve 0*r + 0 + 0*r**g + 2/5*r**4 + 0*r**2 = 0 for r.
0
Let h(j) be the third derivative of -j**6/90 + j**4/18 + 3*j**2 + 2*j. Factor h(b).
-4*b*(b - 1)*(b + 1)/3
Let x = 400 + -5998/15. Let o(a) be the first derivative of 0*a**2 + x*a**3 - 1/15*a**6 - 3/10*a**4 + 6/25*a**5 + 0*a - 1. Factor o(k).
-2*k**2*(k - 1)**3/5
Let l(q) = 5*q**3 - 17*q**2 - 20*q. Let c(b) = -35*b**3 + 120*b**2 + 140*b. Let v(s) = -2*c(s) - 15*l(s). Factor v(t).
-5*t*(t - 4)*(t + 1)
Let m(d) be the first derivative of d**5/180 + d**4/18 + 2*d**3/9 - 2*d**2 + 4. Let b(z) be the second derivative of m(z). Suppose b(y) = 0. Calculate y.
-2
Let r(u) be the third derivative of -7*u**6/120 - 3*u**5/20 - u**4/12 + u**2. Factor r(p).
-p*(p + 1)*(7*p + 2)
Let k(a) = 5*a**5 + 4*a**4 - 3*a**3 - 4*a**2 - 2*a - 3. Let l = -1 - 0. Let j(x) = x**5 - x**3 - 1. Let v(n) = l*k(n) + 3*j(n). Find w such that v(w) = 0.
-1, 0, 1
Let o(y) be the first derivative of 4*y**5/15 - y**4/4 - 5*y**3/9 + y**2/2 + y/3 - 2. Factor o(f).
(f - 1)**2*(f + 1)*(4*f + 1)/3
Let p(s) = s**3 - 7*s**2 - s + 10. Let l be p(7). Find j, given that j**l + 2*j**2 - 4*j**2 + j**3 = 0.
0, 1
Let w be (-22)/18 - 2/(-9). Let r be 3 - (0/1 - w). What is b in b**3 + 2*b**3 - r*b**3 = 0?
0
Suppose -3 + 8*t - 4*t**2 + 11 + 6*t**2 = 0. Calculate t.
-2
Let h(m) be the third derivative of m**8/1680 + m**7/350 - m**6/120 - m**5/100 + m**4/30 - 14*m**2. Suppose h(w) = 0. What is w?
-4, -1, 0, 1
Suppose 5*u - 39 = -t + 2, 4*t = -2*u + 2. Factor 4*i + 3*i**4 + 9*i**3 + 0*i**3 + u*i**2 - i.
3*i*(i + 1)**3
Suppose -5*a = q - 15, 4*a + 8 = -5*q + 41. Let t = 1182 - 3512/3. Determine v so that -20/3*v + 49/3*v**3 + t*v**2 + 25/3*v**q - 8/3 - 80/3*v**4 = 0.
-2/5, 1, 2
Let l = 21 - -28. Let v = l + -46. Solve 105/2*a**3 - 147/4*a**4 + 9/4*a**2 - v - 15*a = 0 for a.
-2/7, 1
Factor 68*m + 176*m**2 - 67*m - 97*m - 7*m**5 + 16 + 51*m**4 - 140*m**3.
-(m - 2)**3*(m - 1)*(7*m - 2)
Factor 4/7*t**2 - 2*t**4 + 0 - 10/7*t**3 + 0*t.
-2*t**2*(t + 1)*(7*t - 2)/7
Suppose -8*s + 20 = -3*s. Factor 2*u**4 - 3*u**4 - u**4 + 0*u**s.
-2*u**4
Let x = 7 + -2. Suppose -x*y + 9 = -2*y. Suppose -1/4*p**5 + 3/4*p + 1/4 + 1/2*p**2 - 3/4*p**4 - 1/2*p**y = 0. What is p?
-1, 1
Let l(i) be the third derivative of -5*i**8/8 + 103*i**7/105 + 101*i**6/60 - 23*i**5/6 + i**4/3 + 4*i**3 + 20*i**2. Suppose l(w) = 0. Calculate w.
-1, -2/7, 3/5, 2/3, 1
Let -3*b**3 + 23 + 24*b**2 + 9 - 6*b**2 + 8*b**2 - 64*b = 0. Calculate b.
2/3, 4
Let w be (-1 - -2)/(-2)*-8. Suppose -w*f - 30 = -5*l, -3*l - 2*f + 1 = -f. Determine a, given that 0*a**3 + 0*a + 2*a**2 - 3*a**4 + 1 + 3*a - l*a**3 - a**5 = 0.
-1, 1
Suppose 3*p + 2 - 14 = 0. Determine y, given that 0*y**2 + 6*y**2 + 12*y**4 + p*y**5 - 4*y**2 + 9*y**3 + y**5 = 0.
-1, -2/5, 0
Let b be (4193/42)/(2/(-3)). Let j = -149 - b. Factor 0*s + j*s**2 - 3.
3*(s - 2)*(s + 2)/4
Let m = 7 - 6. Let y be (-4)/12*(-1 - m). Find b, given that -1/3*b**2 - 1/3 + y*b = 0.
1
Let n(l) = -l**2 - l - 1. Let h(c) = -c + 2*c**3 + 8*c**3 - 36*c**2 - 5*c + 2*c**3 - 3*c**4 - 21. Let g(r) = h(r) - 18*n(r). Let g(p) = 0. What is p?
1
Let k(h) be the third derivative of -h**6/1320 + h**5/132 - h**4/33 + 2*h**3/33 + 4*h**2. Let k(i) = 0. What is i?
1, 2
Determine y so that 87*y**2 + 43*y - 192 - 90*y**2 + 5*y = 0.
8
Let q(l) = -3*l**2 + 3*l - 2. Let y(s) = 5*s**2 + 17*s + 8. Let d(o) = -2*o**2 - 6*o - 3. Let b(z) = -11*d(z) - 4*y(z). Let t(a) = 8*b(a) + 5*q(a). Factor t(c).
(c - 2)*(c + 1)
Fact