4 - 180*q**3 + 96*q**2 - 16*q + 7. Let p(u) = 50*u**4 - 90*u**3 + 48*u**2 - 8*u + 3. Let l(f) = -7*p(f) + 3*y(f). Factor l(j).
-2*j*(j - 1)*(5*j - 2)**2
Let d(y) be the second derivative of y**8/1680 + y**7/420 - y**6/360 - y**5/60 - y**3/3 - 4*y. Let u(x) be the second derivative of d(x). Factor u(h).
h*(h - 1)*(h + 1)*(h + 2)
Let q(v) = 27*v**4 + 156*v**3 + 219*v**2 + 123*v + 24. Let o(p) = 7*p**4 + 39*p**3 + 55*p**2 + 31*p + 6. Let b(k) = 9*o(k) - 2*q(k). Factor b(f).
3*(f + 1)**2*(f + 2)*(3*f + 1)
Solve 8*f - 14*f + 15*f - 3*f**2 = 0.
0, 3
Let 249*f**3 - 124*f**3 - f**5 - 124*f**3 = 0. What is f?
-1, 0, 1
Let t(s) = -2*s**4 - 3*s**3 + s**2 - 3*s - 2. Let c(z) = -6*z**4 - 8*z**3 + 4*z**2 - 8*z - 6. Let i(y) = 3*c(y) - 8*t(y). Factor i(r).
-2*(r - 1)**2*(r + 1)**2
Let g(h) = 4*h**2. Let j(q) be the first derivative of -q**4/4 - 13*q**3/3 - 6. Let i = -2 - -9. Let y(p) = i*g(p) + 2*j(p). What is n in y(n) = 0?
0, 1
Let b be (-1)/(-22)*(-1 + 5). Factor 2/11*r**3 + 0 + 0*r**2 + 0*r - b*r**5 + 0*r**4.
-2*r**3*(r - 1)*(r + 1)/11
Let y(t) be the second derivative of t**6/30 - t**5/10 - t**4/12 + t**3/3 - 2*t. Factor y(m).
m*(m - 2)*(m - 1)*(m + 1)
Let b(c) be the second derivative of -c**6/45 + c**4/6 + 2*c**3/9 - c. Factor b(u).
-2*u*(u - 2)*(u + 1)**2/3
Let x(a) be the third derivative of -a**7/840 + a**6/240 + a**5/20 - a**4/3 - 6*a**2. Let d(n) be the second derivative of x(n). Factor d(g).
-3*(g - 2)*(g + 1)
Let a be ((-1)/12)/((-220)/(-297)). Let v = a + 21/16. Let 0 + v*j**5 + 4*j**4 + 2/5*j + 12/5*j**2 + 24/5*j**3 = 0. What is j?
-1, -1/3, 0
Let 0*i**2 + i + 2/3 - 1/3*i**3 = 0. What is i?
-1, 2
Let w(k) be the second derivative of k**7/168 - k**6/60 + k**4/24 - k**3/24 - 4*k. Factor w(l).
l*(l - 1)**3*(l + 1)/4
Factor -3/4 + 3/2*t - 3/4*t**2.
-3*(t - 1)**2/4
Let s be (-1)/(-3) - (2 + 17/(-9)). Let k(r) be the first derivative of -1/3*r - 3 - s*r**3 + 1/5*r**5 - 1/18*r**6 + 1/2*r**2 - 1/6*r**4. Factor k(q).
-(q - 1)**4*(q + 1)/3
Let h be -4 - (-7)/(42/27). Let a(y) be the second derivative of y**3 - y**2 - y + 1/10*y**5 + 0 - h*y**4. Factor a(g).
2*(g - 1)**3
Suppose -3*x = 5*c + 7 - 18, 5*c + 3 = -x. Let q = x - 3. Factor -3*i**4 + 3*i**4 - i**q - 1 + 2*i**2.
-(i - 1)**2*(i + 1)**2
Let d(y) = y**3 + 6*y**2 - 2. Let j be d(-6). Let r be (j/3)/((-2)/6). Factor 3*q**r - 3*q**2 - 6*q**4 - 4*q**2 - 10*q**3.
-2*q**2*(q + 1)*(3*q + 2)
Let t(x) be the first derivative of -x**6/27 - 4*x**5/9 - 25*x**4/18 + 40*x**3/27 + 80*x**2/9 - 128*x/9 - 18. Factor t(i).
-2*(i - 1)**2*(i + 4)**3/9
Let s(z) be the third derivative of z**7/630 - z**6/180 + z**5/180 - 2*z**2. Factor s(a).
a**2*(a - 1)**2/3
Let y(w) be the second derivative of w**4/3 - 2*w**3/3 - 4*w**2 + 15*w. Find f, given that y(f) = 0.
-1, 2
Let b = 30/101 - 5299/18180. Let s(d) be the third derivative of -b*d**5 + 0*d**4 + 1/360*d**6 + 0*d + 0*d**3 + 0 - 2*d**2. Factor s(c).
c**2*(c - 1)/3
Determine s so that -2/13*s**3 + 2/13*s**4 + 2/13*s + 12/13 - 14/13*s**2 = 0.
-2, -1, 1, 3
Suppose -5*s = -5*k - 25, 4*s - 7 = -4*k + 13. Suppose -s + 21 = 4*m. Determine f, given that -f**3 + 1/4*f**m + f**2 + 0*f + 0 = 0.
0, 2
Suppose 0 - 3/7*p + 5/7*p**2 = 0. Calculate p.
0, 3/5
Let i be (-103)/(-15) + (-14)/(-105). Let u = i - 4. Let 2/11*z**2 + 0*z + 2/11*z**u + 0 - 2/11*z**4 - 2/11*z**5 = 0. Calculate z.
-1, 0, 1
Let i(k) be the second derivative of -k**6/6 - 17*k**5/4 - 105*k**4/4 + 135*k**3/2 + 11*k. Solve i(o) = 0 for o.
-9, 0, 1
Let d(p) be the second derivative of p**4/36 - p**3/18 - p**2/3 + 21*p. Factor d(m).
(m - 2)*(m + 1)/3
Let b(n) = -n**3 + 7*n**2 + 10*n - 16. Let v be b(8). Factor -1/2*j**2 - j + v.
-j*(j + 2)/2
Let o(h) = -h - 1. Suppose 0 = 2*v - 6 - 8. Suppose -2*y + v*y = -15. Let q(a) = 5*a**3 + 8*a**2 + 4*a + 1. Let u(c) = y*o(c) - q(c). Factor u(t).
-(t + 1)**2*(5*t - 2)
Let z(i) = 7*i**2 - 8*i + 1. Let t(u) = 6*u**2 - 8*u + 2. Let h(y) = -3*t(y) + 2*z(y). Solve h(v) = 0.
1
Let c be 11 + (-4 - (0 + -2)). Suppose -c = 3*j - 18. Factor 1/2 + 1/2*g - 1/2*g**j - 1/2*g**2.
-(g - 1)*(g + 1)**2/2
Factor -36*h**2 + 4 + 14*h + h + 20*h**3 - 3*h.
4*(h - 1)**2*(5*h + 1)
Let h(a) be the third derivative of a**9/3780 - a**8/840 + a**7/630 - a**4/4 - 4*a**2. Let d(q) be the second derivative of h(q). Factor d(u).
4*u**2*(u - 1)**2
Factor 1/2*x**2 - 1/2 - 1/2*x + 1/2*x**3.
(x - 1)*(x + 1)**2/2
Let p(y) be the second derivative of y**8/11200 + y**7/4200 - y**6/1200 - y**5/200 + y**4/4 + 2*y. Let b(h) be the third derivative of p(h). Factor b(s).
3*(s - 1)*(s + 1)**2/5
Let n = -6 - -7. Let x be (n/11)/(1/4). Factor 0*t**2 - x*t**4 + 0 + 0*t - 2/11*t**3.
-2*t**3*(2*t + 1)/11
Let k(t) be the third derivative of -t**5/140 + 5*t**4/56 - 2*t**3/7 + 14*t**2. Find i, given that k(i) = 0.
1, 4
Let c(l) = -l**2 + 1. Let w(g) = 5*g**4 - 7*g**3 + 3*g**2 + 7*g - 8. Let i(k) = 6*c(k) + w(k). Let i(m) = 0. What is m?
-1, 2/5, 1
Find w such that -w**4 + 6*w**4 - 52*w**3 + 15*w**2 + 5*w**5 + 27*w**3 = 0.
-3, 0, 1
Let f = 3289/9 + -365. Factor 0 + 10/9*c**4 + f*c**3 + 0*c + 0*c**2 + 2/3*c**5.
2*c**3*(c + 1)*(3*c + 2)/9
Suppose 13 = -4*a + 5*l - 17, -44 = 4*a + 2*l. Let z be (1 - (-11)/a)*-4. Let 2/5*p**2 + 2/5*p + 0 - z*p**4 - 2/5*p**3 = 0. Calculate p.
-1, 0, 1
Let a = -37 - -37. Suppose 0*i + a + 1/4*i**3 + 0*i**2 + 1/4*i**5 - 1/2*i**4 = 0. What is i?
0, 1
Let n(b) = -12*b**2 + 8*b - 5. Let m be (24/20)/((-1)/5). Let h be (m - 0)/(-2) + 2. Let w(a) = -23*a**2 + 17*a - 9. Let s(f) = h*n(f) - 3*w(f). Factor s(t).
(t - 1)*(9*t - 2)
Let q(c) = 147*c**5 - 70*c**4 - 79*c**3 - 12*c**2. Let m(a) = 49*a**5 - 23*a**4 - 26*a**3 - 4*a**2. Let b(y) = 7*m(y) - 2*q(y). Suppose b(h) = 0. Calculate h.
-2/7, 0, 1
Suppose 0 = 7*x + 4*x - 44. Let m(d) be the first derivative of -1/8*d**2 + 1/6*d**3 + 0*d + 1 - 1/16*d**x. Factor m(b).
-b*(b - 1)**2/4
Let o(x) be the third derivative of x**6/24 - 5*x**4/24 + 19*x**2. Let o(z) = 0. What is z?
-1, 0, 1
Let r(g) = -144*g - 1292. Let b(j) = -j**2 - 1. Let f(y) = 4*b(y) + r(y). Factor f(p).
-4*(p + 18)**2
Suppose -39 = 5*y + 4*s, 3*y - 6*y + 2*s - 19 = 0. Let u(g) = -g + 1. Let l be u(y). Suppose -l*i**3 + 4/3 + 10/3*i - 8/3*i**2 = 0. Calculate i.
-1/2, 2/3
Let o(x) be the third derivative of x**5/60 + x**4/24 - 5*x**2. Let r(s) = 4*s**2 + 5*s + 1. Let z(c) = 3*o(c) - r(c). Let z(l) = 0. What is l?
-1
Factor -2/5*p**3 + 1/5 - 2/5*p**2 + 1/5*p**4 + 1/5*p**5 + 1/5*p.
(p - 1)**2*(p + 1)**3/5
Solve 19*m**3 + 305*m**4 - m**2 - 7*m**2 - 277*m**4 + m**3 = 0.
-1, 0, 2/7
Let o = -7/43 - 3634/129. Let r = o + 29. Factor 0 + 4/3*z + r*z**2.
2*z*(z + 2)/3
Let f = -3 - -5. Let t be (-3 - 1)*f/(-4). Factor -2 - t*c**4 + 4*c**2 - 3*c + 6*c - 3*c.
-2*(c - 1)**2*(c + 1)**2
Let a(h) be the third derivative of -h**9/20160 + h**8/8960 + h**4/8 + 3*h**2. Let k(r) be the second derivative of a(r). Let k(l) = 0. Calculate l.
0, 1
Let t be -1 + (-2 + 6 - -4). Suppose 2*l = t*l. Solve l + 0*z - 3/4*z**2 - 9/4*z**3 - 9/4*z**4 - 3/4*z**5 = 0.
-1, 0
Let p(d) be the first derivative of -d**6/6 + 4*d**5/5 - d**4 - 2*d**3/3 + 5*d**2/2 - 2*d + 4. Factor p(q).
-(q - 2)*(q - 1)**3*(q + 1)
Suppose u + g + 0*g + 26 = 0, -g = -3*u - 70. Let o = u - -24. Factor -1/2*z**2 + o + 0*z**3 + 0*z + 1/2*z**4.
z**2*(z - 1)*(z + 1)/2
Let w(c) be the third derivative of -c**9/5040 - c**8/448 - c**7/120 - c**6/80 - c**4/6 - 6*c**2. Let y(k) be the second derivative of w(k). Factor y(n).
-3*n*(n + 1)**2*(n + 3)
Factor -j**4 - 2*j**2 - 2*j**2 - 3*j**4 + 8*j**2.
-4*j**2*(j - 1)*(j + 1)
Let m = -39 + 34. Let o be 2/m + (-2)/(-5). What is p in o - 1/5*p + 1/5*p**3 + 2/5*p**2 - 2/5*p**4 = 0?
-1, 0, 1/2, 1
Let m = 853/2 - 425. Factor 0 + 3/2*p**2 - m*p.
3*p*(p - 1)/2
Let n(c) = c**2 - c. Let i(r) = -2*r**2 + r + 1. Suppose 5*t - l = -6*l - 5, -1 = t + 5*l. Let k(u) = t*i(u) - n(u). Factor k(a).
(a - 1)*(a + 1)
Let c(p) be the second derivative of -p**4/12 + 2*p**3/3 - 3*p**2/2 + 3*p. Determine f, given that c(f) = 0.
1, 3
Suppose 0 = 7*l - 10 - 11. Let x(v) be the second derivative of 0*v**l + 0*v**2 - 2*v - 1/2*v**4 + 3/20*v**5 + 0. Factor x(u).
3*u**2*(u - 2)
Suppose -2*j + 17 = -3. Suppose -i - 4*i = -j. Factor 0*y**2 + 3*y + 44*y**3 - y + 18*y**5 + 48*y**4 + 16*y**i.
2*y*(y + 1)**2*(3*y + 1)**2
Let h(n) be the second derivative of -n**7/1