 3 + 1/10*b**2 + w*b. Factor q(p).
p*(p + 1)/5
Suppose -5*l + 5 = -20. Suppose -h = -l*i - 25, -h - 3*h = 5*i + 25. Find f, given that h - 1/4*f**2 + 1/2*f = 0.
0, 2
Suppose -3*h + 27 = -3*s, 0*h - h + 4*s + 21 = 0. Solve -o**3 + 2 - 4*o**4 + 0*o**5 + 2*o**2 - o**h - 3*o**3 + 5*o = 0 for o.
-2, -1, 1
Let g be (-180)/(-22) + (-4)/22. Let z = -9 + g. Let t(i) = i**3 - i**2 - 1. Let l(n) = -n**3 - n**2 - 1. Let r(j) = z*l(j) + t(j). Factor r(y).
2*y**3
Let f(l) = -4*l**2 + 5*l - 5. Let r(k) = 1. Let p(m) = f(m) + 4*r(m). Suppose p(a) = 0. What is a?
1/4, 1
Let u(n) be the second derivative of n**4/3 - 2*n**3 + 4*n**2 - 7*n. Determine c so that u(c) = 0.
1, 2
Suppose 0 = -0*y + 2*y + x - 12, 3*y + 4*x = 8. Let j be -3 + 3*10/y. What is p in 1/4*p - j*p**3 - 1/2 + p**2 = 0?
-2/3, 1
Let j(m) = 25*m**4 - 8*m**3 - 75*m**2 + 37*m. Let i(c) = 38*c**4 - 12*c**3 - 112*c**2 + 56*c. Let z(h) = -5*i(h) + 8*j(h). Find v, given that z(v) = 0.
-2, 0, 2/5, 2
Let s(u) be the third derivative of 0*u**7 + 7*u**2 + 0 + 1/1008*u**8 + 0*u**3 + 0*u**5 + 0*u - 1/360*u**6 + 0*u**4. Factor s(m).
m**3*(m - 1)*(m + 1)/3
Let m(f) be the first derivative of 2*f**3/15 - 2*f/5 + 6. Let m(b) = 0. Calculate b.
-1, 1
Let d(s) be the first derivative of 3 - 4/5*s**5 + 2/3*s**3 - 3*s**2 + 2*s + 3/2*s**4. What is k in d(k) = 0?
-1, 1/2, 1
Suppose -3*f + 3*r + 10 = 2*r, r = 5*f - 20. Let y(z) be the second derivative of z + 1/3*z**3 + 0 - 1/6*z**4 - 1/10*z**f + z**2. What is n in y(n) = 0?
-1, 1
Suppose 3*t + 4 = -4*j, 24 = -0*j - j + 5*t. Let z be (-5)/(10/j)*2. What is h in -h**3 - 4*h**5 + z*h**5 - h**2 + h**4 + h**5 = 0?
-1, 0, 1
Suppose 2*n = n + 4*w - 10, 4*n + 10 = w. Let j be (9/4 + n)*0. Factor j - 1/3*t + 1/3*t**2.
t*(t - 1)/3
Let m(t) be the second derivative of -2*t**7/147 - 4*t**6/35 - 13*t**5/35 - 4*t**4/7 - 8*t**3/21 + 9*t. Let m(u) = 0. What is u?
-2, -1, 0
Let n(w) = -4*w**2 + 7*w. Let q(j) = -3*j**2 + 5*j. Let l(t) = -5*n(t) + 7*q(t). Factor l(g).
-g**2
Let p(z) be the second derivative of -3*z**5/80 + z**4/16 + z**3/8 - 3*z**2/8 - 3*z. Solve p(f) = 0 for f.
-1, 1
Suppose 0 = -2*d + 6 + 6. Let w be (-4)/(-1 + d/(-1)). Factor -2/7*f**3 - w*f**2 - 2/7*f + 0.
-2*f*(f + 1)**2/7
Let q(z) be the third derivative of z**6/240 - z**4/48 + 2*z**2. Factor q(m).
m*(m - 1)*(m + 1)/2
Let m = 21/16 + 3/16. Factor 3/2*v**4 - m*v + 0 + 9/2*v**2 - 9/2*v**3.
3*v*(v - 1)**3/2
Let g(r) = -75*r**3 + 51*r**2 + 19*r + 2. Let k(n) = -74*n**3 + 50*n**2 + 20*n + 2. Let j(y) = -4*g(y) + 6*k(y). Find h, given that j(h) = 0.
-1/6, 1
Let v = 357 + -355. Factor 2 - 1/4*z**3 + 3/2*z**v - 3*z.
-(z - 2)**3/4
Suppose -20 = 11*c - 42. Determine k so that 16/3*k + 8/3 + 10/3*k**c + 2/3*k**3 = 0.
-2, -1
Suppose 0 = 4*o - 7*o. Let h(l) be the third derivative of o*l + 1/80*l**5 + 0 + 0*l**4 - 1/6*l**3 - 1/480*l**6 + l**2. Let h(r) = 0. Calculate r.
-1, 2
Factor 1/4*i**2 - 1/4*i**3 + 1/4*i - 1/4.
-(i - 1)**2*(i + 1)/4
Let u be 5 - 6/9*18/4. Find s, given that 5/6*s - 1/3 + 1/6*s**3 - 2/3*s**u = 0.
1, 2
Factor 0 + 0*q + 4/5*q**3 + 0*q**2.
4*q**3/5
Find r such that 4/5*r**5 + 8/5 - 8/5*r**3 + 4/5*r - 16/5*r**2 + 8/5*r**4 = 0.
-2, -1, 1
Factor -k + 0*k**2 + 5*k + 4*k**2.
4*k*(k + 1)
Let r(f) = f - 13. Let z be r(15). Suppose h - 1 = -z*o - 8, 4*h = -2*o + 2. Factor 2/3*g**h + 2/3*g - 4/3*g**2 + 0.
2*g*(g - 1)**2/3
Let -l**4 + 3*l**3 - 10598*l**2 + 10604*l**2 - 2*l**4 = 0. What is l?
-1, 0, 2
Let a(y) be the second derivative of y**8/3360 - y**7/840 + y**5/120 - y**4/48 + y**3/6 - 2*y. Let d(i) be the second derivative of a(i). Solve d(u) = 0 for u.
-1, 1
Let r(t) = -3*t**3 + 17*t**2 + 22*t + 2. Let f(c) = -5*c**3 + 35*c**2 + 45*c + 5. Let z(v) = -2*f(v) + 5*r(v). Factor z(y).
-5*y*(y - 4)*(y + 1)
Factor 2*h**3 + 2/13*h**5 + 12/13*h**4 + 8/13*h + 24/13*h**2 + 0.
2*h*(h + 1)**2*(h + 2)**2/13
Let z(n) be the first derivative of -9*n - 2 - 1/3*n**3 - 3*n**2. Find l, given that z(l) = 0.
-3
Let o(f) be the third derivative of f**9/120960 - f**8/40320 - f**5/12 - 4*f**2. Let p(z) be the third derivative of o(z). Suppose p(m) = 0. What is m?
0, 1
What is t in -t**3 + 0 + 2/3*t + 1/3*t**5 - 1/3*t**4 + 1/3*t**2 = 0?
-1, 0, 1, 2
Let w be ((1/4)/((-12)/(-128)))/2. Let d(u) be the second derivative of 4*u**2 - 1/2*u**4 + 0 - w*u**3 + 1/5*u**5 + 1/15*u**6 + u. Factor d(c).
2*(c - 1)**2*(c + 2)**2
Let p(q) be the first derivative of -4/3*q**2 + 16/9*q + 4/9*q**3 - 5 - 1/18*q**4. Solve p(o) = 0.
2
Let h(c) = -7*c**2 - 3*c + 4. Let p be (-2)/(3/15*2). Let m(j) = -11*j**2 - 5*j + 6. Let t(w) = p*m(w) + 8*h(w). Suppose t(x) = 0. Calculate x.
-1, 2
Let q = -41/2 - -373/18. Factor 4/9*i**2 + 0 - q*i.
2*i*(2*i - 1)/9
Let x = -24 + 26. Determine u, given that 0*u + 0 - 1/2*u**x - 8*u**4 + 4*u**3 = 0.
0, 1/4
Let w be 2 - (3 - -1) - -2. Let v = w + 3. Factor -192*y**2 + 88*y**3 - v*y**4 - 4*y**4 + 160*y - 32 - 7*y**4.
-2*(y - 2)**3*(7*y - 2)
Let k = 14 + -6. Suppose k*h + 3*h**2 + 19 - 3*h**2 - 4*h**4 - 8*h**3 - 15 = 0. What is h?
-1, 1
Let -4*y**4 + 16*y**4 - 3*y**2 + 3*y + 159*y**3 - 171*y**3 = 0. Calculate y.
-1/2, 0, 1/2, 1
Suppose u + 2*u = 72. Let o be (u/(-70))/((-10)/35). Let -o*h**4 + 0*h + 0 - 2*h**5 + 0*h**2 + 4/5*h**3 = 0. What is h?
-1, 0, 2/5
Let z = 9 - 2. Suppose 2 = -2*u + 3*f, -1 = -3*u - f + z. Solve -5*s**u - s**3 + s**2 + s**5 + 2*s**2 + 2*s**4 = 0 for s.
-2, -1, 0, 1
Let f(a) be the second derivative of -a**6/30 - 3*a**5/20 - a**4/6 - 5*a. Factor f(y).
-y**2*(y + 1)*(y + 2)
Let v = 217 + -2379/11. Factor -2/11*c**3 + 8/11*c**2 - v*c + 0.
-2*c*(c - 2)**2/11
Let k = 11 - 8. Factor 2*n**2 + 0*n + n**3 + 0*n**k + n.
n*(n + 1)**2
Let f(v) be the second derivative of 0 - 3*v + 0*v**2 - 1/36*v**4 + 0*v**3. Determine t so that f(t) = 0.
0
Factor 4*a**2 + 6*a**4 + 6*a**3 - 5*a**2 - 2*a**3 - a**2.
2*a**2*(a + 1)*(3*a - 1)
Let y(t) = t**3 - 3*t**2 + 2*t + 2. Let v(d) = 4*d**3 - 10*d**2 + 5*d + 5. Let b(o) = 2*v(o) - 7*y(o). Solve b(u) = 0 for u.
-2, -1, 2
Let k = -4 + 6. Suppose -8 = -d - k*s + 3*s, 5 = -5*d - 4*s. Suppose -4*r - 2*r**4 + 2 - r**d + 3*r**3 + 2*r**3 = 0. Calculate r.
-1, 1
Suppose -3*p = p - 8. Solve -35*l**p + 35*l**2 + 3*l - 3*l**3 = 0 for l.
-1, 0, 1
Factor 16/9*o - 56/9*o**2 + 0 + 44/9*o**3 - 10/9*o**4.
-2*o*(o - 2)**2*(5*o - 2)/9
Let d(q) = 15*q - 1. Let y be d(1). Factor 32*m**3 + 4*m - 7*m + 7*m - 22*m**2 - y*m**4.
-2*m*(m - 1)**2*(7*m - 2)
Suppose 3*m + 36 = -171. Let j = m - -209/3. Factor 0 - j*o - 4/3*o**2 - 2/3*o**3.
-2*o*(o + 1)**2/3
Factor -4/5 - 1/5*u**2 + 4/5*u.
-(u - 2)**2/5
Suppose -2*c - 4*h + 5*h + 4 = 0, 5 = 5*c - 5*h. Factor 7/3*z - 7/3*z**c + 2/3 - 2/3*z**2.
-(z - 1)*(z + 1)*(7*z + 2)/3
Let i(z) be the second derivative of -z**7/7 - 2*z**6/35 + 6*z**5/5 + 4*z**4/7 + 13*z - 2. Let i(m) = 0. Calculate m.
-2, -2/7, 0, 2
Let p(q) = -26*q**2 + 2*q + 12*q**3 - 12*q + 12*q**2 - 4*q**4 + 6*q**4. Let g(k) = -k**3 + k**2 + k. Let w(h) = -10*g(h) - p(h). Find x such that w(x) = 0.
-2, 0, 1
Let t(b) be the second derivative of -b**4/24 - b**3/6 - 3*b. Factor t(g).
-g*(g + 2)/2
Suppose -272*x - 22 = -283*x. Factor 1/5*s + 0 + 1/5*s**3 + 2/5*s**x.
s*(s + 1)**2/5
Let g = 112 + -110. Factor -1/3*u - 1/3*u**g + 2/3.
-(u - 1)*(u + 2)/3
Factor -547*c**4 + c**2 + 276*c**4 + 272*c**4 - 2*c**3.
c**2*(c - 1)**2
Let l(d) be the second derivative of -d**7/147 - d**6/105 + d**5/70 + d**4/42 - 2*d + 1. Factor l(m).
-2*m**2*(m - 1)*(m + 1)**2/7
Let w(f) = -f**2 + 6*f + 3. Let r be w(6). Suppose 0*o = -o + r. Factor v**2 + 0*v**2 + 0*v**2 + o*v - 5*v.
v*(v - 2)
Let x(a) be the second derivative of a**8/20160 - a**7/7560 - a**4/12 + 3*a. Let i(r) be the third derivative of x(r). Let i(u) = 0. Calculate u.
0, 1
Let s(d) be the third derivative of d**7/1050 + d**6/100 + d**5/25 + d**4/12 + d**3/10 - 8*d**2. Factor s(i).
(i + 1)**3*(i + 3)/5
Suppose 0 = 8*n - 7*n. Let a(y) be the second derivative of 1/20*y**5 + 0 + n*y**2 - 1/12*y**4 + y + 0*y**3. Factor a(x).
x**2*(x - 1)
Factor -2*f**3 + 8*f**2 + 2*f + 13*f**2 - 17*f**2 - 4.
-2*(f - 2)*(f - 1)*(f + 1)
Suppose 36 = 4*o + 5*f, -2*o - 4*f + 20 = -o. Let u = o - -4. Solve -21*z**5 - 23*z**3 - 17*z**4 - 83*z**3 + 119*z**4 - u*z + 48*z**2 - 15*z**5 = 0.
0, 1/2, 2/3, 1
Let j(k) be the third derivative of k**7/1680 + k**6/240 + k**5/120 - 7*k**2. Find y, given that j