 = 4*s**4 + 2*s**3 + 4*s**2 - 6*s + 6. Suppose 3*a - 14 = y, -y = -a + 2*a - 6. Let d(i) = y*h(i) - 6*u(i). Factor d(p).
4*p**2*(p + 1)**2
Determine s so that -s**2 - 1/2*s + 0 - 1/2*s**3 = 0.
-1, 0
Factor -2/11*h**2 - 4/11*h + 16/11.
-2*(h - 2)*(h + 4)/11
Find x, given that 0*x**3 + 0 + 4/3*x + 8/3*x**4 - 8/3*x**2 - 4/3*x**5 = 0.
-1, 0, 1
Let u = -22/5 + 49/10. Factor 1/2*p + u*p**4 + 0 - 1/2*p**3 - 1/2*p**2.
p*(p - 1)**2*(p + 1)/2
Let q(n) be the third derivative of n**5/30 - n**4/4 + 2*n**3/3 - 11*n**2. Determine s so that q(s) = 0.
1, 2
Factor 4/5*d**2 + 0*d - 16/5.
4*(d - 2)*(d + 2)/5
Determine i so that 8*i**3 - 28*i**2 + 56*i - 43 - 4*i**3 + 11 = 0.
1, 2, 4
Suppose -2/9*t**5 + 2/9*t + 0*t**3 + 4/9*t**2 + 0 - 4/9*t**4 = 0. What is t?
-1, 0, 1
Let k(v) = 10*v**4 + 9*v**3 - 23*v**2 + 3*v + 9. Let s(f) = -81*f**4 - 72*f**3 + 183*f**2 - 24*f - 72. Let c(w) = 33*k(w) + 4*s(w). Factor c(i).
3*(i - 1)**2*(i + 3)*(2*i + 1)
Let 0*d - 4/11*d**3 + 0 + 0*d**2 - 2/11*d**4 = 0. Calculate d.
-2, 0
Suppose 5*x - 4*n = 0, 3*n - 5*n = -4*x. Suppose x = -p - 4*v + 15, p + v = 2*p. Factor 9/5*s**4 - 8/5*s**2 + 0 - 4/5*s + 3/5*s**p.
s*(s - 1)*(3*s + 2)**2/5
Let d(o) be the third derivative of -o**7/840 - o**6/120 + o**4/6 + 2*o**3/3 - 5*o**2. Factor d(w).
-(w - 2)*(w + 2)**3/4
Let b(r) be the third derivative of -r**8/10080 + r**6/1080 - r**4/12 + 2*r**2. Let y(v) be the second derivative of b(v). What is j in y(j) = 0?
-1, 0, 1
Let q(i) = i**2 + 5*i - 3. Let t be ((-12)/14)/(6/42). Let o be q(t). Let -4*j**4 + 6*j**o + 0*j**3 + j**5 - 4*j**2 + j + 0*j**3 = 0. What is j?
0, 1
Let a(b) be the second derivative of 1/42*b**4 + 0 + 2/7*b**2 - 11*b + 1/7*b**3. Factor a(h).
2*(h + 1)*(h + 2)/7
Suppose -2*z = 4*x + 2 - 28, 2*z + 6 = 0. Let x*c**5 - 6 - 7 + 5 + 3*c**4 - 26*c**2 + 32*c**3 + 31*c**4 - 40*c = 0. What is c?
-2, -1, -1/4, 1
Let z be (7/(-8))/(-7)*6. Let p(y) be the first derivative of 0*y + 0*y**2 + z*y**4 + 1/6*y**6 + 3/5*y**5 - 2 + 1/3*y**3. Let p(l) = 0. Calculate l.
-1, 0
Let u(v) be the third derivative of -2*v**7/35 + 13*v**6/40 - 3*v**5/4 + 7*v**4/8 - v**3/2 + 2*v**2. Determine n so that u(n) = 0.
1/4, 1
Suppose -2*v + 6 = 4*q - 18, -3*q + 16 = v. Let a = -35/3 + 12. Let z**v + 0 - a*z**5 + 1/3*z**2 - z**3 + 0*z = 0. What is z?
0, 1
Let y(u) be the third derivative of u**8/1680 - u**7/840 - u**6/360 + u**5/120 - u**3/2 + 3*u**2. Let l(w) be the first derivative of y(w). Factor l(b).
b*(b - 1)**2*(b + 1)
Let t(v) be the third derivative of -v**7/8820 - v**6/2520 - v**4/6 + 3*v**2. Let h(m) be the second derivative of t(m). Determine j, given that h(j) = 0.
-1, 0
Let y = -58 - -65. Let q(p) be the second derivative of 2*p + 1/20*p**5 + 0*p**4 + 0 - 1/42*p**y + 0*p**2 + 0*p**3 + 0*p**6. Suppose q(x) = 0. Calculate x.
-1, 0, 1
Factor 4/7*a - 2/7*a**2 + 2/7 - 4/7*a**3.
-2*(a - 1)*(a + 1)*(2*a + 1)/7
Let t(z) be the second derivative of -z**6/40 + 3*z**5/20 - z**4/4 - 6*z. Solve t(a) = 0 for a.
0, 2
Solve 0*y + 0 + 2/5*y**5 - 8/5*y**4 - 4/5*y**2 + 2*y**3 = 0.
0, 1, 2
Let i(d) = 2*d**2 - 5*d + 11. Let w = -11 - -17. Let m(p) = 2*p**2 - 6*p + 12. Suppose -3 - 4 = s. Let l(x) = s*m(x) + w*i(x). Factor l(g).
-2*(g - 3)**2
Let t(l) be the first derivative of -l**6/3 - 4*l**5/5 + 4*l**3/3 + l**2 + 13. Find q such that t(q) = 0.
-1, 0, 1
Let u = 0 + 2. Let x be 4/(-10) + 12/5. Factor y - 1 + 0*y**u - 6*y**3 + 5*y**3 + y**x.
-(y - 1)**2*(y + 1)
Let r be (1*(-3)/(-27))/((-10)/(-6)). Let t(y) be the second derivative of -y + 0*y**5 + 0 + 1/75*y**6 - r*y**4 + 1/5*y**2 + 0*y**3. What is k in t(k) = 0?
-1, 1
Let b = 7 - 7. Let 3*j**4 + b*j + 7*j**2 + 2*j + 8*j**3 + 0*j = 0. Calculate j.
-1, -2/3, 0
Let d(u) = -3*u**4 - 2*u**3 - 3*u**2 + 2. Let t(x) = x**4 - x**3 - 1. Let h(l) = d(l) + 2*t(l). Solve h(m) = 0 for m.
-3, -1, 0
Suppose 3*v + 0 - 9 = 0. Determine j so that 12*j**5 - 8*j**4 - 15*j**v - 9*j - 31*j**4 + 12*j**3 + 39*j**2 = 0.
-1, 0, 1/4, 1, 3
Let a(s) be the first derivative of -s**3/5 + 18*s**2/5 - 33*s/5 - 18. Factor a(o).
-3*(o - 11)*(o - 1)/5
Let f(u) = 2 + 2*u + u**2 + u - 3. Let q(a) = a**2 + 2*a - 1. Let r(x) = -2*x + 4. Let i be r(3). Let g(p) = i*f(p) + 3*q(p). Factor g(k).
(k - 1)*(k + 1)
Let b(n) be the second derivative of -n**8/15680 + n**6/560 + n**5/140 - 5*n**4/12 + 5*n. Let v(g) be the third derivative of b(g). Solve v(r) = 0.
-1, 2
Let f be (-1)/(-1) - (-7 - -4). Suppose -2*r - 4 - 4 = 0, -19 = -l + f*r. Factor 0 - 2/3*i**4 + 0*i + 2/3*i**2 + 0*i**l.
-2*i**2*(i - 1)*(i + 1)/3
Let q(n) be the first derivative of n**3/12 - n**2/2 + n + 68. Solve q(f) = 0 for f.
2
Let c(s) be the second derivative of -s**5/130 - s**4/13 - 4*s**3/13 - 8*s**2/13 + 32*s. Find h, given that c(h) = 0.
-2
Let v = -1 + 0. Let z be (3/(-6))/v*1. Let -1 + 3/2*q - z*q**2 = 0. Calculate q.
1, 2
Let w(o) = -o**2 - 8*o - 2. Let u be w(-7). Let c be u + -4 + 2/(-6). What is p in 0*p + 0 + c*p**2 = 0?
0
Factor -3/2 + 2*t - 1/2*t**2.
-(t - 3)*(t - 1)/2
Find t such that 8/3*t + 2*t**3 + 8*t**2 - 10/3*t**4 + 0 = 0.
-1, -2/5, 0, 2
Suppose 0 = -5*d + 42 - 22. Factor 4/7*m**3 + 0 + 8/7*m**5 + 2*m**d + 0*m - 2/7*m**2.
2*m**2*(m + 1)**2*(4*m - 1)/7
Let v(r) = r**3. Let o(f) = 4*f**3 + f**2 + 2*f. Let m(k) = -o(k) + 5*v(k). Find g such that m(g) = 0.
-1, 0, 2
Let w(y) be the first derivative of -y**4/4 - 5*y**3/3 - 3*y**2/2 + 9*y - 4. Factor w(h).
-(h - 1)*(h + 3)**2
Let q(d) be the third derivative of d**8/168 - d**7/105 - d**6/20 + d**5/30 + d**4/6 - 22*d**2. Factor q(g).
2*g*(g - 2)*(g - 1)*(g + 1)**2
Let n(t) = -5*t**3 + 32*t**2 - 62*t + 38. Let x(m) = 10*m**3 - 65*m**2 + 125*m - 75. Let z(u) = 5*n(u) + 2*x(u). Solve z(f) = 0.
2
Let x(m) be the third derivative of -2*m**7/105 + 2*m**6/15 - 3*m**2. Factor x(s).
-4*s**3*(s - 4)
Let i = -13 - -28. Let j be 13 - i - (-32)/14. Suppose -4/7*p + j*p**2 + 0 = 0. Calculate p.
0, 2
Factor 24/5*s + 2*s**3 + 16/5 - 36/5*s**2.
2*(s - 2)**2*(5*s + 2)/5
Let v(l) be the third derivative of l**10/529200 - l**5/15 - l**2. Let k(s) be the third derivative of v(s). Factor k(o).
2*o**4/7
Let k = 3 + 12. Let t = k - 5. Let 2*z**2 - 2 - 8*z - 2*z**3 + 0*z + t*z**3 = 0. Calculate z.
-1, -1/4, 1
Let k(a) be the second derivative of 8*a**6/135 - a**5/15 - 7*a**4/9 - 34*a**3/27 - 2*a**2/3 + 39*a. Let k(x) = 0. What is x?
-1, -1/4, 3
Let m(n) be the third derivative of -2*n**7/105 + 2*n**6/15 - n**5/3 + n**4/3 + 6*n**2. Let m(g) = 0. What is g?
0, 1, 2
Let z be 4/30 - ((-201)/180 + 1). Find a, given that z + 3/4*a**2 - 1/4*a**3 - 3/4*a = 0.
1
Let k = -5 - -1. Let q = k + 4. Let -2/3*l**5 + 0 + 2/3*l**4 + q*l + 0*l**3 + 0*l**2 = 0. What is l?
0, 1
Let n(k) = k - 4. Let v be n(12). Suppose -t = w - 8, v = -0*t - 3*t + 5*w. Suppose -1/5*x**t + x + 2/5 + 3/5*x**2 - 1/5*x**3 = 0. What is x?
-1, 2
Factor 6 - 22*c**2 + 2*c + 1 + 20*c**2 - 3.
-2*(c - 2)*(c + 1)
Suppose -2*h - 9 = h. Let s be -1 - (h + 4 + -2). Factor 1/3*o - 1/3*o**3 + 0 + s*o**2.
-o*(o - 1)*(o + 1)/3
Let w = -5 + 5. Let t(r) be the first derivative of 1/4*r**5 + 0*r + w*r**2 + 1 + 1/12*r**3 + 1/12*r**6 + 1/4*r**4. Solve t(n) = 0.
-1, -1/2, 0
Factor 2/3*s**2 + 0 + 0*s**3 - 1/3*s**5 - 2/3*s**4 + 1/3*s.
-s*(s - 1)*(s + 1)**3/3
Let q(s) be the first derivative of 0*s**2 + 0*s - 5 + 2/3*s**3. Determine j, given that q(j) = 0.
0
Suppose 18 - 6 = 2*y. Let m(p) be the second derivative of -2*p - 16/45*p**y - 10/9*p**3 - 1/3*p**2 - 4/3*p**5 - 11/6*p**4 + 0. Factor m(t).
-2*(t + 1)**2*(4*t + 1)**2/3
Factor 0*a**3 - 1/4*a**4 + 0*a + 0 + 1/4*a**2.
-a**2*(a - 1)*(a + 1)/4
Factor -3/5*a**2 + 9/5*a - 6/5.
-3*(a - 2)*(a - 1)/5
Suppose l + l = 6. Factor t - l - 1 + 4 - 2*t**2.
-t*(2*t - 1)
Let o(f) be the second derivative of f**4/9 + 4*f**3/9 + 2*f**2/3 + 6*f. Let o(m) = 0. Calculate m.
-1
What is q in -81*q**4 - 5*q - 15*q - 230*q**3 - 175*q**2 + 22 - 34*q**4 - 2 - 20*q**5 = 0?
-2, -1, 1/4
Let a = -3161 - -15717/5. Let q = a + 18. Factor q + 4/5*j**3 + 0*j**2 - 2/5*j**4 - 4/5*j.
-2*(j - 1)**3*(j + 1)/5
Suppose 4*b - 69 = -61. Factor 2/3*d**b + 0 - 4/3*d**4 - 1/3*d**3 + d**5 + 0*d.
d**2*(d - 1)**2*(3*d + 2)/3
Let u = -11 - -11. Let l be -3 - -1*(u + 3). Determine i, given that -8/3*i**2 + l + 8/3*i + 2/3*i**3 = 0.
0, 2
Let s(p) = -2*p**2 + 17*p - 28. Let v be s(6). Suppose 0 - 2/3*c**4 - 2/3*c + 2/3*c**v + 