a(g) - 3*t(g). Let q(s) = 0. What is s?
-12
Let b be 2 - (4/22 - 240/110). Factor 1/4*k**b + 1/4*k**2 + 0*k + 0 - 1/2*k**3.
k**2*(k - 1)**2/4
Determine f so that -80*f - 8*f**3 + 60 - f**3 + 35*f**2 + 4*f**3 = 0.
2, 3
Let p(d) be the first derivative of -d**7/420 - d**6/60 + 5*d**3/3 + 3. Let a(o) be the third derivative of p(o). Factor a(i).
-2*i**2*(i + 3)
Let d(l) = l + 13. Let k be d(-9). Suppose 2*x = 7*x - 25, -2 = k*p - 2*x. Factor -4/3*z**3 + 0 + 1/3*z**p + 0*z + 4/3*z**4.
z**2*(2*z - 1)**2/3
Let k(m) be the first derivative of m**4/10 + 2*m**3/5 + 3*m**2/5 + 2*m/5 - 23. Factor k(h).
2*(h + 1)**3/5
Let w be (-4)/(-16) + (-415)/(-20). Let j be (7/(w/(-2)))/(-4). Factor j*r**2 + 0 - 1/3*r.
r*(r - 2)/6
Let q(o) be the first derivative of -3*o**6/2 - 12*o**5 - 36*o**4 - 48*o**3 - 24*o**2 + 5. Determine k, given that q(k) = 0.
-2, -2/3, 0
Let m(l) be the second derivative of -l**6/120 + l**5/40 + 7*l**3/6 - 8*l. Let x(k) be the second derivative of m(k). Determine c so that x(c) = 0.
0, 1
Let c(p) = 18*p + 92. Let y be c(-5). Determine a, given that 1/4*a**y - 1/4 + 0*a = 0.
-1, 1
Suppose 4 = 2*y - 0*y. Factor 4*l + 2 + 2*l + y*l**3 - l**2 + 5*l**2 + 2*l**2.
2*(l + 1)**3
Suppose 0 = d - 3 + 1. Factor 0*x**2 - 3*x + 0 + 2 + 6*x**2 - 5*x**d.
(x - 2)*(x - 1)
Factor 0*u - 1/3*u**2 + 0.
-u**2/3
Let n be 3*-1*(-8)/12. Factor h**3 - 19*h + n - 3*h**2 + 18*h + h**2.
(h - 2)*(h - 1)*(h + 1)
Factor 4/11*o**2 + 0*o + 2/11*o**3 + 0 - 2/11*o**4.
-2*o**2*(o - 2)*(o + 1)/11
Let n(z) be the third derivative of z**5/15 + 10*z**2. Suppose n(j) = 0. Calculate j.
0
Let l(a) = -a**3 + 7*a**2 - 7*a + 9. Let b be l(6). Suppose n = -t + b, -5 = 4*n - 1. Find s, given that 2*s**2 - 2 + 3*s**3 + 3*s**3 - t*s**3 - 7*s + 5*s = 0.
-1, 1
Let g(y) be the first derivative of -y**6/120 - y**5/80 + y**4/48 + y**3/24 + y + 2. Let c(o) be the first derivative of g(o). Factor c(z).
-z*(z - 1)*(z + 1)**2/4
Suppose c = -4*l + 18, -2*l + 58 = -4*c + 184. Let p be 0 - 2 - (-550)/c. Solve 70/3*h**3 - 20/3*h + p*h**4 + 4/3 - h**2 = 0.
-1, 2/7
Let m = 20 + -20. Let y(u) be the second derivative of 1/6*u**3 + m - 3*u + 1/12*u**4 + 0*u**2. Factor y(o).
o*(o + 1)
Let x = 14/39 - -1010/663. Factor 2/17*a**2 + x + 16/17*a.
2*(a + 4)**2/17
Suppose -4*i + 5*j - 2 = 0, j + 0*j - 6 = -2*i. Let w be 2/(i + 2/(-8)). Factor -w*x**2 + 12/7*x**3 + 0 + 2/7*x + 2/7*x**5 - 8/7*x**4.
2*x*(x - 1)**4/7
Let n(g) = -g**3 - 3*g**2 + g + 3. Let x be n(-3). Suppose -2*v + 0*v = x. Factor -1/4*t**3 + v*t**2 + 1/4*t + 0.
-t*(t - 1)*(t + 1)/4
Let x(y) = -2*y**3 - 25*y**2 + 7*y - 7. Let z(q) = -q**3 - 8*q**2 + 2*q - 2. Let i(l) = 2*x(l) - 7*z(l). Suppose i(n) = 0. What is n?
-2, 0
Let g(m) be the first derivative of m**3 - 39*m**2 + 507*m - 24. Factor g(k).
3*(k - 13)**2
Let z be -3 + (4 - (-6)/2). Factor -2*f + 3*f - 3*f - z*f - 3*f**2 + 3*f**3.
3*f*(f - 2)*(f + 1)
Factor -7/8*o**3 + 5/8*o**2 + 1/4*o + 0.
-o*(o - 1)*(7*o + 2)/8
Let d(m) be the second derivative of -m**5/4 + 5*m**3/2 - 5*m**2 - 10*m. Solve d(k) = 0.
-2, 1
Let l = 4117/6669 - 1/513. Factor 2/13*w**4 - 8/13*w + 4/13*w**3 + l - 6/13*w**2.
2*(w - 1)**2*(w + 2)**2/13
Let o(s) be the first derivative of -3/20*s**4 - 1/15*s**3 + 1/5*s**2 + 0*s - 4. Factor o(l).
-l*(l + 1)*(3*l - 2)/5
Suppose -13*w - 795 = -847. Factor 0 + 2/9*n**w - 2/9*n**2 - 2/9*n**3 + 2/9*n.
2*n*(n - 1)**2*(n + 1)/9
Let s = 3595/7 + -513. Suppose 6/7*g - 2/7*g**2 - s = 0. Calculate g.
1, 2
Factor -80*u**2 - 11*u**3 - 18*u - 5*u**3 - 4*u**3 - 47*u - 15.
-5*(u + 3)*(2*u + 1)**2
Let k be 3 + -6 + 7 - (-52)/(-14). Factor k*h**2 + 2/7*h + 0.
2*h*(h + 1)/7
Let f(m) = -4*m**5 - 10*m**3 + 2*m. Let a(u) = -7*u**5 - 19*u**3 + 4*u. Let i(x) = -6*a(x) + 11*f(x). Factor i(y).
-2*y*(y - 1)**2*(y + 1)**2
Let q(w) be the second derivative of w**4/108 + 6*w + 3. Factor q(z).
z**2/9
Let g(m) be the third derivative of 0 + 0*m + 1/210*m**7 + 0*m**3 + 3*m**2 - 1/60*m**6 + 0*m**4 + 1/60*m**5. Let g(c) = 0. What is c?
0, 1
Let f(o) be the first derivative of -5*o**3/6 - 5*o**2/2 - 5*o/2 - 3. Let f(g) = 0. Calculate g.
-1
What is h in 7*h + 4*h**5 + 4 - 12*h**2 + 2*h**2 - 10*h**3 + 6*h**4 - h = 0?
-2, -1, -1/2, 1
Find d, given that -1/5*d**4 + 1/5*d - 1/5 + 1/5*d**5 + 2/5*d**2 - 2/5*d**3 = 0.
-1, 1
Let z(b) be the second derivative of 0 + 0*b**2 + 1/6*b**4 - 2*b - 1/30*b**5 - 2/9*b**3. Factor z(h).
-2*h*(h - 2)*(h - 1)/3
Let j = 1 - -2. Suppose j*i + i - 24 = 0. Solve -i*a**3 + a**5 + 6*a**3 - a**4 = 0.
0, 1
Suppose 0*v + 6 = 3*v. Let k = 5 - v. Factor -2*g + 4*g - 2*g - g**2 + 2*g**k - g**4.
-g**2*(g - 1)**2
Let h(j) = -j + 16. Let y be 80/6 + 11/(-33). Let v be h(y). Factor 4/3*o**2 - 2/3*o**v - 2/3*o + 0.
-2*o*(o - 1)**2/3
Let t(j) be the second derivative of 0 - 10*j - 1/102*j**4 - 4/51*j**3 - 4/17*j**2. Solve t(g) = 0 for g.
-2
Let x(l) = -l**4 - 3*l**3 - 2*l**4 - 5*l**2 + 4*l**3. Let a = -9 + 7. Let o(r) = -r**4 - 2*r**2. Let s(g) = a*x(g) + 5*o(g). Solve s(m) = 0 for m.
0, 2
Let l(y) = -y**2 + 5*y + 8. Let u be l(6). Factor -9*h**u - 3/2 - 6*h**3 - 3/2*h**4 - 6*h.
-3*(h + 1)**4/2
Suppose 0*b = -4*b. Let r be b + 2 + (-14)/8. Factor 0 + 1/2*p**2 - 1/2*p**4 + 0*p**3 - r*p**5 + 1/4*p.
-p*(p - 1)*(p + 1)**3/4
Let z(o) = -o**2 + 4*o. Let y be z(4). Let j(k) be the third derivative of 0 - 1/270*k**5 + 1/108*k**4 + 0*k + y*k**3 - k**2. Determine v so that j(v) = 0.
0, 1
Let x = 73/2 + -36. Let z be 11*(0 - 2/(-8)). Factor 9/4*p**2 + z*p + x.
(p + 1)*(9*p + 2)/4
Let n(j) be the first derivative of j**6/21 - 8*j**5/35 + 3*j**4/7 - 8*j**3/21 + j**2/7 - 18. Let n(q) = 0. Calculate q.
0, 1
Let n(i) be the second derivative of i**4/9 + i**3/3 + i**2/3 + 3*i. Let n(w) = 0. Calculate w.
-1, -1/2
Let v(k) = 11*k**2 - 31*k + 59. Suppose 0 = -4*l + 3 + 5. Let o(y) = y + 5*y**2 - 17*y - 10 + 17 + 22. Let q(t) = l*v(t) - 5*o(t). Factor q(d).
-3*(d - 3)**2
Let z(x) = -31*x + 3 + 30*x - x**2 - 2 + x**3. Let o(m) = 3*m**4 - 21*m**3 + 12*m**2 + 21*m - 15. Let u(p) = o(p) + 15*z(p). Factor u(w).
3*w*(w - 2)*(w - 1)*(w + 1)
Solve 0 - 2/3*y**3 + 8/3*y**2 - 8/3*y = 0.
0, 2
Find z, given that 725*z**3 + z - z**2 - z**4 - z - 723*z**3 = 0.
0, 1
Suppose 48 = 18*x - 6*x. Solve 0*o + 0 - 2/9*o**3 - 2/9*o**x + 0*o**2 = 0.
-1, 0
Let h(d) = -2*d**3 + 4*d**2 + 6*d - 6. Let v(g) = g**3 - 4*g**2 - 5*g + 5. Let r(b) = 5*h(b) + 6*v(b). Factor r(m).
-4*m**2*(m + 1)
Let h(g) be the first derivative of 0*g**2 - 1 + 4*g - 4/3*g**3. Factor h(t).
-4*(t - 1)*(t + 1)
Let v(f) be the third derivative of -f**5/60 + f**4/12 - 6*f**2. Factor v(m).
-m*(m - 2)
Suppose 0*q + 4*q = -4. Let c be (4/14)/(q/(-1)). Determine a so that c*a**2 + 6/7*a**3 - 4/7 + 2/7*a**4 - 6/7*a = 0.
-2, -1, 1
Determine j so that -2/7 + 9/7*j**2 + j = 0.
-1, 2/9
Let h = -6 - -10. Suppose h*m - 6 = 6. Factor 4*p**4 - 5*p**4 + 0*p**3 + p**3 + 0*p**m.
-p**3*(p - 1)
Find p such that -26/9*p**3 + 28*p**4 - 8/9*p + 0 - 18*p**5 - 56/9*p**2 = 0.
-2/9, 0, 1
Factor -2/3*h**3 + 8/3*h**2 - 8/3*h + 0.
-2*h*(h - 2)**2/3
Let t(n) be the second derivative of 1/18*n**3 + 1/3*n**2 - 1/36*n**4 + 5*n + 0. Factor t(i).
-(i - 2)*(i + 1)/3
Let w(t) = 5*t**5 - t**4 + 14*t**3 - 10*t**2 + t + 3. Let p(b) = 4*b**5 - 2*b**4 + 13*b**3 - 10*b**2 + 2*b + 2. Let r(i) = 4*p(i) - 3*w(i). Factor r(h).
(h - 1)**5
Let m(f) be the third derivative of -3*f**6/20 + 7*f**5/10 + 17*f**4/12 + f**3 - 11*f**2. Factor m(k).
-2*(k - 3)*(3*k + 1)**2
Let v = 91 + -65. Suppose n = -5*h + 16 + 6, -5*h - 3*n + v = 0. Let -1/2 + 1/4*t**5 - 7/4*t - 2*t**2 + 1/2*t**h - 1/2*t**3 = 0. Calculate t.
-1, 2
Let l(g) be the third derivative of 2*g**7/945 + g**6/270 - 17*g**2. Factor l(z).
4*z**3*(z + 1)/9
Let x(v) be the second derivative of 8/33*v**3 + 4/11*v**2 + v + 1/110*v**5 + 5/66*v**4 + 0. Factor x(q).
2*(q + 1)*(q + 2)**2/11
Let s(d) = d**2 - 7. Let j be s(3). Factor -j*t + 6*t + 2*t - t**4 + 4*t**4 - 9*t**2.
3*t*(t - 1)**2*(t + 2)
Solve -b**3 + 140*b + 5*b**3 - 2*b**3 - 108*b - 16*b**2 = 0.
0, 4
Let b(g) = -g**2 - 8*g + 3. Let w be b(-8). Factor -4*i**2 + i**4 + w*i**3 + 3*i**2 - 4*i**3 + i.
i*(i - 1)**2*(i + 1)
Suppose -3*x - 4*x + x = 0. Let a(b) be the second derivative of x + 1/36*b**4 + 2/3*b**2 - 3*b - 2/9*b**3. Determine h, given that a(h) = 0.
2
Factor 0*d - 6/5*d**3 + 0 - 3/5*d**5 + 0*d**2 - 9/5*d**4.
-3*d**3*(d + 