 3/4*a.
-3*a*(5*a + 2)/8
Factor -40*q - 80 - 5*q**2 + 11*q**2 - 11*q**2.
-5*(q + 4)**2
Let d(b) be the first derivative of -b**3/9 + b**2/2 - 12. Factor d(i).
-i*(i - 3)/3
Factor -45/2*r + 3/2*r**3 - 12 - 9*r**2.
3*(r - 8)*(r + 1)**2/2
Suppose -4 = -2*r + 36. Find g, given that 6 - 8*g**3 + 28*g**5 - 22*g**2 - 21*g**3 + r*g**4 - 4 + g = 0.
-1, -1/2, 2/7, 1
Let p(q) be the first derivative of 3*q**5/5 - 3*q**4/4 + 8. Factor p(n).
3*n**3*(n - 1)
Let s(y) = 4*y**2 + 7*y + 6. Let i be s(-1). What is w in -3/2*w**2 - i + 9/2*w = 0?
1, 2
Let t(a) be the second derivative of a**6/45 - a**5/15 + a**4/18 - 15*a. Factor t(v).
2*v**2*(v - 1)**2/3
Let j = -149/55 + 32/11. Factor j*o**2 + 0 + 3/5*o.
o*(o + 3)/5
Determine n so that -8*n**3 + 4*n - 2*n**2 + 0*n + 2*n**4 + 4*n**3 = 0.
-1, 0, 1, 2
Solve 6 - 3*i**2 - 2 + 6*i - 3 - 4 = 0 for i.
1
Let k(t) be the third derivative of t**6/30 + 3*t**5/5 + 4*t**4 + 32*t**3/3 - t**2 + 6*t. Suppose k(b) = 0. Calculate b.
-4, -1
Let j(g) be the third derivative of g**8/336 + 4*g**7/525 - g**6/150 - 15*g**2. Solve j(z) = 0 for z.
-2, 0, 2/5
Let v be (4/(-6))/((-12)/(-414)). Let k = v - -40. Factor -1 + t**2 + k*t - 17*t.
(t - 1)*(t + 1)
Let j(b) be the first derivative of -3*b**3/4 - 3*b**2/4 + 3*b/4 - 2. Solve j(g) = 0 for g.
-1, 1/3
Factor -56/3*y - 1/3*y**5 - 43/3*y**3 - 11/3*y**4 - 16/3 - 73/3*y**2.
-(y + 1)**3*(y + 4)**2/3
Let 8*w**2 + 3 + 140*w**3 + 2*w**4 - 148*w**3 - 3 = 0. What is w?
0, 2
Solve 60*n**2 + 240*n + 294 + 26 + 41*n**3 - 36*n**3 = 0 for n.
-4
Let p(b) = 8*b**2 + 9*b + 64. Let q(k) = -k**2 + k. Let f(x) = 4*p(x) + 28*q(x). Solve f(t) = 0.
-8
Let t(m) = -m**2 - m. Let s(x) = 2*x**2. Let v(a) = -s(a) - t(a). Factor v(i).
-i*(i - 1)
Let j(y) be the second derivative of -4/5*y**2 + 4*y + 0*y**3 + 0 + 1/30*y**4. Suppose j(s) = 0. Calculate s.
-2, 2
Suppose -2*g = -3*g + 12. Factor -2 - 3*l**4 - g*l**2 + 0*l**4 + 8*l**3 + l**4 + 8*l.
-2*(l - 1)**4
Let v(s) be the third derivative of s**5/30 + s**4/12 - 2*s**3/3 - 11*s**2. Factor v(b).
2*(b - 1)*(b + 2)
Let u be 0 + 0 + 4/2. Let m be u/(-9) + 2/9. Determine f, given that m*f - 2/5*f**3 + 0*f**2 + 0 + 0*f**4 + 2/5*f**5 = 0.
-1, 0, 1
Let g = -7 - -2. Let w = -3 - g. Let m(x) = -12*x**4 - 14*x**3 - 7*x**2. Let p(s) = -s**4 - s**3 - s**2. Let i(t) = w*m(t) - 18*p(t). Factor i(d).
-2*d**2*(d + 2)*(3*d - 1)
Suppose -4/7*x**2 + 0*x + 0 = 0. What is x?
0
Let b(z) = -42 - z**2 + 41 + 2*z + z**4 - 2*z - z**3. Let g(a) = -a**5 + 5*a**4 - 3*a**3 - 5*a**2 - 4. Let h(m) = 12*b(m) - 3*g(m). What is q in h(q) = 0?
-1, 0, 1
Let p = -10/41 + 152/287. Suppose -4/7*n**2 + 6/7*n - p = 0. What is n?
1/2, 1
Suppose 4*v + 3*q - 33 = -2*q, 26 = 3*v + 4*q. Factor w**4 - w**v + 3*w - 9*w - w**5 + w**3 + 6*w.
-w**2*(w - 1)**2*(w + 1)
Let v(d) be the second derivative of 4/21*d**3 + 0*d**2 + 11/10*d**5 + 2*d + 0 - 16/21*d**4 - 7/15*d**6. Factor v(x).
-2*x*(x - 1)*(7*x - 2)**2/7
Suppose 0 = 7*v - 5*v. Let j(a) be the second derivative of 1/40*a**5 - 1/12*a**4 + 1/12*a**3 + v + 2*a + 0*a**2. Find b, given that j(b) = 0.
0, 1
Let s(n) be the second derivative of -n**5/10 + n**4/6 + 2*n**3/3 - 2*n - 7. Factor s(g).
-2*g*(g - 2)*(g + 1)
Let m = 334/3 - 110. Let -m + 2/3*x**2 + 2/3*x = 0. What is x?
-2, 1
Let u(v) be the third derivative of 1/40*v**5 + 1/8*v**4 - v**2 + 1/3*v**3 + 0*v + 0 + 1/480*v**6. Factor u(q).
(q + 2)**3/4
Let b = -125 + 125. Find p such that 0*p**2 + p**4 - 1/2*p + b + 3/2*p**3 = 0.
-1, 0, 1/2
Factor -2*g**3 + 7*g**3 + 0*g**2 + 5*g + g**2 - 11*g**2.
5*g*(g - 1)**2
Let h = 8 - -1. Let s be (h + -1)/2 - -2. Solve 6*m**4 + 2*m**2 - 4*m**4 - s*m**2 + 2 = 0 for m.
-1, 1
Let p(d) be the first derivative of d**5/80 + d**4/24 + 2*d + 6. Let o(k) be the first derivative of p(k). Let o(t) = 0. What is t?
-2, 0
Factor g**4 + 2*g + 1 - 2*g**4 - 2*g**3 + 0*g.
-(g - 1)*(g + 1)**3
Suppose 6*b + 1 - 13 = 0. Solve 16/3*p + 2*p**b - 6*p**3 - 8/3 = 0 for p.
-1, 2/3
Let c(i) be the first derivative of i**6/24 + i**5/5 + i**4/4 - i**3/6 - 5*i**2/8 - i/2 - 20. Factor c(u).
(u - 1)*(u + 1)**3*(u + 2)/4
Determine v, given that -v**3 - 1/3*v**4 - v**2 + 0 - 1/3*v = 0.
-1, 0
Let a = 207 + -207. Factor -2/5*k**3 + 2/5*k**5 + a*k + 2/5*k**4 - 2/5*k**2 + 0.
2*k**2*(k - 1)*(k + 1)**2/5
Let w(n) be the third derivative of -n**7/42 - n**6/12 - n**5/12 + 8*n**2. Factor w(t).
-5*t**2*(t + 1)**2
Let a(w) = w**2 + 7*w. Let b be a(-7). Let h(g) be the third derivative of 0 + b*g**3 + 1/6*g**4 + 0*g + 2*g**2 - 1/30*g**5. Factor h(i).
-2*i*(i - 2)
Let b(k) be the second derivative of k**7/3780 + k**6/540 - k**4/27 - k**3 + 3*k. Let y(i) be the second derivative of b(i). Factor y(d).
2*(d - 1)*(d + 2)**2/9
Let c(l) be the second derivative of -l**5/20 - l**4/12 + 5*l**3/6 - 3*l**2/2 + 22*l. Factor c(j).
-(j - 1)**2*(j + 3)
Suppose -f = -5 + 3. Suppose 20 = 12*i - 28. Suppose -125/3*u**5 + 8/3*u + 52/3*u**f + 0 + 30*u**3 - 25/3*u**i = 0. What is u?
-2/5, 0, 1
Let n be (-2)/(-6) + 1/(-3). Suppose n = 3*o - 0*o - 6. Factor -x + 8*x**3 - 10*x**4 - 8*x**2 - 12*x**2 - 9*x - 2*x**5 - o - 28*x**3.
-2*(x + 1)**5
What is w in -4*w**3 + 18*w + 6*w**3 - 19*w**2 + 7*w**2 = 0?
0, 3
Let a(t) = 3*t**2 + 2*t - 2. Let h be a(-2). Let j(c) = -c**2 + 6*c + 4. Let n be j(h). Let 5*m**3 - 4*m**2 - 2*m**3 + 4*m**n - m - 2*m**3 = 0. Calculate m.
-1, -1/4, 0, 1
Find c, given that -3*c + 3*c**3 - 7*c**3 + 12*c**2 - 12 + 7*c**3 = 0.
-4, -1, 1
Let f(j) = -j**2 - 11*j - 12. Let i be f(-9). Suppose q - 18 = -i*s + s, 0 = 4*q - 12. Factor 0 - 2/7*v + 0*v**s - 4/7*v**4 + 2/7*v**5 + 4/7*v**2.
2*v*(v - 1)**3*(v + 1)/7
Let f(y) be the third derivative of -y**5/60 + 7*y**4/12 - 49*y**3/6 - 8*y**2. Factor f(s).
-(s - 7)**2
Let q(u) = -u**3 + 8*u**2 + 10*u - 6. Let m be q(9). Factor m*v - 2*v + v + 6*v**2 - 6*v.
2*v*(3*v - 2)
Let c(i) = -3*i**2 - 22*i + 18. Let y be c(-8). Suppose -2*w**2 - 2*w + 14/3*w**3 + 4/3 - y*w**4 = 0. What is w?
-2/3, 1
Suppose d + 4 + 1 = k, 0 = -5*k - 3*d - 15. Let s(x) be the third derivative of k - x**2 - 49/60*x**6 - 21/5*x**5 - 5*x**4 - 8/3*x**3 + 0*x. Factor s(a).
-2*(a + 2)*(7*a + 2)**2
Suppose 0 = 2*p - p. Suppose -m + 6 = 2*g - 5*m, p = -5*g + 4*m + 15. Suppose 0 + 11/2*d**4 + 13/2*d**g + 0*d + d**2 = 0. Calculate d.
-1, -2/11, 0
Let p(s) = s**2 + 12*s + 3. Let r be p(-12). What is t in 0*t - 2/5*t**r + 1/5*t**2 + 1/5*t**4 + 0 = 0?
0, 1
Let w(c) be the first derivative of -2 + 1/2*c**2 + 1/2*c**4 + 0*c - c**3. Suppose w(a) = 0. What is a?
0, 1/2, 1
Let v(l) = -l**4 + l**3 - l**2 + l + 1. Let n(i) = 6*i**4 + 10*i**3 + 6*i**2 - 14*i - 10. Let d(u) = -n(u) - 2*v(u). Determine b, given that d(b) = 0.
-2, -1, 1
Let z(w) be the second derivative of -w**5/30 + w**3/9 + 2*w + 1. Determine a so that z(a) = 0.
-1, 0, 1
Let j(g) be the first derivative of 1/6*g**4 + 2/9*g**3 + 0*g**2 + 0*g - 2/15*g**5 + 3 - 1/9*g**6. Let j(f) = 0. What is f?
-1, 0, 1
Let l be -4 - (-1 + (-2)/(-1)). Let s be (-10)/(-4) + l/10. Factor g + 4*g - g - 2 - s*g**2.
-2*(g - 1)**2
Let d = -17 - -19. Let p be (70/(-120))/(d/(-8)). Factor -5/3*w**2 + 2/3*w - p*w**3 + 0.
-w*(w + 1)*(7*w - 2)/3
Factor 3/2 + 3/4*m - 3/2*m**2 - 3/4*m**3.
-3*(m - 1)*(m + 1)*(m + 2)/4
Let n = 3923/360 + -87/8. Let c(m) be the second derivative of -m + n*m**6 + 0*m**4 + 1/15*m**5 - 1/3*m**2 - 2/9*m**3 + 0. Factor c(b).
2*(b - 1)*(b + 1)**3/3
Let q be 1/(-2) - (-198)/12. Let h = q - 14. Factor -4/3*c**3 + 4/3*c + 0*c**h - 2/3*c**4 + 2/3.
-2*(c - 1)*(c + 1)**3/3
Let w = -1389/7 - -199. Factor -w*b**5 + 0 + 0*b**2 + 0*b + 2/7*b**3 - 2/7*b**4.
-2*b**3*(b + 1)*(2*b - 1)/7
Suppose 80 = -3*w + 8*w. Suppose 4*y = v + w, -5*v + 4 + 4 = 2*y. What is f in -4*f**4 + f - f - y*f**2 - 5*f**3 + 3*f**2 = 0?
-1, -1/4, 0
Let q be ((-8)/(-40))/(-2*3/(-6)). Factor 2/5*s**5 + q*s**2 + 0*s + 0 + 0*s**3 - 3/5*s**4.
s**2*(s - 1)**2*(2*s + 1)/5
Let h = -10 + 13. Factor 12*y - h*y**4 + 12*y**3 - 24*y**2 + 4*y**3 - y**3.
-3*y*(y - 2)**2*(y - 1)
Let u(g) be the first derivative of 0*g + 1/3*g**3 + 5/8*g**4 + 0*g**2 - 6. Solve u(h) = 0 for h.
-2/5, 0
Factor 0 + 2/9*i**2 + 0*i - 2/9*i**3.
-2*i**2*(i - 1)/9
Let a(o) = o**5 + 10*o**4 + 6*o**3 + 4*o**2 - 5*o. Let q(l) = -l**5 - 9*l**4 - 6*l**3 - 4*l**2 + 4*l. Let p(x) = 5*a(x) + 6*q(x). Suppose p(r) = 0. Calculate r.
-1, 0
Let z(m) = -4*m**4 + 7*m**3