80*x**6 - 2*x. Let o(d) be the first derivative of m(d). Factor o(i).
i*(i + 1)**2/4
Factor -1/3*w - 2/3 + 1/3*w**2.
(w - 2)*(w + 1)/3
Suppose 8*b**3 - 4 + 4*b**5 - 8*b**2 - b**4 + 13*b**4 - 13*b + b = 0. Calculate b.
-1, 1
Factor -4/5*u**2 + 16/5*u - 12/5.
-4*(u - 3)*(u - 1)/5
Factor -a**4 + a**5 + 0*a + a**3 + 5*a + 3*a - 7*a**3 + 4*a**2.
a*(a - 2)**2*(a + 1)*(a + 2)
Determine c, given that 32/9 - 16/9*c + 2/9*c**2 = 0.
4
Let r(j) be the first derivative of 2*j**6/15 + j**5/4 + j**4/12 - 2*j - 4. Let o(h) be the first derivative of r(h). What is m in o(m) = 0?
-1, -1/4, 0
Let m(h) be the second derivative of h**5/50 + h**4/15 + h**3/15 + 5*h. Determine b so that m(b) = 0.
-1, 0
Suppose 2*u - 4 = 6. Let g(f) be the third derivative of -1/12*f**4 + 0 - 1/60*f**6 + 1/15*f**u + 2*f**2 + 0*f**3 + 0*f. Factor g(y).
-2*y*(y - 1)**2
Let o(x) be the first derivative of 4*x**3/3 - 12*x**2 + 36*x - 6. Factor o(m).
4*(m - 3)**2
Let h = -6 - -9. Suppose -8 = n + 5*s, -2*n - h*s - 6 = 2*s. Factor -4*b**4 + 4*b**3 - n*b**2 + 2*b**4 + 0*b**2.
-2*b**2*(b - 1)**2
Let r be (8 + 8 - 15)/(1/4). Suppose 0*f**2 - 2/3 - 4/3*f + 2/3*f**r + 4/3*f**3 = 0. What is f?
-1, 1
Let b be (8 + -11 - 3) + 8. What is y in -3/4*y**3 + 1/4*y**b + 0*y + 0 - 1/4*y**5 + 3/4*y**4 = 0?
0, 1
Let k(s) = 2*s**4 - 19*s**3 + 21*s**2 + 27*s. Let a(r) = r**3 - r**2 + r. Let x(l) = 10*a(l) + 2*k(l). Find p such that x(p) = 0.
-1, 0, 4
Solve 10 + 4*r**2 + 8 + 4*r - 18 = 0 for r.
-1, 0
Solve 0*g**2 + 0 + 4/5*g**4 + 16/5*g - 12/5*g**3 = 0 for g.
-1, 0, 2
Let k = -2 + 5. Determine n, given that 10*n**k - 11*n**3 - n**4 + 2*n**3 = 0.
0, 1
Factor 6*h**2 + 0*h**3 - 3/2*h**5 + 0 - 9/2*h**4 + 0*h.
-3*h**2*(h - 1)*(h + 2)**2/2
Let s(l) = -4*l + 3. Let n be s(-3). Let x = 23 - n. Factor -22 - 2*u**4 + 8*u - 10*u**4 + 22 - 22*u**3 + x*u**2 + 18*u**5.
2*u*(u - 1)**2*(3*u + 2)**2
Let f(t) be the second derivative of -1/3*t**3 + 1/24*t**4 + t**2 + 5*t + 0. Suppose f(v) = 0. Calculate v.
2
Factor 51/2*r - 3/4*r**2 - 867/4.
-3*(r - 17)**2/4
Let y(h) be the first derivative of 1/9*h**2 + 2/27*h**3 - 2 - 4/9*h. What is a in y(a) = 0?
-2, 1
Solve 3 + 12*o - 5 + 12*o**2 + 5 = 0 for o.
-1/2
Let a(w) be the first derivative of w**7/210 - w**5/20 - w**4/12 + w**2/2 - 3. Let s(v) be the second derivative of a(v). Factor s(r).
r*(r - 2)*(r + 1)**2
Let v(s) be the second derivative of -s**3/6 + 3*s**2 - 5*s. Let j be v(6). Find g, given that 0*g - 2/5*g**5 + 2/5*g**3 + j + 2/5*g**4 - 2/5*g**2 = 0.
-1, 0, 1
Let k(w) = w**2 + 3*w + 2. Let h = 24 + -13. Let b(j) = -5*j**2 - 15*j - 10. Let z(n) = h*k(n) + 2*b(n). Determine s, given that z(s) = 0.
-2, -1
Let a be (-6 - 1)/(-1 + 0). Suppose -11*m - 3*m - 2*m**3 + 12*m**2 + 16 + a*m - 17*m = 0. What is m?
2
Let l = 86/477 - -14/53. Let g(n) be the second derivative of -l*n**3 + 1/3*n**2 + 1/45*n**6 + 0 + 1/3*n**4 - 2/15*n**5 - 2*n. Let g(o) = 0. What is o?
1
Let u(q) be the first derivative of -q**6/360 - q**5/60 - q**4/24 - q**3 + 1. Let m(b) be the third derivative of u(b). Factor m(l).
-(l + 1)**2
Factor -6*u**2 - 3*u**3 + 5*u**4 + 3*u**5 + 0*u**3 + u**4 + 0*u**5.
3*u**2*(u - 1)*(u + 1)*(u + 2)
Let g(z) = 5*z**2 - z. Let n be (-2 + 3 + 0)/1. Let m(l) = -l**2 + l. Let d(r) = n*g(r) + 3*m(r). Determine i so that d(i) = 0.
-1, 0
Factor -13*f**2 + 22*f**2 - 20 - 40*f + 86*f**2 - 35*f**3 + 0*f**3.
-5*(f - 2)*(f - 1)*(7*f + 2)
Let z(v) be the third derivative of v**8/420 - v**7/70 + v**6/30 - v**5/30 - v**3/3 + 8*v**2. Let n(f) be the first derivative of z(f). Solve n(w) = 0.
0, 1
Let q(i) = i**2 + i + 2. Let r be q(0). Suppose 0 = r*n - 3*n + 5. Factor -3/2*j**3 + 0 + j**4 + j**2 - 1/4*j - 1/4*j**n.
-j*(j - 1)**4/4
Suppose 4*b = 1 + 7. Let r - 15 - b*r**3 + 6 + r**5 + 9 = 0. Calculate r.
-1, 0, 1
Let u be (-1 - 4)*((-24)/(-18))/(-4). Factor -u*v - v**2 - 2/3.
-(v + 1)*(3*v + 2)/3
Let c(v) be the first derivative of -2/7*v**2 - 10/21*v**3 - 2 - 2/7*v**4 + 0*v - 2/35*v**5. Suppose c(k) = 0. Calculate k.
-2, -1, 0
Factor -g**4 - 174*g + 139*g - 4*g**4 + 35*g**3 + 5*g**2.
-5*g*(g - 7)*(g - 1)*(g + 1)
Factor 32*h**4 + 16*h**4 - 9*h - 42*h**2 - 12*h**4 + h**5 + 20*h**5 - 12*h**3 + 6.
3*(h - 1)*(h + 1)**3*(7*h - 2)
Let r(v) = -v**4 - v**2 - v - 1. Let c(p) = -10*p**4 - 18*p**2 - 8*p - 12. Let j(k) = c(k) - 12*r(k). Determine d, given that j(d) = 0.
-2, 0, 1
Let w be 3 + 0 - 154/54. Let a(c) be the first derivative of -1/27*c**6 + 1 + w*c**3 + 0*c**4 - 4/45*c**5 + 0*c + 1/9*c**2. Factor a(m).
-2*m*(m - 1)*(m + 1)**3/9
Let z(u) = 13*u**2 + 24*u. Let j(y) = -3*y**2 - 6*y. Let i(h) = -9*j(h) - 2*z(h). Factor i(f).
f*(f + 6)
Suppose 12 + 525*k**2 - 264*k**2 - 264*k**2 = 0. Calculate k.
-2, 2
Let c = -23/78 - -6/13. Let r(q) be the third derivative of -1/12*q**4 + 0*q + 0 - c*q**3 + 3*q**2 - 1/60*q**5. Determine h, given that r(h) = 0.
-1
Suppose 3*t = 5*t. Let c = -3 + t. Let x(l) = 4*l**2 - 5*l - 3. Let o(u) = -7*u**2 + 9*u + 5. Let s(y) = c*o(y) - 5*x(y). Factor s(q).
q*(q - 2)
Suppose -5*r = -r - 16. Suppose j**4 + 9*j + 3*j**2 - 12*j + r*j + 3*j**3 = 0. What is j?
-1, 0
Let f(y) be the first derivative of y**3 - 3*y**2 + 3*y - 1. Factor f(w).
3*(w - 1)**2
Let h(j) = -4*j**4 - 13*j**3 + 3*j**2 - 7*j + 7. Suppose -3*q = 2 + 4. Let g(a) = -a**4 - 4*a**3 + a**2 - 2*a + 2. Let r(n) = q*h(n) + 7*g(n). Factor r(f).
f**2*(f - 1)**2
Let w(v) be the first derivative of v**7/42 - v**5/10 + v**3/6 - 3*v + 4. Let x(o) be the first derivative of w(o). Solve x(d) = 0.
-1, 0, 1
Let i(x) be the third derivative of -3*x**5/20 - x**4/4 + x**3/2 + 6*x**2. Factor i(g).
-3*(g + 1)*(3*g - 1)
Determine v so that -v**4 + 2*v + 44*v**3 + 3*v**2 - 44*v**3 = 0.
-1, 0, 2
Suppose -3*y = -2*y. Suppose 8 = 4*r, y*t + r + 6 = 4*t. Factor 3*u**2 + 6*u - u**2 - 7*u - u**t.
u*(u - 1)
Let o(v) be the third derivative of -v**6/420 + v**5/42 - v**4/12 + v**3/7 - 7*v**2. Factor o(t).
-2*(t - 3)*(t - 1)**2/7
Suppose 0 = 5*w + 2*k - 9, 4*w = 3*w - 2*k - 3. Factor -1/3 - 1/3*c + 1/3*c**2 + 1/3*c**w.
(c - 1)*(c + 1)**2/3
Factor 9/5*r**5 + 0 + 0*r + 1/5*r**2 + 3/5*r**4 - r**3.
r**2*(r + 1)*(3*r - 1)**2/5
Let m be (15/20)/(1/4). Suppose 0 = -2*g - m*g. Factor 0 + 1/5*w**5 + 0*w + g*w**2 - 2/5*w**4 + 1/5*w**3.
w**3*(w - 1)**2/5
Let n(i) be the second derivative of i**8/112 + 3*i**7/70 + 3*i**6/40 + i**5/20 - i**2 + i. Let w(u) be the first derivative of n(u). Find t such that w(t) = 0.
-1, 0
Let n(a) = -a**2 + 20*a - 49. Let z be n(17). Factor 4/9 - 2/9*g**z + 2/9*g.
-2*(g - 2)*(g + 1)/9
Factor -2*z - 21 + 19 - 4*z**2 + 2*z**3 + 6.
2*(z - 2)*(z - 1)*(z + 1)
Solve 3/2*f**4 - 3/4*f**3 + 0*f + 3/4*f**5 - 3/2*f**2 + 0 = 0 for f.
-2, -1, 0, 1
Suppose -2*s = -3*s + 3. Factor 3*t**3 - t**3 + 4*t**s - 14*t**2 + 14*t - 4 - 2*t**2.
2*(t - 1)**2*(3*t - 2)
Let q = 8 + -4. Let k(h) be the second derivative of 0 - h + 1/12*h**q + 3/8*h**3 + 1/4*h**2. What is u in k(u) = 0?
-2, -1/4
Solve -2*y**3 + 0*y - 10*y**2 + 18 + 4*y**3 + 6*y = 0.
-1, 3
Let y(x) = 9*x**2 - 12*x + 3. Let g(o) = -9*o**2 + 11*o - 2. Let n(t) = -5*g(t) - 4*y(t). Suppose n(z) = 0. Calculate z.
-2/9, 1
Let i(h) be the first derivative of 2*h**3/3 - 3*h**2 + 4*h + 14. Factor i(z).
2*(z - 2)*(z - 1)
Let r(d) = 2*d**3 + 5*d**2 - 3*d - 3. Let l(m) = 5*m**3 + 14*m**2 - 8*m - 8. Let n(k) = 3*l(k) - 8*r(k). Factor n(b).
-b**2*(b - 2)
Let i(n) be the first derivative of 2*n**3/33 + 2*n**2/11 + 1. Factor i(g).
2*g*(g + 2)/11
Let o(r) be the first derivative of 16*r**5/45 + 2*r**4/9 - 4*r**3/3 + 11*r**2/9 - 4*r/9 - 6. What is d in o(d) = 0?
-2, 1/2
Let 3/5*m**4 + 9/5*m**3 + 3/5*m + 9/5*m**2 + 0 = 0. What is m?
-1, 0
Determine a so that -5/3*a**4 + a - 2/3 + 7/3*a**2 - a**3 = 0.
-1, 2/5, 1
Let c = -6878/9 - -765. Let v = c - 4/9. Factor -1/3*j**4 - 1/3*j**5 + 2/3*j**3 + 2/3*j**2 - v*j - 1/3.
-(j - 1)**2*(j + 1)**3/3
Let t(q) be the second derivative of -3*q**5/140 - q**4/28 - 2*q. Factor t(a).
-3*a**2*(a + 1)/7
Let n(q) = -6*q**3 + 11*q**2 + 2*q - 5. Let u(y) = -y**2 - y + 4. Let t(h) = -h**2 - h + 3. Let l(p) = 3*t(p) - 2*u(p). Let c(a) = -2*l(a) - n(a). Factor c(x).
3*(x - 1)**2*(2*x + 1)
Let i = 4 - 4. Factor i*k**3 + 0 - k - k**5 + 2*k**3 + 0.
-k*(k - 1)**2*(k + 1)**2
Let a(l) = -2*l**3 - 21*l**2 + 17*l + 60. Let s(y) = -y**3 + 2*y**2 + y. Let p(c) = -a(c) - 3*s(c). Solve p(t) = 0 