t is d?
2
Let 3/5*b**2 + 1/5*b**3 + 0*b - 4/5 = 0. What is b?
-2, 1
Let i(r) be the second derivative of -r**4/6 - r**3/3 - 5*r. Factor i(t).
-2*t*(t + 1)
What is x in 1/3*x**3 - 5/6*x**2 - 1/6 + 2/3*x = 0?
1/2, 1
Let c(r) be the second derivative of r**6/180 - r**4/12 + 2*r**3/9 - 2*r**2 + 2*r. Let i(z) be the first derivative of c(z). Factor i(l).
2*(l - 1)**2*(l + 2)/3
What is p in -3*p + 3/2 + 3/2*p**2 = 0?
1
Let l(p) = 1. Let s(b) = 4*b**2 + 4*b - 10. Let u(a) = -22*l(a) - 2*s(a). Let u(n) = 0. Calculate n.
-1/2
Solve 3 - y**2 + 1/2*y**3 - 5/2*y = 0 for y.
-2, 1, 3
Let n(w) be the third derivative of w**8/336 + w**7/42 + w**6/15 + w**5/15 + 16*w**2. Factor n(k).
k**2*(k + 1)*(k + 2)**2
Let u(v) be the third derivative of -v**8/10080 - v**7/5040 + v**3/2 + 3*v**2. Let f(i) be the first derivative of u(i). Suppose f(n) = 0. What is n?
-1, 0
Solve 2/9 + 4*w**2 + 17/9*w = 0.
-1/4, -2/9
Let t(l) be the first derivative of -1/20*l**5 - 1/120*l**6 - 2 + 0*l - 1/8*l**4 - 1/6*l**3 + 3/2*l**2. Let g(n) be the second derivative of t(n). Factor g(w).
-(w + 1)**3
Suppose 2*c + 4 = 3*p, 2*p + 0*p - 4 = 2*c. Let f be (-1)/1 + 4 + p. Solve 3*x**4 + x**3 + x**3 + f*x**3 - 2*x**3 + x**2 + x**5 = 0.
-1, 0
Let y(x) be the third derivative of x**7/1260 + x**6/144 + x**5/40 + 7*x**4/144 + x**3/18 - 4*x**2. Let y(r) = 0. Calculate r.
-2, -1
Let y(g) be the second derivative of -g**7/1260 - g**6/180 - g**5/90 + 7*g**3/6 - 8*g. Let t(x) be the second derivative of y(x). Solve t(f) = 0.
-2, -1, 0
Let g(l) be the first derivative of -2*l**2 + 4*l + 1/3*l**3 - 4. Solve g(x) = 0.
2
Let i(v) be the second derivative of v**4/20 - 7*v**3/5 + 147*v**2/10 - v. Determine s so that i(s) = 0.
7
Let h be (-1)/(-60)*(3 + -2). Let j(o) be the third derivative of h*o**5 + 1/30*o**6 + 0 + 2*o**2 - 1/6*o**4 - 1/6*o**3 + 0*o. Find q such that j(q) = 0.
-1, -1/4, 1
Let p = -33 - -235/7. Let -2/7*g + 0 - 8/7*g**2 - 18/7*g**5 + p*g**3 + 24/7*g**4 = 0. Calculate g.
-1/3, 0, 1
Suppose -q + 18 = 5*w, 3*w = 2*q + 11 + 5. Suppose -j - j = -w. Solve -10/3*a**2 + 10/3*a**4 + 4/3*a - j*a**5 + 2/3*a**3 + 0 = 0.
-1, 0, 2/3, 1
Let w(i) = -i**3 + 4*i**2 + 4*i - 4. Suppose t - 6*t = 5*k + 10, 20 = -4*k. Let m(q) = -q**3 + 3*q**2 + 3*q - 3. Let j(p) = t*m(p) - 2*w(p). Factor j(r).
-(r - 1)**2*(r + 1)
Let v(k) = -21*k**2 - 3*k - k + 4 - 6. Let l(d) = 336*d**2 + 63*d + 33. Suppose h - 40 + 11 = -q, -120 = -4*q - 3*h. Let g(n) = q*v(n) + 2*l(n). Factor g(o).
-3*o*(7*o + 2)
Let q(s) be the third derivative of s**5/120 - s**4/48 - s**3/6 - 2*s**2. Suppose q(c) = 0. Calculate c.
-1, 2
Let d(v) be the second derivative of -1/2*v**2 + 0 - 1/20*v**6 + 1/4*v**4 - v + 1/30*v**5 - 1/3*v**3. Let b(w) be the first derivative of d(w). Factor b(f).
-2*(f - 1)*(f + 1)*(3*f - 1)
Factor 0*k**2 - 87*k**3 - 4*k**2 + 89*k**3 - 6*k.
2*k*(k - 3)*(k + 1)
Let d(h) be the second derivative of -h**6/45 + h**5/30 + h**4/18 - h**3/9 + 4*h. Find l such that d(l) = 0.
-1, 0, 1
Let t be 4/22 + (-1184)/(-22). Let s = -376/7 + t. Factor 4/7*i + s*i**2 + 0.
2*i*(i + 2)/7
Let g = -3 - -2. Let i be g + 2/2 - -4. Factor s**4 + 13*s**2 - 2*s**i - 12*s**2.
-s**2*(s - 1)*(s + 1)
Let g be (3/2)/((-2)/(-36)). Let m = g - 76/3. Find y, given that 0*y + 0 - 2/3*y**2 + 2/3*y**4 - 5/3*y**3 + m*y**5 = 0.
-1, -2/5, 0, 1
Let n(q) = -2*q**4 + q**2 - q. Let l(w) = 45*w**4 + 20*w**3 - 10*w**2 - 25*w - 40. Let d(u) = l(u) + 25*n(u). Factor d(v).
-5*(v - 4)*(v - 2)*(v + 1)**2
Suppose 4*x - 20 + 196 = 0. Let f be (-8)/x - 7/(-22). Determine g, given that 1/2*g**2 + f*g + 0 = 0.
-1, 0
Let f(x) be the third derivative of 1/60*x**6 + 0*x**3 + 0*x**4 - 1/45*x**5 + x**2 + 0 + 0*x. Solve f(m) = 0.
0, 2/3
Let w(j) be the third derivative of j**6/900 - j**5/75 + j**4/15 - 8*j**3/45 + 7*j**2. Factor w(o).
2*(o - 2)**3/15
Suppose 4*z - 16 = 0, 5*z = 3*v + z + 40. Let j = 10 + v. Find m such that 0 - 2/3*m**j + 1/3*m**3 + 0*m = 0.
0, 2
Let w(s) be the first derivative of 7*s**4 + 8/3*s**3 - 2 + 0*s + 0*s**2. Factor w(k).
4*k**2*(7*k + 2)
Let b(n) be the second derivative of n**4/12 - n**3/6 - n**2 - 9*n. Factor b(u).
(u - 2)*(u + 1)
Suppose 0*y + 5*y = -4*b - 38, b = -y - 8. Let h = -3 - y. Factor d**4 - 2*d**5 + h*d**5 - 5*d**5 + 5*d**5.
d**4*(d + 1)
Let z(t) = -t**3 - 2*t**2 + 2. Let o be z(-2). Find j, given that -3/4*j**3 - 1/4*j - 5/4*j**o + 1/4 = 0.
-1, 1/3
Let v be 12 + -14 - (2/1 + -12). Let i(z) = z + 5. Let b be i(-5). Factor 6*l**3 + b + 2*l**4 + 1/4*l**5 + v*l**2 + 4*l.
l*(l + 2)**4/4
Suppose 0 = -5*v + 20 - 5. Let b(j) be the second derivative of -j - 1/42*j**4 + 1/105*j**6 - 1/70*j**5 + 1/147*j**7 + 0*j**v + 0*j**2 + 0. Factor b(d).
2*d**2*(d - 1)*(d + 1)**2/7
Let q(w) be the third derivative of w**5/60 + w**4/12 + 5*w**2. Let q(n) = 0. What is n?
-2, 0
Factor 1/7*l**2 + 0 + 2/7*l.
l*(l + 2)/7
Let w = 16 + -11. Suppose -w + 0 = o. Let k(l) = 6*l**3 - l. Let j(t) = -7*t**3 + t. Let v(x) = o*j(x) - 6*k(x). Factor v(m).
-m*(m - 1)*(m + 1)
Let v be (-43 - -38)*(-2)/5. Factor 1/4*x**3 + 0*x**v + 0 - 1/4*x.
x*(x - 1)*(x + 1)/4
Factor 0 + s**3 - 5/4*s**2 + 1/4*s.
s*(s - 1)*(4*s - 1)/4
Let m be 1/(-2 + 10/4). Let r be (-18)/(-5 + m)*-1. Let d(x) = 8*x**3 + 2*x**2 - 2*x - 2. Let j(c) = -c**3. Let t(h) = r*j(h) - d(h). Factor t(p).
-2*(p - 1)*(p + 1)**2
Let j(h) be the third derivative of -h**6/300 + h**5/50 + h**4/10 - 8*h**3/15 - 7*h**2 - 2*h. Solve j(c) = 0 for c.
-2, 1, 4
Let s(c) be the third derivative of c**10/196560 + c**9/98280 + c**4/24 - 4*c**2. Let k(y) be the second derivative of s(y). Factor k(d).
2*d**4*(d + 1)/13
Let u be 3 + -1 + 50/(-22). Let n = u + 26/55. Suppose -n*z**4 - 1/5 + 2/5*z**2 + 0*z + 0*z**3 = 0. Calculate z.
-1, 1
Let t(l) be the first derivative of -6 - 1/8*l**2 + 0*l - 1/12*l**3. Let t(a) = 0. What is a?
-1, 0
Suppose -12 - 1/3*q**2 + 4*q = 0. Calculate q.
6
Suppose 0 = j + 3*j - 12. Factor -t**2 - 2*t + j*t - 2*t.
-t*(t + 1)
Let l(r) be the third derivative of 25*r**8/168 - 17*r**7/21 + 53*r**6/30 - 29*r**5/15 + 13*r**4/12 - r**3/3 - 47*r**2. Factor l(v).
2*(v - 1)**3*(5*v - 1)**2
Factor 32/7*h + 16/7 - 8/7*h**3 + 5/7*h**4 - 24/7*h**2.
(h - 2)**2*(h + 2)*(5*h + 2)/7
Let n = 1/10 - 0. Let d(l) be the first derivative of 1/15*l**6 + 0*l**2 + 0*l**3 + 0*l + n*l**4 - 4/25*l**5 - 2. Factor d(f).
2*f**3*(f - 1)**2/5
Let r be (-81)/(-15) + 8/(-20). Suppose 5*y + 24 + 1 = 5*q, 0 = 4*q + y - r. What is l in 0*l - 2/9*l**q - 2/9*l**5 - 2/3*l**4 + 0 - 2/3*l**3 = 0?
-1, 0
Let s(c) be the third derivative of c**7/840 - c**5/240 - 6*c**2. Factor s(b).
b**2*(b - 1)*(b + 1)/4
Let p = -4358/3 + 1456. Factor 2/3*x**2 + 2*x**5 + 2/3*x**3 + 0 + 0*x - p*x**4.
2*x**2*(x - 1)**2*(3*x + 1)/3
Let p = -34/15 + 203/30. What is x in x**3 - 1/2*x + 6*x**4 + 0 - 2*x**2 - p*x**5 = 0?
-1/3, 0, 1
Suppose 0 = 8*j - 24 - 0. Factor 4/9*t**4 + 0 + 8/9*t**2 - 2/9*t - 10/9*t**j.
2*t*(t - 1)**2*(2*t - 1)/9
Let s(t) = t**4 + t**3 + t + 1. Let p(q) = -2*q**5 - 12*q**4 - 6*q**3 + 20*q**2 + 4*q - 20. Let h(l) = p(l) + 4*s(l). Factor h(k).
-2*(k - 1)**2*(k + 2)**3
Suppose -2*l - 5*l**2 - 8*l**2 + 19*l**2 - 5*l**2 = 0. Calculate l.
0, 2
Let z = -2 + 6. Factor -3*v**5 - 16*v**2 + 3*v**z + 16*v**2 + 6*v**3.
-3*v**3*(v - 2)*(v + 1)
Let q(u) be the first derivative of -u**4/38 + 4*u**3/57 - u**2/19 + 8. Solve q(o) = 0.
0, 1
Let j(u) be the second derivative of -u**6/120 + 11*u**5/80 - u**4/2 - 3*u**3/2 + 25*u. Let j(p) = 0. What is p?
-1, 0, 6
Let d(a) be the second derivative of a**6/180 + a**5/45 + a**4/36 - a**3/2 - a. Let l(i) be the second derivative of d(i). Suppose l(p) = 0. What is p?
-1, -1/3
Let g(d) be the third derivative of -d**10/5040 - d**9/3780 + d**8/3360 - 5*d**4/24 + d**2. Let y(a) be the second derivative of g(a). Factor y(z).
-2*z**3*(z + 1)*(3*z - 1)
Let s(c) be the second derivative of 0*c**3 + 3*c + 0 + 1/60*c**4 - 1/100*c**5 + 0*c**2. Suppose s(z) = 0. What is z?
0, 1
Let i(g) be the second derivative of g**5/130 - g**4/26 + g**3/13 - g**2/13 - 2*g. Determine p so that i(p) = 0.
1
Factor 1/4*a**2 - 7/4*a + 0.
a*(a - 7)/4
Suppose -x = -3*x. Suppose x = 5*o - 5*b - 15, -o + 3 = 3*b. Suppose -q**2 - 3*q - 3*q**2 + 18*q**o - 14*q**4 + 3*q = 0. Calculate q.
0, 2/7, 1
Find d such that 0 + 3*d**4 + 3*d**2 + 3/4*d**5 + 9/2*d**3 + 3/4*d = 0.
-1, 0
Suppose