, 4*g + 2 = -5*t. Let n be g/21 - 68/(-84). Factor -n - 1/3*v + 1/3*v**2.
(v - 2)*(v + 1)/3
Let b(n) be the second derivative of n**5/20 + n**4/6 + n**3/6 + 9*n. Find m such that b(m) = 0.
-1, 0
Let b be (-23)/15 + 8 + -9 + 3. Let y(j) be the second derivative of 2/5*j**2 + 0 - b*j**3 - 3/10*j**4 - 2*j. Find d such that y(d) = 0.
-1, 2/9
Let j be 1*(-2 - -4 - 0). Solve -7*a**2 - 11*a**2 + 28*a - j*a**3 + 6*a**3 - 2*a**2 - 12 = 0 for a.
1, 3
Let h be 1/54*219 - 4. Let c(d) be the third derivative of 1/60*d**5 + 1/360*d**6 + 1/24*d**4 + h*d**3 + 0*d - 2*d**2 + 0. Factor c(s).
(s + 1)**3/3
Let u(q) be the first derivative of q**6/6 + 2*q**5/5 - q**4/2 - 4*q**3/3 + q**2/2 + 2*q - 10. Determine h, given that u(h) = 0.
-2, -1, 1
Suppose 5/3*o**2 + 0 + 4/3*o**3 + 1/3*o = 0. What is o?
-1, -1/4, 0
Let n(v) be the third derivative of -5*v**7/49 + 13*v**6/42 - 34*v**5/105 + v**4/6 - v**3/21 + 5*v**2. Let n(u) = 0. Calculate u.
1/5, 1/3, 1
Let k(j) = 20*j**2 - 16*j + 8. Let h(r) = r**2 + 1. Let p(z) = 24*h(z) - k(z). Factor p(a).
4*(a + 2)**2
Let u(x) = x + 4. Let s be u(-5). Let a be s/(1/(2/(-1))). Factor -3*r**2 - r**3 + 2*r**a + 0*r**2.
-r**2*(r + 1)
Let x(l) be the first derivative of -4/15*l**3 + 6 - 8/5*l + 6/5*l**2. What is w in x(w) = 0?
1, 2
Let r(p) be the second derivative of -1/12*p**4 + 0*p**2 + 0 + 1/6*p**3 + 3*p. Factor r(u).
-u*(u - 1)
Let l(u) be the first derivative of -1 - 1/5*u**2 + 1/30*u**3 + 4*u + 1/60*u**4. Let a(f) be the first derivative of l(f). Factor a(b).
(b - 1)*(b + 2)/5
Let g(m) be the third derivative of 2*m**2 + 0*m + 1/30*m**6 + 1/35*m**7 + 0*m**4 + 1/90*m**5 + 1/126*m**8 + 0 + 0*m**3. Factor g(h).
2*h**2*(h + 1)**2*(4*h + 1)/3
Let g(v) be the first derivative of v**5/5 - 2*v**3/3 + v + 13. Find o, given that g(o) = 0.
-1, 1
Suppose -5*a - 4 = -4*l, 0 = l - 1. Suppose 0*b + 0*b**3 + 3/2*b**4 + a + 0*b**2 = 0. Calculate b.
0
Let j(f) = -3*f**2 - 6*f + 4. Let t(i) = -5*i - 4*i + 4*i + 3 - 2*i**2. Let u(m) = -3*j(m) + 4*t(m). Factor u(x).
x*(x - 2)
Let m(q) = 2*q**2 - 2*q - 8. Let s be m(-2). Factor -2/3*j**2 - 2/3*j**3 + 0 + 2/3*j**s + 2/3*j.
2*j*(j - 1)**2*(j + 1)/3
Let n(m) = -m - 9. Let c be n(-12). Let l(y) be the first derivative of -c*y**2 + 1/2*y**4 + 1 + 0*y**3 + 4*y. Let l(h) = 0. Calculate h.
-2, 1
Let d(h) be the second derivative of h**4/102 + h**3/17 - 45*h. Suppose d(k) = 0. Calculate k.
-3, 0
Factor 5*j + 20*j**2 - 10/3 + 35/3*j**3.
5*(j + 1)**2*(7*j - 2)/3
Let t be 22/10 + 1/(-5). Factor 1/4*h + 3/4*h**3 + 3/4*h**t + 1/4*h**4 + 0.
h*(h + 1)**3/4
Suppose 61*t - 72*t = -33. Find d such that 2/9*d - 8/9*d**2 + 4/9*d**4 + 4/9 + 2/9*d**5 - 4/9*d**t = 0.
-2, -1, 1
Let v(f) be the first derivative of 4/3*f**3 + f**4 - 7 + 0*f + 0*f**2. Factor v(c).
4*c**2*(c + 1)
Let i(m) be the first derivative of -28*m**3/3 + 18*m**2 - 8*m + 17. Factor i(k).
-4*(k - 1)*(7*k - 2)
Let x(y) = -y**3 + 4*y**2 - 5*y + 6. Let v = 7 - 12. Let n(s) = -s**3 + 4*s**2 - 5*s + 7. Let w(u) = v*x(u) + 4*n(u). Let w(q) = 0. What is q?
1, 2
Let s**3 - 2*s**2 - 1/6*s**4 + 0 + 4/3*s = 0. Calculate s.
0, 2
Let t(v) = -3*v**4 - 10*v**3 + 10*v + 5. Let y(a) = -2*a**4 - 10*a**3 + 10*a + 5. Let w(s) = -3*t(s) + 2*y(s). Solve w(d) = 0 for d.
-1, 1
Let v = -2/43 - -268/215. Factor 9/5*u + 1/5*u**5 + 14/5*u**3 + v*u**4 + 2/5 + 16/5*u**2.
(u + 1)**4*(u + 2)/5
Let j(a) = 75*a**3 + 294*a**2 - 146*a + 22. Let c(z) = z**3 - z**2 + z - 1. Let r(i) = 6*c(i) + j(i). Factor r(f).
(f + 4)*(9*f - 2)**2
Let c = -3 - -8. Find t such that -4*t**c - 2*t**5 + 4*t**4 + 2*t**5 = 0.
0, 1
Suppose 0*n = -n - 2*y + 14, 5*n = 2*y + 34. Let z(a) = -a**2 - 4*a - 1. Let t be z(-3). Factor -2*o**4 - 2 - 5*o**3 - n*o - 12*o**t - o**3 - 2*o**3.
-2*(o + 1)**4
Let f(p) be the second derivative of -p**6/360 - p**3/2 + 3*p. Let o(b) be the second derivative of f(b). Factor o(a).
-a**2
Let 0 - 2/5*a + 2*a**2 = 0. Calculate a.
0, 1/5
Solve 3*a**3 + 9*a**5 + 6*a + 24*a**4 - 6*a - 6*a**2 + 6*a**3 = 0 for a.
-2, -1, 0, 1/3
Suppose 0 = l - 1 - 2. Factor -13*y + 13*y - 9*y**l - 6*y**2 + 3*y**5.
3*y**2*(y - 2)*(y + 1)**2
Let p(n) be the first derivative of -3 + 0*n + 6*n**2 + 231/4*n**4 - 147/5*n**5 - 32*n**3. Factor p(x).
-3*x*(x - 1)*(7*x - 2)**2
Let n be (-14)/(-147)*-3 - (-132)/70. Let k(y) be the first derivative of -n*y**4 + 1 + 6/5*y**5 + 0*y - 2/15*y**3 + 2/5*y**2. Suppose k(l) = 0. Calculate l.
-1/3, 0, 2/5, 1
Let s(n) be the second derivative of -n**9/3024 + n**8/840 - n**6/180 + n**5/120 + 2*n**3/3 + 2*n. Let o(l) be the second derivative of s(l). Factor o(i).
-i*(i - 1)**3*(i + 1)
Let r(t) be the third derivative of -t**8/560 - t**7/350 + t**6/100 - 28*t**2. Determine q so that r(q) = 0.
-2, 0, 1
Let t be 0/3 + (-8)/(-24). Let n(x) be the first derivative of -4/3*x + 2/9*x**3 - t*x**2 - 1. Let n(z) = 0. Calculate z.
-1, 2
Factor -15/4*x**2 + 9/4*x + 3/4*x**3 + 27/4.
3*(x - 3)**2*(x + 1)/4
Let b(m) be the second derivative of 0*m**3 + 0*m**2 + 2*m - 1/20*m**5 + 0*m**4 + 0 + 1/30*m**6. Factor b(u).
u**3*(u - 1)
Let a be -4*1 + (-180)/(-42). Let v(z) be the first derivative of -4/7*z**2 - a*z**4 + 2/35*z**5 + 2/7*z + 4/7*z**3 - 2. Factor v(p).
2*(p - 1)**4/7
Let m(d) be the second derivative of d**5/120 + d**4/18 + 5*d**3/36 + d**2/6 + 3*d. Factor m(f).
(f + 1)**2*(f + 2)/6
Let s = -282 - -1137/4. Suppose s*u**2 + 1/4 + 3/2*u = 0. What is u?
-1/3
Let b(o) be the second derivative of -o**6/40 - 3*o**5/20 + 2*o**3 - 2*o**2 + o. Let z(a) be the first derivative of b(a). Factor z(k).
-3*(k - 1)*(k + 2)**2
Suppose 2/9*s**3 + 16/9*s**2 + 0 - 2*s = 0. What is s?
-9, 0, 1
Suppose 4*k + 4*k - 32 = 0. Solve 3/2*w + 9/2*w**2 + 3/2*w**k + 0 + 9/2*w**3 = 0.
-1, 0
Suppose 5*i = 18 + 7. Let g be (-22)/(-5) + 3/i. Factor -n**2 - n**g - n**5 - 2*n**3 + n**2 + 4*n**4.
-2*n**3*(n - 1)**2
Let m(z) = -8*z**2 + 23*z - 20. Let l(b) = 23*b**2 - 68*b + 60. Let w(i) = 3*l(i) + 8*m(i). Factor w(d).
5*(d - 2)**2
Let k = -27/2 - -15. Factor k*a**3 - 3/2*a**2 + 3/2*a**4 - 3/2*a**5 + 0 + 0*a.
-3*a**2*(a - 1)**2*(a + 1)/2
Factor -2/7*b**4 - 64/7*b**3 - 768/7*b**2 - 4096/7*b - 8192/7.
-2*(b + 8)**4/7
Let j(y) be the second derivative of y**6/150 - y**5/50 - y**4/20 + 6*y - 1. Factor j(g).
g**2*(g - 3)*(g + 1)/5
Suppose 3*a = 4*v - 23, -v - 7*a - 48 = 3*a. Solve 1/2*b**v + 0 + 0*b - 1/2*b**3 = 0.
0, 1
Let h(g) = -g**3 - 6*g**2 + 2*g + 6. Let l be h(-6). Let y = 6 + l. Let -2/3*x**2 + 2/3*x**4 + y - 4*x**5 + 14/3*x**3 - 2/3*x = 0. Calculate x.
-1, -1/3, 0, 1/2, 1
Find s such that -8/9*s**2 - 4/9 - 2*s = 0.
-2, -1/4
Let q be (9/6)/((-6)/32). Let m(k) = 14*k**3 + 14*k**2 - 4*k. Let y(n) = 5*n**3 + 5*n**2 - n. Let j(w) = q*y(w) + 3*m(w). Solve j(i) = 0 for i.
-2, 0, 1
Let y(b) = b**4 + b**3 - b**2 + b + 1. Let x(v) = -4*v**3 - v**4 + 4 + v**4 + 5*v**4 + 2*v + 10*v**3 - 5*v**2. Let p(n) = -x(n) + 4*y(n). Factor p(t).
-t*(t - 1)*(t + 1)*(t + 2)
Let l(z) be the first derivative of z**6/6 - 3*z**5 + 75*z**4/4 - 125*z**3/3 + 5. Determine x so that l(x) = 0.
0, 5
Let a = 19 + -16. Factor -2*h - 6*h - 2*h**3 - 5*h**3 + 5*h**a - 8*h**2.
-2*h*(h + 2)**2
Factor -30/13*n**2 + 14/13*n**3 - 2/13*n**4 + 2*n - 8/13.
-2*(n - 4)*(n - 1)**3/13
Let y(p) be the second derivative of p**7/210 - p**6/150 - p**5/100 + p**4/60 - 4*p. Factor y(z).
z**2*(z - 1)**2*(z + 1)/5
Suppose -20 = -6*u + 2*u. Factor -2/3*r**2 - 2*r**4 + 0 + 0*r - 2/3*r**u - 2*r**3.
-2*r**2*(r + 1)**3/3
Let w(z) be the third derivative of -z**8/5880 - z**7/980 - z**6/420 - z**5/420 - z**3/6 + z**2. Let l(k) be the first derivative of w(k). Factor l(x).
-2*x*(x + 1)**3/7
Let m be (18 - 6)/(3/2). Factor -21*g**4 + 0*g**5 + 4*g**5 + 29*g**4 - m*g**2 - 4*g.
4*g*(g - 1)*(g + 1)**3
Let z(y) = -y**3 - 11*y**2 - 9*y + 13. Suppose 3*w - 3*m - 9 = -54, w + m + 5 = 0. Let t be z(w). Factor 1/3*k + 0 + 1/3*k**t + 2/3*k**2.
k*(k + 1)**2/3
Let y(h) be the second derivative of 0*h**5 + 0*h**4 + 3*h + 0*h**3 + 0*h**2 + 1/126*h**7 - 1/90*h**6 + 0. Determine b so that y(b) = 0.
0, 1
Let k(w) be the first derivative of -w**6/360 - w**5/90 - w**4/72 - w**2 + 1. Let f(v) be the second derivative of k(v). Factor f(l).
-l*(l + 1)**2/3
Let -4/5*k**2 + 16/5*k + 0 = 0. What is k?
0, 4
Let w(q) be the third derivative of -1/525*q**7 - 1/336*q**8 + 0 + 1/120*q**6 + 0*q**3 + 0*q**4 - q**2 + 0*q + 1