t y be j(15). Let a(z) be the third derivative of -1/30*z**6 - 1/6*z**y + 1/6*z**4 - z**2 + 0 + 1/60*z**5 + 0*z. Factor a(i).
-(i - 1)*(i + 1)*(4*i - 1)
Let f(k) be the first derivative of 2*k**3/21 - 4. What is o in f(o) = 0?
0
Let i = 341 - 3065/9. Let r(o) be the first derivative of -1/6*o**4 - 3 + 0*o - 1/3*o**2 + i*o**3. What is u in r(u) = 0?
0, 1
Let c(s) = 4*s**2 - 46*s - 41. Let d(a) = a**2 - 9*a - 8. Suppose 2*t + 4*h - 10 = 3*t, -3*h - 18 = -5*t. Let m(f) = t*c(f) - 33*d(f). Factor m(g).
-3*(g - 3)*(3*g + 2)
Let g = -2 - -5. Let r**g + 2 - 7*r**2 - 2*r - 2*r**5 - 2*r**3 + 5*r**3 + 3*r**2 + 2*r**4 = 0. What is r?
-1, 1
Suppose 8 - 2/3*u**3 - 32/3*u + 14/3*u**2 = 0. Calculate u.
2, 3
Suppose -3*l = -14 + 5. Suppose -4*g = a - 5, g + 3*a - l - 12 = 0. Determine f so that -1/2*f**4 + 1/2*f**2 + 0 + g*f + 2*f**5 - 2*f**3 = 0.
-1, 0, 1/4, 1
Let k(r) = -r**2 + 6*r + 15. Let x be k(8). Let s be ((-8)/12)/2*x. Factor -s*a + 1/2*a**2 - 1/6*a**3 + 0.
-a*(a - 2)*(a - 1)/6
Let s(x) = x - 5. Let w be s(5). Suppose 8 = 3*j - r, w = -2*j + 2*r - 6*r - 4. Find y such that 4*y - y**j - 4*y + y**4 = 0.
-1, 0, 1
Let l = 173 + -861/5. Let -l - 2/5*s**2 + 6/5*s = 0. What is s?
1, 2
Solve -15*s**2 - 12*s**4 + 43*s**2 - 16*s**2 - 16*s**2 + 16*s**3 = 0.
0, 1/3, 1
Let l = 61/45 + -1/45. Find p such that -l*p**2 + 2/3*p**5 - 1/3 + 5/3*p**4 + 2/3*p**3 - 4/3*p = 0.
-1, -1/2, 1
Factor 0*d + 2/5*d**2 + 0*d**3 - 1/5 - 1/5*d**4.
-(d - 1)**2*(d + 1)**2/5
Suppose 0 = 3*q - 6, 5*q - 26 + 1 = -3*t. Factor 2*s**4 + 2*s**t - 3*s**2 + 3*s**2 - 4*s**5.
-2*s**4*(s - 1)
Let r(f) be the second derivative of 3/5*f**2 + 9/100*f**5 - 1/10*f**4 - 3/10*f**3 + 0 + 6*f. Factor r(w).
3*(w - 1)*(w + 1)*(3*w - 2)/5
Determine x so that -43*x**2 - 2*x**4 - 2*x + 49*x**2 + 6*x = 0.
-1, 0, 2
Let r be (-9)/6 - 22/(-12). Let a(t) be the third derivative of 1/12*t**6 - r*t**3 + 2*t**2 + 0*t - 1/12*t**4 + 0 + 1/10*t**5 + 2/105*t**7. Factor a(c).
2*(c + 1)**3*(2*c - 1)
Suppose k - 4*k = -12. Let f(u) be the third derivative of -1/54*u**k - 1/540*u**6 + 1/90*u**5 - 2*u**2 + 0*u**3 + 0*u + 0. Factor f(w).
-2*w*(w - 2)*(w - 1)/9
Let n(y) = -y**2 + 6*y + 12. Let t be n(7). Let u(k) be the second derivative of -1/10*k**t + 0*k**3 + k + 1/6*k**4 + 0 + 0*k**2. Factor u(j).
-2*j**2*(j - 1)
Let n(p) be the first derivative of -p**4/6 - 2*p**3/21 + 4*p + 3. Let k(z) be the first derivative of n(z). Determine c, given that k(c) = 0.
-2/7, 0
Let s(z) = z**2 + 1. Let i be s(1). Find c such that 0*c + 3/4*c**i + 0 = 0.
0
Let l(a) be the second derivative of -1/9*a**3 - 1/4*a**4 - 1/20*a**5 + 2/45*a**6 + 0*a**2 + 4*a + 0. Let l(z) = 0. Calculate z.
-1, -1/4, 0, 2
Let g = -473 + 476. Suppose -8/3*b**4 + 0 - 2/3*b - 8/3*b**2 - 2/3*b**5 - 4*b**g = 0. What is b?
-1, 0
Let j(l) be the second derivative of -3*l**5/20 + l**3/2 + l. Suppose j(n) = 0. Calculate n.
-1, 0, 1
Let k(u) be the first derivative of -5*u**3/3 - 20*u**2 - 75*u + 23. Factor k(f).
-5*(f + 3)*(f + 5)
Find u such that 4/5*u - 4/5*u**3 + 8/5*u**2 - 8/5 = 0.
-1, 1, 2
Solve 5/4*s - 5/4*s**3 - 15/4 + 15/4*s**2 = 0.
-1, 1, 3
Let q(k) be the first derivative of -k**5/120 + k**4/24 - k**2 - 1. Let o(j) be the second derivative of q(j). Solve o(l) = 0 for l.
0, 2
Let c(d) be the second derivative of d**5/510 + d**4/102 + d**3/51 + 3*d**2 + 4*d. Let h(k) be the first derivative of c(k). Factor h(w).
2*(w + 1)**2/17
Let l(r) be the second derivative of r**6/75 + r**5/50 - r**4/10 - r**3/3 - 2*r**2/5 - 29*r. Factor l(x).
2*(x - 2)*(x + 1)**3/5
Let u(c) = -9*c**4 + 5*c**3 - 13*c**2 - 5*c - 17. Let p = 3 - 1. Let w(a) = -a - 1 - 3 - p*a**4 + 0 + a**3 - 3*a**2. Let q(z) = -6*u(z) + 26*w(z). Factor q(r).
2*(r - 1)**3*(r + 1)
Factor -27 - 88*i + 51 + 460 + 4*i**2.
4*(i - 11)**2
Let m(c) be the third derivative of c**10/10080 - c**8/2240 + c**4/6 + 5*c**2. Let i(w) be the second derivative of m(w). Factor i(f).
3*f**3*(f - 1)*(f + 1)
Let r be (-12)/8*2 - 3/(-1). Find i, given that r + 0*i + 0*i**2 + 2/15*i**3 = 0.
0
Determine j so that 4/7*j**2 - 4/7 + 0*j = 0.
-1, 1
Factor 1/4*x**2 + 1/8*x**5 - 3/8*x**4 + 1/8 + 1/4*x**3 - 3/8*x.
(x - 1)**4*(x + 1)/8
Let y(t) = 243*t**4 + 35*t**3 - 167*t**2 + 45*t + 2. Let g(n) = -4130*n**4 - 595*n**3 + 2840*n**2 - 765*n - 35. Let v(j) = -2*g(j) - 35*y(j). Factor v(x).
-5*x*(x + 1)*(7*x - 3)**2
Let n = -102 - -102. Factor 2/5*c**2 + n*c - 2/5*c**4 + 0 + 0*c**3.
-2*c**2*(c - 1)*(c + 1)/5
Let x(h) = -h**4 + 4*h**3 + 13*h**2 + 2*h + 6. Let u(k) = -2*k**4 + 9*k**3 + 27*k**2 + 5*k + 13. Let d(s) = -6*u(s) + 13*x(s). Find r such that d(r) = 0.
-4, 0, 1
Let y(t) be the first derivative of 0*t**2 + 1/15*t**5 + 0*t - 8 - 2/9*t**3 - 1/12*t**4. Let y(w) = 0. Calculate w.
-1, 0, 2
Factor -16*b**3 + 10*b**5 - 48*b**4 - 17*b**5 - 29*b**5.
-4*b**3*(3*b + 2)**2
Suppose -56/11*o + 74/11*o**4 - 14/11*o**5 - 146/11*o**3 + 134/11*o**2 + 8/11 = 0. What is o?
2/7, 1, 2
Let d be (-2)/2 - -2 - -2. Let u(w) be the second derivative of 1/4*w**3 + d*w + 0 - 1/24*w**4 - 1/60*w**6 - 3/40*w**5 + 1/2*w**2. Let u(l) = 0. Calculate l.
-2, -1, 1
Factor -1/2*i**3 + 2*i**2 - 1/2*i**4 + 2*i + 0.
-i*(i - 2)*(i + 1)*(i + 2)/2
Suppose 3*p = 2*q + 19, p - q + 0*q = 7. Suppose p*k - 2*k = 6. Suppose 12*u**2 - 8*u + 1 + k*u**4 - 8*u**3 + 0*u**3 + 1 = 0. What is u?
1
Suppose -21 = -3*k + 3*y, -19 = 3*k + 6*y - y. Suppose -3*x = 4*q - 0*x + 1, -k*q = x - 1. Factor -10*h**4 - 6*h**2 - 34*h**3 - 2*h**q + 50*h**5 + 2*h**3.
2*h**2*(h - 1)*(5*h + 2)**2
Factor -8/3 - 8*h + 14/3*h**2.
2*(h - 2)*(7*h + 2)/3
Let f(m) = 3*m**4 - m**3 - 2*m**2 + 5. Let r(z) be the first derivative of -4*z**5/5 + z**4/4 + z**3 - 7*z + 1. Let b(t) = 7*f(t) + 5*r(t). Factor b(a).
a**2*(a - 1)**2
Let b(p) be the second derivative of -1/63*p**7 + 0*p**2 + 2/9*p**4 - 10*p + 4/45*p**6 - 1/9*p**3 - 1/5*p**5 + 0. Find f, given that b(f) = 0.
0, 1
Let 6*l**3 + 6*l**3 + 5*l**3 - 18*l**3 = 0. Calculate l.
0
Let b(l) be the second derivative of 3*l**5/100 + l**4/10 - 4*l. Factor b(n).
3*n**2*(n + 2)/5
Let v(u) be the third derivative of 0*u**4 - 1/300*u**5 + 0*u - 2*u**2 + 0 + 1/6*u**3 - 1/900*u**6. Let i(z) be the first derivative of v(z). Solve i(d) = 0.
-1, 0
Let s = 30 - 26. Let y(z) be the first derivative of -1/8*z**s - 2 + 0*z + 1/10*z**5 + 0*z**3 + 0*z**2. Determine r so that y(r) = 0.
0, 1
Let z(h) be the first derivative of h**5/5 + h**4 - 2*h**3/3 - 6*h**2 + 9*h + 21. Factor z(g).
(g - 1)**2*(g + 3)**2
Suppose 8*h = -3*h + 55. Factor 20/7*o**3 + 2/7 + 10/7*o**4 + 20/7*o**2 + 10/7*o + 2/7*o**h.
2*(o + 1)**5/7
Let o(q) be the first derivative of -q**6/2 + 9*q**4/4 - 2*q**3 - 6. Factor o(i).
-3*i**2*(i - 1)**2*(i + 2)
Let d be (20/5)/((-2)/5). Let l be ((-8)/90)/(d/25). Suppose 0*k - l*k**2 + 0 = 0. What is k?
0
Let l be (-65)/78*(-1 + 9/15). Factor -2/9*p - 1/9*p**3 + l*p**2 + 0.
-p*(p - 2)*(p - 1)/9
Let j(l) be the third derivative of 1/48*l**6 - 1/6*l**3 + 0*l - 3/40*l**5 + 7/48*l**4 + 0 - 1/420*l**7 - l**2. Let j(u) = 0. Calculate u.
1, 2
Let -5/4 - 5/4*o**3 + 5/4*o**2 + 5/4*o = 0. What is o?
-1, 1
What is x in 5*x**3 - 4*x**3 + x**3 + 5*x**5 - 7*x**5 = 0?
-1, 0, 1
Let h be (3/6)/((3/12)/1). Let 1/2*a - h*a**2 - a**3 + 1 + 1/2*a**5 + a**4 = 0. Calculate a.
-2, -1, 1
Let f(p) = -p**2 - 5*p + 8. Let n be f(-6). Let g be 3 + (0 - (n + -4)). Factor g*w**4 + 4*w**5 - w**4 - 2*w**5 + 2*w**3.
2*w**3*(w + 1)**2
Let w(z) be the first derivative of z**5/150 + z**4/60 - 7*z**2/2 + 4. Let p(a) be the second derivative of w(a). Let p(s) = 0. Calculate s.
-1, 0
Let l(a) be the second derivative of -a**7/42 - a**6/10 - a**5/10 - 9*a. Let l(o) = 0. What is o?
-2, -1, 0
Let 9/7*g**3 + 0 - 9/7*g - 3/7*g**2 + 3/7*g**4 = 0. What is g?
-3, -1, 0, 1
Let h(r) be the first derivative of r**7/525 - r**5/150 + r**2 + 3. Let f(l) be the second derivative of h(l). Suppose f(d) = 0. What is d?
-1, 0, 1
Let p(q) = q + 20. Let n be p(-17). Let m(r) be the second derivative of -r - 7/20*r**5 + 1/6*r**4 + 7/6*r**n - r**2 + 0. Factor m(j).
-(j - 1)*(j + 1)*(7*j - 2)
Let k be 3 - ((-4)/(-8) + 1). Factor 0*i**2 - k*i - 3/4*i**4 + 3/4 + 3/2*i**3.
-3*(i - 1)**3*(i + 1)/4
Let d be 56/(-36)*12/(-14). Let l(i) be the second derivative of -d*i**2 - 2*i - 1/6*i**4 - 2/3*i**3 + 0 - 1/60*i**5. Determine x so that l(x) = 0.
-2
Suppose 25 = 5*l