k(d) be the first derivative of o(d). Suppose k(m) = 0. What is m?
-1/4, 0, 2/3
Solve 2/13*o**3 + 4/13*o**5 + 0*o**2 + 6/13*o**4 + 0 + 0*o = 0.
-1, -1/2, 0
Factor 9*q**4 + 11*q**5 - 8*q**5 - 4*q**2 - 8*q**2.
3*q**2*(q - 1)*(q + 2)**2
Let n(j) = -20*j**2 + 24*j - 22. Let g(u) = u**2 - 1. Let h(b) = 5*b**2 + b - 7. Let f(o) = -6*g(o) + h(o). Let q(t) = 44*f(t) - 2*n(t). Factor q(l).
-4*l*(l + 1)
Suppose 0 = t + t - 4. Find a, given that -2/3*a**t + 0 + 2/3*a**4 - 4/3*a + 4/3*a**3 = 0.
-2, -1, 0, 1
Suppose 2*n + 2*n - p = 15, 4*n = 3*p + 21. Let x(f) be the third derivative of 0*f + 0 + 1/12*f**4 + 4*f**2 + 1/2*f**n + 1/180*f**5. Factor x(q).
(q + 3)**2/3
Let t(x) be the first derivative of x**4/10 + 4*x**3/15 + x**2/5 - 5. Factor t(c).
2*c*(c + 1)**2/5
Factor 3/2*k**4 + 9/2*k**2 + 0*k + 0 - 15/2*k**3 + 3/2*k**5.
3*k**2*(k - 1)**2*(k + 3)/2
Determine w, given that -8*w - 18*w**4 + 16*w**2 + w**3 + 0*w**3 + 5*w**3 = 0.
-1, 0, 2/3
Suppose 0 = -6*u + 5*u + 3. What is j in 42*j**2 - 3*j**3 - 2*j**4 + u*j - 39*j**2 - j**4 = 0?
-1, 0, 1
Let m be (-98)/(-48) - (-2)/(-1). Let p(r) be the third derivative of 2*r**2 + 0 + 1/120*r**6 + 0*r - 1/3*r**3 - m*r**4 + 1/30*r**5. Factor p(q).
(q - 1)*(q + 1)*(q + 2)
Let m(k) be the third derivative of -k**6/660 + k**2 + 3*k. Factor m(f).
-2*f**3/11
Factor -16/5*j - 12/5*j**2 + 16/5.
-4*(j + 2)*(3*j - 2)/5
Let n(r) be the second derivative of -r**3/6 + 3*r**2/2 + 4*r. Let t be n(3). Factor t + 0*c + 0*c**2 - 1/2*c**3.
-c**3/2
Let q(x) be the first derivative of -x**4/16 + x**3 - 6*x**2 + 16*x - 7. Solve q(b) = 0 for b.
4
Let d(b) be the first derivative of b**4/16 - b**2/8 + 11. Factor d(h).
h*(h - 1)*(h + 1)/4
Let w be 5/2 + 5/(-10). Factor 2 + 0*x**2 + w*x**2 - 3*x**2 - 11 + 6*x.
-(x - 3)**2
Factor -1/7*k**3 - 1/7 + 1/7*k + 1/7*k**2.
-(k - 1)**2*(k + 1)/7
Let b(m) be the first derivative of m**4/8 + m**3/3 + m**2/4 - 5. Find t such that b(t) = 0.
-1, 0
Let i(b) be the first derivative of 1/4*b**4 + 0*b**2 - 2 - 4*b + b**3. Let i(c) = 0. Calculate c.
-2, 1
Let c(w) be the third derivative of -w**8/672 - w**7/84 - 3*w**6/80 - 7*w**5/120 - w**4/24 - 15*w**2. What is s in c(s) = 0?
-2, -1, 0
Let q(a) be the third derivative of 3*a**2 + 0 - 1/840*a**7 + 0*a - 1/480*a**6 + 1/96*a**4 + 1/240*a**5 + 0*a**3. Factor q(n).
-n*(n - 1)*(n + 1)**2/4
Suppose -3*u - 4*q = 2*u - 30, q + 3 = 4*u. Let y(a) be the first derivative of 0*a**u - 2 + 2/25*a**5 - 1/10*a**4 + 0*a + 0*a**3. Factor y(r).
2*r**3*(r - 1)/5
Let z(w) be the third derivative of -w**7/8820 - w**6/1260 - w**4/8 + 6*w**2. Let h(b) be the second derivative of z(b). Solve h(u) = 0 for u.
-2, 0
Let s be 2/(-3) + (-51)/(-9). Let z(a) be the second derivative of -1/60*a**6 + 2*a + 0*a**s + 1/24*a**4 + 0*a**2 - 1/24*a**3 + 0 + 1/168*a**7. Solve z(p) = 0.
-1, 0, 1
Let q(r) be the third derivative of -r**6/200 - r**5/50 + 3*r**4/40 - 3*r**2. Determine a so that q(a) = 0.
-3, 0, 1
Let v(g) be the second derivative of -g**8/3360 + g**7/420 - g**6/120 + g**5/60 - g**4/4 - g. Let i(j) be the third derivative of v(j). Solve i(s) = 0 for s.
1
Let h(c) be the second derivative of 7*c**4/18 - 10*c**3/9 + c**2 + 10*c. Let h(u) = 0. Calculate u.
3/7, 1
Factor -o**3 - 2 + 0*o**3 + 2*o**2 - 2*o - 6*o**2 - 3*o.
-(o + 1)**2*(o + 2)
Let d be 2/4*(-46 + 2). Let s be 1 + d/(-10) - 3. Factor 1/5*x**4 + 0 - 2/5*x**3 - s*x**2 + 2/5*x.
x*(x - 2)*(x - 1)*(x + 1)/5
Let z be -2 + 10 + 300/(-40). What is x in x**2 + 0 + 1/2*x + z*x**3 = 0?
-1, 0
Let r(n) be the first derivative of -n**4/14 + 3*n**2/7 - 4*n/7 + 2. Find v, given that r(v) = 0.
-2, 1
Suppose -3*i - 18 = -i. Let t be (-195)/(-27) + 2/i. Find c such that t*c**2 + 7*c**2 + 6*c - 4 - 16*c = 0.
-2/7, 1
Suppose f = 3*f - 4*s + 34, -5*s + 65 = -4*f. Let d = f + 18. Factor 2/3*g**4 + 0 - 2/3*g**2 - 1/3*g + 0*g**d + 1/3*g**5.
g*(g - 1)*(g + 1)**3/3
Let c(s) = -s**2 - 1. Let g(f) = -f**2 + 3*f. Let n(p) = -2*c(p) + g(p). Let z be n(-3). Factor 2*x**3 + x**3 - 4*x**2 - 7*x**2 + 2*x**z + 6*x.
3*x*(x - 2)*(x - 1)
Let a be (-33)/(-220) + (-1)/(-10). Factor 1/4 - a*v**2 + 0*v.
-(v - 1)*(v + 1)/4
Find p such that 2/5*p**2 + 4/5*p - 6/5 = 0.
-3, 1
Solve -92/7*a**2 + 12/7*a**3 + 36/7*a**4 + 52/7*a - 8/7 = 0 for a.
-2, 1/3, 1
Let k be 36/27*18/3. Suppose 3*u - 6 = 2*x, 4*u - 4*x - k = -5*x. Factor 0*b + 1/2*b**u + 0 + 1/2*b**3.
b**2*(b + 1)/2
Let f(i) be the third derivative of 0*i + i**3 - 9*i**2 + 0 + 1/180*i**6 - 1/18*i**5 + 1/12*i**4. Factor f(d).
2*(d - 3)**2*(d + 1)/3
Let u(f) be the second derivative of f**6/75 - f**5/10 + f**4/10 + f**3/3 - 4*f**2/5 - 8*f. Let u(h) = 0. Calculate h.
-1, 1, 4
Let c(d) be the third derivative of 0 - 2*d**2 + 1/224*d**8 + 0*d**4 + 0*d + 0*d**7 + 0*d**3 + 0*d**5 - 1/80*d**6. Factor c(g).
3*g**3*(g - 1)*(g + 1)/2
Let j(i) be the third derivative of i**5/20 - i**4/2 + 4*i**2. Factor j(m).
3*m*(m - 4)
Let a = -17 - -21. Factor 1/2*t**a - 1/2 + t**3 + 0*t**2 - t.
(t - 1)*(t + 1)**3/2
Suppose -v**4 - 1/3*v**2 - v**3 + 0*v + 0 - 1/3*v**5 = 0. Calculate v.
-1, 0
Let m(g) be the first derivative of -1/8*g**4 + 0*g**5 - 3 + 4/3*g**3 + 0*g + 1/120*g**6 + 0*g**2. Let y(i) be the third derivative of m(i). Factor y(f).
3*(f - 1)*(f + 1)
Let s(n) = 6*n + 21. Let k be s(-3). Let b(d) be the second derivative of -4/3*d**2 - 11/18*d**4 + 3*d - 14/9*d**k + 0 - 1/12*d**5. Factor b(c).
-(c + 2)**2*(5*c + 2)/3
Let l(u) be the third derivative of u**5/150 - u**4/60 - 2*u**3/15 + 4*u**2. Factor l(r).
2*(r - 2)*(r + 1)/5
Factor t**4 - 5/4*t**3 - 1/4*t**5 + 0*t + 0 + 1/2*t**2.
-t**2*(t - 2)*(t - 1)**2/4
Suppose 0 = -3*t - 3, 0 = 5*y - 0*t - t - 11. Factor 0 + 4/5*n + 12/5*n**y + 6/5*n**4 + 13/5*n**3 + 1/5*n**5.
n*(n + 1)**2*(n + 2)**2/5
Let o(s) be the first derivative of s**4/18 - 4*s**3/27 + s**2/9 + 35. Determine b, given that o(b) = 0.
0, 1
Let p(r) be the second derivative of 0 + 7/6*r**4 + 4*r + 5/3*r**3 - 2*r**2. Solve p(d) = 0.
-1, 2/7
Let y(p) = 2*p**2 - 9*p - 7. Let u(b) = -b**2 + 3*b + 2. Let c(k) = -7*u(k) - 2*y(k). Factor c(a).
3*a*(a - 1)
Let z = 13 - 21. Let s(b) = -11*b**5 + 8*b**4 + 14*b**3 + 5*b - 8. Let l(m) = -7*m**5 + 5*m**4 + 9*m**3 + 3*m - 5. Let c(o) = z*l(o) + 5*s(o). Factor c(h).
h*(h - 1)**2*(h + 1)**2
Let b = 59 - 59. Let d = 0 + 0. Factor d + 1/4*i**2 + 0*i**3 - 1/4*i**4 + b*i.
-i**2*(i - 1)*(i + 1)/4
Let q(j) = -8*j**5 + 5*j**4 + j**3 - 5*j**2 + 7. Let g(c) = -7*c**5 + 4*c**4 + c**3 - 4*c**2 + 6. Let w(n) = 7*g(n) - 6*q(n). Solve w(x) = 0 for x.
-2, -1, 0, 1
Let w = 2 + 2. Let p = 4 - w. Factor 2*v**2 - 2*v**4 + p + 2*v**3 - 2*v + 0.
-2*v*(v - 1)**2*(v + 1)
Let s(r) be the second derivative of -r**7/294 + r**6/42 - 9*r**5/140 + r**4/12 - r**3/21 - 3*r. Let s(l) = 0. Calculate l.
0, 1, 2
Suppose -31*h + 29*h + 8 = 0. Let -2*v**2 + 2*v + 2 + h*v**3 + 4*v - 10*v**3 = 0. Calculate v.
-1, -1/3, 1
Suppose -2*s + 0 = -4. Suppose 24*w**3 + 23*w**4 - 23*w**2 + 4*w**5 + 7*w**s - 3*w**4 - 32*w = 0. What is w?
-2, 0, 1
Let b(n) be the first derivative of -n**6/21 - 14. Factor b(a).
-2*a**5/7
Let v = -692 - -4808/7. Let s = v + 136/21. Factor 2*i**2 + s + 10/3*i.
2*(i + 1)*(3*i + 2)/3
Let w = -4 + 3. Let p(y) = -y**5 - y**4 - y**3 + y**2 + y + 1. Let c(f) = -4*f**5 - f**4 + 8*f**3 - 5*f**2 + f + 1. Let m(q) = w*p(q) + c(q). Factor m(g).
-3*g**2*(g - 1)**2*(g + 2)
Let z(b) be the second derivative of b**5/20 - b**4/6 + b**3/6 + b. Find j such that z(j) = 0.
0, 1
Let q be (-28)/126 + (-1172)/(-90). Let n = 66/5 - q. Factor 1/5*i**2 + 0 + n*i.
i*(i + 2)/5
Let x(u) be the first derivative of -u**4/6 + u**3/3 + 2*u**2 + 7*u - 8. Let n(j) be the first derivative of x(j). Solve n(v) = 0.
-1, 2
Suppose 3*n - 3 = 2*d, n = d + 3*d + 11. Let j = n - -3. Suppose j + 3*k**4 - 26*k**3 - 16*k + 2*k + 7*k**4 + 30*k**2 - 2*k**4 = 0. Calculate k.
1/4, 1
Let b(k) be the first derivative of -1/15*k**3 + 1/5*k - 1/20*k**4 + 1/10*k**2 - 3. Let b(f) = 0. Calculate f.
-1, 1
Let -2*o - 5*o**2 + 124 - 127 - 5*o - o**3 = 0. What is o?
-3, -1
Let u(p) = 2*p - 10. Let h be u(7). Let 3*a**2 + 2*a + h*a**3 - 2*a**3 + a**2 = 0. Calculate a.
-1, 0
Let t(l) be the first derivative of -4*l**5/7 - 29*l**4/14 - 10*l**3/7 + 8*l**2/7 + 8*l/7 + 63. Determine r, given that t(r) = 0.
-2, -1, -2/5, 1/2
Let d = -9 + 12. Factor d*f - 12*f + 0*f**2 + f**2 - 4*f**2