Let w(b) = c(b) - 5*v(b). Find z such that w(z) = 0.
-1, -1/2, 1, 2
Let h(k) be the second derivative of -k**5/60 + k**4/18 + k**3/6 - 31*k. Solve h(n) = 0.
-1, 0, 3
Let a(c) be the third derivative of -c**8/336 + 8*c**7/735 - c**6/210 - c**5/30 + 11*c**4/168 - c**3/21 + 7*c**2. Suppose a(k) = 0. What is k?
-1, 2/7, 1
Let p(y) be the first derivative of -2/3*y**3 - 3 + 1/6*y**4 + 2*y + y**2. Let j(f) be the first derivative of p(f). Suppose j(v) = 0. What is v?
1
Suppose 0 = 4*o - g - 12, 3*g + 4 = -2*o + g. Factor 2*y**3 + 0 + 8/3*y**o - 2/3*y**5 - 8/3*y - 4/3*y**4.
-2*y*(y - 1)**2*(y + 2)**2/3
Factor -2/9*n + 4/9 + 2/9*n**4 + 2/9*n**3 - 2/3*n**2.
2*(n - 1)**2*(n + 1)*(n + 2)/9
Solve z**2 + 4*z + 3*z - 13*z**2 + 4*z**4 + z = 0 for z.
-2, 0, 1
Let s(v) = v**4 - 7*v**3 - v**2. Let w(p) = p**4 - 6*p**3 - p**2. Let h(n) = -6*s(n) + 7*w(n). Determine i, given that h(i) = 0.
-1, 0, 1
Factor 2*a**2 + 110 - 56*a + 429 - 147.
2*(a - 14)**2
Let w(i) be the third derivative of i**6/540 + i**5/90 - i**4/12 + 5*i**3/27 - 2*i**2. Find l, given that w(l) = 0.
-5, 1
Let y(r) = 4*r**3 + r**2 - r - 1. Let z be y(2). Let g be (3 + 1)*11/z. Factor m**2 + g*m + 1/3.
(m + 1)*(3*m + 1)/3
Suppose 4*k + 23 = 5*v, -k = -5*v - 6*k + 50. Let u be (20/(-7))/((-2)/v). Factor 3*z + 5*z + u*z**2 - 5*z**2 - 4.
(z + 2)*(5*z - 2)
Let r = -46 + 46. Factor 3*n**2 + r*n**3 - 3/2 - 3/2*n**4 + 0*n.
-3*(n - 1)**2*(n + 1)**2/2
Let q(k) be the first derivative of -k**6/27 + 8*k**5/45 - k**4/3 + 8*k**3/27 - k**2/9 + 2. Factor q(m).
-2*m*(m - 1)**4/9
Suppose 123 = -3*s - 5*b, s + 5*b + 31 = -20. Let f = s + 38. Let -1/3*i**f + 1 - 2/3*i = 0. What is i?
-3, 1
Let d(x) be the first derivative of -3*x**5/20 - 3*x**4/16 + x**3/2 + 13. Factor d(w).
-3*w**2*(w - 1)*(w + 2)/4
Let y(p) be the third derivative of -p**7/840 - p**6/480 - 7*p**2. Find b, given that y(b) = 0.
-1, 0
Let k(p) be the second derivative of p**5/5 + 2*p**4/3 + 2*p**3/3 + 2*p. Solve k(h) = 0.
-1, 0
Let p(c) be the third derivative of c**7/350 - c**6/25 + 6*c**5/25 - 4*c**4/5 + 8*c**3/5 - 18*c**2. Solve p(q) = 0.
2
Let n(r) be the first derivative of -2*r**5/15 - r**4/6 + 2*r**3/3 + 5*r**2/3 + 4*r/3 - 10. Factor n(l).
-2*(l - 2)*(l + 1)**3/3
Let k(o) be the third derivative of o**5/20 + o**4/4 - 3*o**3/2 + o**2. Find d such that k(d) = 0.
-3, 1
Let l be 280/637 + 14/(-49). Let 0 - 2/13*c - l*c**2 = 0. Calculate c.
-1, 0
Let f(r) be the first derivative of -1 + 4*r + 1/3*r**3 - 2*r**2. Solve f(l) = 0 for l.
2
Let m(b) = -4*b**4 + 8*b**3 - 9*b**2 + 2*b - 1. Let l(d) = d**4 + d**3 + d + 1. Let t(u) = -l(u) - m(u). Factor t(n).
3*n*(n - 1)**3
Let b(n) be the first derivative of 1/6*n**4 - 2*n + 0*n**3 + 2 + 0*n**2 - 1/10*n**5. Let f(o) be the first derivative of b(o). Factor f(i).
-2*i**2*(i - 1)
Find b such that 8*b - 3*b + 5*b**4 - 9*b**3 + b**3 - 3*b + b**2 = 0.
-2/5, 0, 1
Let y(b) be the second derivative of -b**7/2100 - b**6/450 + b**5/300 + b**4/30 - b**3 - 3*b. Let v(l) be the second derivative of y(l). What is m in v(m) = 0?
-2, -1, 1
Let o = -327 + 332. Let -1/3*p**2 + p**3 + 1/3*p**o + 0*p - p**4 + 0 = 0. What is p?
0, 1
Let i(d) be the second derivative of 0 + 1/135*d**6 - 3*d + 1/27*d**3 - 1/54*d**4 - 1/90*d**5 + 0*d**2. Suppose i(k) = 0. What is k?
-1, 0, 1
Let l(d) = -d - 2. Let t be l(-4). Suppose 2*a - 27 = -2*a - 5*q, 9 = -t*a + 5*q. Factor -4*y**5 + 3*y**5 - a*y**2 + 3*y**3 + 3*y**4 + 2*y**5 - 4*y**5.
-3*y**2*(y - 1)**2*(y + 1)
Let m(z) be the first derivative of z**6/15 - 2*z**5/5 + 9*z**4/10 - 14*z**3/15 + 2*z**2/5 - 12. Suppose m(p) = 0. What is p?
0, 1, 2
Let s(p) be the second derivative of p**7/63 - p**6/45 - p**5/10 + p**4/18 + 2*p**3/9 - 7*p. Find t such that s(t) = 0.
-1, 0, 1, 2
Let f(j) be the third derivative of j**5/20 + 7*j**2. Let f(x) = 0. What is x?
0
Let l(n) = -6*n**4 + 8*n**3 - 12*n**2 + 8*n - 2. Let v(x) = -7*x**4 + 8*x**3 - 12*x**2 + 8*x - 2. Let f(q) = -5*l(q) + 4*v(q). Determine i, given that f(i) = 0.
1
Factor 14*w - 5*w**2 + 5*w**4 - 10*w + 22*w - 30*w**3 + 4*w.
5*w*(w - 6)*(w - 1)*(w + 1)
Solve -4/7 + 18/7*y - 18/7*y**3 + 4/7*y**2 = 0.
-1, 2/9, 1
Let h(m) = 2*m - 4. Let s be h(6). Factor 2*r**5 + 10*r**4 + 2*r**2 + 6*r**5 + s*r**4 + 12*r**3.
2*r**2*(r + 1)**2*(4*r + 1)
Let b(k) be the first derivative of -2/3*k**3 + 4/27*k**6 + 16/45*k**5 - 1/6*k**4 + 0*k**2 + 4 + 0*k. Find f such that b(f) = 0.
-3/2, 0, 1
Let h(o) be the third derivative of -o**7/350 - 7*o**6/600 + o**5/300 + 7*o**4/120 + o**3/15 - 4*o**2. What is p in h(p) = 0?
-2, -1, -1/3, 1
Let d(f) = -f**2 + 2. Let b be d(0). Suppose -b*w**2 + 2*w**4 - 7*w**3 + 5*w**2 - 5*w**4 + 6*w**5 + w**3 = 0. What is w?
-1, 0, 1/2, 1
Let r(q) be the third derivative of -q**7/2625 - q**6/375 - q**5/250 + q**4/75 + 4*q**3/75 + 19*q**2. Let r(d) = 0. What is d?
-2, -1, 1
Let q(c) be the second derivative of c**4/6 + 38*c**3/9 + 8*c**2 + 39*c. Find p such that q(p) = 0.
-12, -2/3
Let w(v) be the first derivative of 9*v**2 + 3 - 12*v - 3*v**3 + 3/8*v**4. Solve w(b) = 0 for b.
2
Let o(n) be the second derivative of -n**8/560 + n**7/70 - n**6/20 + n**5/10 - n**4/8 + n**3 + 4*n. Let z(s) be the second derivative of o(s). Factor z(c).
-3*(c - 1)**4
Determine i so that 2/7*i + 4/7 - 2/7*i**2 = 0.
-1, 2
Let g(c) = c - 4. Let r be g(4). Let p = -101/18 + 55/9. Let r - p*b**2 + 0*b = 0. What is b?
0
Let k(i) be the first derivative of 9*i**5/5 - 3*i**4/4 - 3*i**3 + 3*i**2/2 - 14. Let k(l) = 0. What is l?
-1, 0, 1/3, 1
Determine t so that -11*t**3 + 6*t**5 + 2*t**2 - 4*t**5 + 17*t**3 + 6*t**4 = 0.
-1, 0
Let n(l) be the first derivative of -l**8/1120 - l**7/560 - 5*l**3/3 - 2. Let y(z) be the third derivative of n(z). Solve y(x) = 0.
-1, 0
Let s(v) be the first derivative of v**7/420 - v**6/240 - v**5/120 + v**4/48 - v**2 + 3. Let f(x) be the second derivative of s(x). Solve f(n) = 0 for n.
-1, 0, 1
Let f(a) = -a**5 + 3*a**4 - 5*a**3 + a**2 + 2*a. Let x(j) = 8*j**5 - 24*j**4 + 41*j**3 - 8*j**2 - 17*j. Let v(t) = 51*f(t) + 6*x(t). Factor v(s).
-3*s**2*(s - 1)**3
Let w(g) be the third derivative of 0*g + 0*g**4 + 0 + 0*g**3 - 1/45*g**5 - 1/60*g**6 - g**2 - 1/315*g**7. Solve w(j) = 0 for j.
-2, -1, 0
Let c = -51417490 - -131011753601/2548. Let x = 1/2548 - c. Find n, given that -x*n**5 + 68/7*n**4 + 0 - 8/7*n - 32/7*n**2 + 2/7*n**3 = 0.
-2/5, -1/3, 0, 1, 2
Let q(r) = -3*r**3 + 5*r**2 + 2*r. Let o(t) = -t**3 + t**2 + t. Let y(j) = 6*o(j) - 3*q(j). Factor y(z).
3*z**2*(z - 3)
Let i = 15 - 13. What is g in 10 + g - g**i - 3 - 5 = 0?
-1, 2
Let v = 10 + -6. Factor -8*f + 5*f**3 + f**3 + 2*f**4 - 4*f**v.
-2*f*(f - 2)**2*(f + 1)
Let g(s) = -s**2 + 6*s - 4. Let m be g(4). Suppose 12 = 5*r + r. Factor z - z**r + 0*z**2 + 2*z - m*z.
-z*(z + 1)
Suppose 4*w - 4*c - 5 = 3, 2 = w - 2*c. Factor 6*g - 1 + 9 - 4*g**3 + w*g + 4*g.
-4*(g - 2)*(g + 1)**2
Let l(a) be the third derivative of -a**7/210 - a**6/120 + 2*a**2. Find k such that l(k) = 0.
-1, 0
Let z(j) = 2*j**5 - 7*j**4 + 5*j**3 + 5*j**2 + 5*j - 5. Let y(m) = 2*m**5 - 8*m**4 + 6*m**3 + 6*m**2 + 6*m - 6. Let o(l) = -5*y(l) + 6*z(l). Factor o(k).
2*k**4*(k - 1)
Suppose 6 = -8*t + 10*t. Let i(x) be the first derivative of -1/3*x**t - x + x**2 - 2. Factor i(p).
-(p - 1)**2
Let w = -14 - -17. Suppose -w*d + 4*p - 10 = -0, -2 = -5*d + 2*p. Factor -2/9*f**d + 4/9*f - 2/9.
-2*(f - 1)**2/9
Suppose q = -k + 5*q + 4, -4*k + 5*q = -5. Let a(i) be the first derivative of -2*i - 1/4*i**4 + 3/2*i**2 + k*i**3 - 2. Factor a(s).
-(s - 1)**2*(s + 2)
Let p(j) be the third derivative of 3*j**2 - 1/300*j**6 + 1/60*j**4 + 0 + 0*j**3 + 0*j + 0*j**5. Factor p(d).
-2*d*(d - 1)*(d + 1)/5
Factor -4 - 2 + 6*g**2 - 2*g**3 - 2.
-2*(g - 2)**2*(g + 1)
Let s(c) be the third derivative of -3/160*c**6 + 0*c + 5*c**2 - 1/24*c**3 + 0 - 7/96*c**4 - 1/16*c**5. Factor s(r).
-(r + 1)*(3*r + 1)**2/4
Suppose 0 = -5*h - t + 25, 7*t - 3*t - 40 = -5*h. Factor -12 - h*b**2 - 131*b**2 + b + 243*b**3 - 97*b.
3*(b - 1)*(9*b + 2)**2
Let x(o) be the third derivative of 7*o**6/240 + 13*o**5/60 + 13*o**4/48 - o**3/2 - 5*o**2. Solve x(t) = 0 for t.
-3, -1, 2/7
Let x(w) be the second derivative of -1/4*w**4 - 3/10*w**6 + 0*w**2 + 3/5*w**5 + 0*w**3 + 3*w + 0. Factor x(c).
-3*c**2*(c - 1)*(3*c - 1)
Let m be 22/(-4) - (-2)/(-4). Let f be 6*(m/(-9))/2. Factor 6*l - 3*l + l