- 1)*(o + 1)**2
Let r(q) be the first derivative of -4 - 18/7*q + 6/7*q**2 - 2/21*q**3. Let r(v) = 0. Calculate v.
3
Let s(b) be the second derivative of 0*b**2 + 0 - 3*b - 7/20*b**4 - 1/5*b**3. Suppose s(r) = 0. What is r?
-2/7, 0
Let s = -20 - -23. Let w(k) be the second derivative of 0*k**2 + 0*k**4 + 0 + 1/30*k**6 + 0*k**s - k + 1/20*k**5. Factor w(z).
z**3*(z + 1)
Factor 28*u**2 - 31*u**2 - u**3 - 8*u**3.
-3*u**2*(3*u + 1)
Let 0 + 0*x**3 - 1/8*x**5 + 1/8*x + 1/4*x**4 - 1/4*x**2 = 0. Calculate x.
-1, 0, 1
Let q be ((-12)/(-3))/(-2 + 3). Factor 2 + 3 - 4*z - 7 - 9*z**q + 2*z**2 + 1 + 12*z**3.
-(z - 1)**2*(3*z + 1)**2
Let w(i) be the second derivative of i**5/20 - i**4/12 + i**3/6 + 3*i**2/2 - 3*i. Let b be w(0). Find p such that -p**3 - 6*p**2 - p**3 - 5 + b - 6*p = 0.
-1
Let l(x) be the first derivative of -1/16*x**4 + 1/12*x**3 + 4 + 1/8*x**2 - 1/4*x. Factor l(i).
-(i - 1)**2*(i + 1)/4
Let 16/7 - 12/7*n**2 + 8/7*n - 10/7*n**3 - 2/7*n**4 = 0. What is n?
-2, 1
Let v(i) = 3*i. Let n be v(-1). Let d be n/(-18) + 1/3. Solve 0 + 0*z - d*z**4 + z**3 - 1/2*z**2 = 0.
0, 1
Let w(n) be the first derivative of 2*n**3/21 + 2*n**2 + 14*n + 43. Factor w(h).
2*(h + 7)**2/7
Let m(p) be the third derivative of -7*p**5/12 - 15*p**4/8 - 5*p**3/3 - 6*p**2. Suppose m(q) = 0. Calculate q.
-1, -2/7
Let w(y) be the second derivative of 2*y**7/49 + 10*y**6/21 + 71*y**5/35 + 29*y**4/7 + 92*y**3/21 + 16*y**2/7 - 17*y + 1. Find f, given that w(f) = 0.
-4, -2, -1, -1/3
Let g(n) be the first derivative of -n**4/2 + 10*n**3/3 - 8*n**2 + 8*n - 17. Factor g(w).
-2*(w - 2)**2*(w - 1)
Let p be (0 - 0)/(-2 - -1). Suppose p*t = -2*t - 4*r + 26, 25 = 5*t + 2*r. Suppose -k**2 + 6*k - 3*k**t + 2*k**3 - 3*k - k = 0. Calculate k.
-2, 0, 1
Let m be 1*(2 + (-3 - -1)). Factor 0 + 1/3*p**3 - 1/3*p**2 + m*p.
p**2*(p - 1)/3
Let r(y) = 6*y. Let b be r(1). Factor -b*q + q**2 + 4*q**2 - 2*q**2.
3*q*(q - 2)
Let d be 126/27 + 2/(-3). Let q be (-3)/(1/d*-6). Factor 0*w**4 + 0 + 0*w**q + 4/3*w**3 - 2/3*w**5 - 2/3*w.
-2*w*(w - 1)**2*(w + 1)**2/3
Let f = 18 + -18. Let n(p) be the second derivative of 1/21*p**4 - 2/105*p**6 - 2*p - 1/21*p**3 + 1/147*p**7 + 0*p**5 + f + 0*p**2. Suppose n(d) = 0. What is d?
-1, 0, 1
Solve -3/5*a + 3/5*a**3 - 9/5*a**2 + 9/5 = 0 for a.
-1, 1, 3
Suppose 8 = -3*t - t, 0 = -2*h - 2*t. Let k(f) be the second derivative of 0*f**h - 2*f + 1/42*f**4 - 1/21*f**3 + 0. Let k(y) = 0. Calculate y.
0, 1
Let q be 2/6*(174/(-42) + 5). Factor q - 6/7*u + 6/7*u**2 - 2/7*u**3.
-2*(u - 1)**3/7
Let f(k) be the second derivative of -5*k + 0 + 1/6*k**2 + 1/4*k**3 + 1/18*k**4. Solve f(w) = 0 for w.
-2, -1/4
Let n be -2 - 16/6*-1. Factor n*l + 1/3*l**2 + 1/3.
(l + 1)**2/3
Suppose 0 = 5*m - p - 15, 0 = 4*m + m + 2*p. Let w(n) be the first derivative of 2*n - 2/3*n**3 - 1/4*n**4 + 3 + 1/2*n**m. Factor w(v).
-(v - 1)*(v + 1)*(v + 2)
Let w = -2 + 2. Factor 5*r**4 + 2 - 3*r**4 + w - 4*r**2.
2*(r - 1)**2*(r + 1)**2
Let x(a) = 15*a**2 - 325*a + 2565. Let g(o) = -22*o**2 + 487*o - 3847. Let f(v) = 5*g(v) + 7*x(v). Find u, given that f(u) = 0.
16
Find z such that 24*z**3 + 16*z**2 + 16*z**4 + 2074 - 2074 + 4*z + 4*z**5 = 0.
-1, 0
Let d(f) be the third derivative of 0*f**3 + 1/600*f**6 + 0*f**4 + 1/1050*f**7 - 1/1680*f**8 + 0 + 0*f + 3*f**2 - 1/300*f**5. Let d(o) = 0. Calculate o.
-1, 0, 1
Let q(c) be the second derivative of c**5/20 + c**4/3 + 2*c**3/3 + 13*c. Factor q(d).
d*(d + 2)**2
Let u(q) be the first derivative of -7/12*q**6 + 8 - 5/8*q**2 + 19/16*q**4 + 13/12*q**3 - 1/2*q - 11/20*q**5. Determine r, given that u(r) = 0.
-1, -2/7, 1/2, 1
Solve 12*z - 4*z**3 + 2*z**4 + 2*z - 2 - 10*z = 0 for z.
-1, 1
Let j(v) be the third derivative of -v**7/5040 - v**6/480 - v**5/120 + v**4/8 - 2*v**2. Let q(w) be the second derivative of j(w). Factor q(p).
-(p + 1)*(p + 2)/2
Let q(o) = 2*o**3 + 13*o**2 - 23*o + 14. Let s(k) = 8*k**3 + 53*k**2 - 91*k + 56. Let z(n) = 26*q(n) - 6*s(n). Find t, given that z(t) = 0.
-7, 1
Factor 0 + 4/7*n**3 - 2/7*n**2 + 2/7*n**4 - 4/7*n.
2*n*(n - 1)*(n + 1)*(n + 2)/7
Let u(l) be the second derivative of -7/30*l**5 + 0 + 4*l + 2/3*l**2 + 1/6*l**4 + 7/9*l**3 - 1/9*l**6. Solve u(r) = 0 for r.
-1, -2/5, 1
Let a(k) be the second derivative of -25*k**7/126 + 11*k**6/18 + 14*k**5/15 + k**4/3 - 10*k. Determine z, given that a(z) = 0.
-2/5, 0, 3
Suppose 0*n = 3*n - 27. Let r = n + -7. Factor 4/5*m**r + 2/5*m**3 + 0 + 0*m.
2*m**2*(m + 2)/5
Let r(s) = -s - 2. Let w be r(-8). Let l = -3 + w. Solve -b**5 - 3*b + l*b**4 - 3*b**3 + 3*b + b**2 = 0.
0, 1
Let s be 1 - (-3)/(-6)*4/(-2). Factor 27/7*c - 27/7 - 9/7*c**s + 1/7*c**3.
(c - 3)**3/7
Let r(w) = w**2 - w + 5. Let m = -3 - -3. Let l be r(m). Determine p, given that -2*p**l - 2*p**3 + 5*p**3 - p**3 = 0.
-1, 0, 1
Let x be -2 - (-7 + 5) - (-2 + -1). Factor 2/3*z**4 - 2*z**2 - 10/3*z - 4/3 + 2/3*z**x.
2*(z - 2)*(z + 1)**3/3
Let j(v) be the third derivative of 0*v + 0*v**4 + 0*v**5 - 5/1008*v**8 + 0*v**3 - 1/210*v**7 + 1/180*v**6 + 0 - 2*v**2. Suppose j(g) = 0. Calculate g.
-1, 0, 2/5
Let s be (9/2)/9*(-4)/(-30). Let i(y) be the third derivative of 2*y**2 + 0 + 0*y + s*y**4 + 1/60*y**5 - 2/15*y**3. Factor i(h).
(h + 2)*(5*h - 2)/5
Let k be 0 - 9/72*(-5 - 1). Solve 0 + k*j**3 + 0*j + 1/4*j**5 - 3/4*j**4 - 1/4*j**2 = 0.
0, 1
Let w(d) be the second derivative of -d**6/120 + d**4/8 - 2*d**3/3 - 2*d. Let b(l) be the second derivative of w(l). Determine q so that b(q) = 0.
-1, 1
Let t(q) be the first derivative of -2*q**3/21 + 2*q**2 - 14*q + 5. Let t(b) = 0. What is b?
7
Let -5/2*s + 5/2*s**2 - 5/6*s**3 + 5/6 = 0. What is s?
1
Factor -4/5*k**2 + 0 + 1/10*k**3 + 8/5*k.
k*(k - 4)**2/10
Let z(j) be the third derivative of -j**7/1260 - j**6/360 + j**5/360 + j**4/72 + 5*j**2. Factor z(v).
-v*(v - 1)*(v + 1)*(v + 2)/6
Let k(a) be the third derivative of -a**7/840 + a**6/360 + a**5/120 + a**4/8 + 3*a**2. Let w(n) be the second derivative of k(n). Determine s so that w(s) = 0.
-1/3, 1
Let y = -17 + 17. Determine i so that -12 - 9*i**3 - 21*i - 24*i**2 + y + 6 = 0.
-1, -2/3
Let t be (4 + -6)/(-2*(-3)/(-2)). Factor t*n**2 + 2/3 + 4/3*n.
2*(n + 1)**2/3
Factor 4/5*j**4 - 4/5*j**2 + 0 - 4/5*j + 4/5*j**3.
4*j*(j - 1)*(j + 1)**2/5
Let p(v) be the second derivative of -v**4/4 + v**3 - 3*v**2/2 + 3*v. Determine g so that p(g) = 0.
1
Let z(r) be the third derivative of -r**9/17280 - r**8/4480 - r**7/5040 - r**5/30 - 8*r**2. Let p(o) be the third derivative of z(o). Factor p(v).
-v*(v + 1)*(7*v + 2)/2
What is w in 1/2*w**2 - 1 + 1/2*w = 0?
-2, 1
Let x(h) = 62*h**3 - 152*h**2 + 100*h - 4. Let t(r) = r**3 - r**2 + r + 1. Let k(g) = 12*t(g) - x(g). Solve k(m) = 0.
2/5, 2
Let m(y) be the second derivative of y**6/45 - y**5/10 + y**4/6 - y**3/9 - 6*y. Factor m(x).
2*x*(x - 1)**3/3
Let z = -1/1343 - -1427/112812. Let n(v) be the third derivative of 0 - v**2 + 0*v**3 + 1/210*v**5 + z*v**4 + 0*v. Factor n(l).
2*l*(l + 1)/7
Suppose 5*x = 4*r + 2, 2*x + 0*x = -5*r + 14. Determine p, given that -13*p - 6 + 20*p**r + 3 + 5 = 0.
1/4, 2/5
Let w(s) = -25*s - 1. Let o be w(-2). Let u = 345/7 - o. Factor -4/7 - 6/7*y - u*y**2.
-2*(y + 1)*(y + 2)/7
Suppose 4*v - 6*v = -40. Let u be (-92)/v + 2 + 3. Solve -4/5*j**2 + 0*j + 2/5*j**4 + u + 0*j**3 = 0 for j.
-1, 1
Suppose -2*l - 9 + 49 = -4*r, 88 = 5*l - 4*r. Factor l*f**2 - 3*f**2 - 28*f**4 + 6*f**3 + 7*f**3 - 3*f + 5*f.
-f*(f - 1)*(4*f + 1)*(7*f + 2)
Let m be (2 + 3/1)*2. Let r be (-4)/m - 282/(-30). Determine k, given that -2*k**2 + 0*k**2 + r - 7 = 0.
-1, 1
Let u(d) = -4*d**3 - 2. Let m(t) = -t**3 - t**2 + t - 1. Let y = 10 + -12. Let l(a) = y*u(a) + 6*m(a). Factor l(i).
2*(i - 1)**3
Let r = 112 - 109. Determine y so that -3/4*y**3 + 21/4*y**2 - r + 0*y - 9/4*y**4 + 3/4*y**5 = 0.
-1, 1, 2
Let o(w) be the first derivative of w**3/3 - 3*w**2/2 + 2*w + 27. Factor o(p).
(p - 2)*(p - 1)
Let h = -11/6 + 13/6. Let k(s) be the first derivative of 2/3*s**4 + 1 - 4/3*s**3 - h*s**2 - 1/3*s**6 + 4/3*s + 8/15*s**5. Suppose k(b) = 0. Calculate b.
-1, -2/3, 1
Let t(o) be the first derivative of -o**4/2 + 64*o**3/3 - 256*o**2 + 53. Factor t(s).
-2*s*(s - 16)**2
Let h = -5/117 + 2/13. Let j(f) be the third derivative of -h*f**3 - 1/360*f**6 + 1/24*f**4 + 2*f**2 + 0 + 0*f + 0*f**5. Suppose j(l) = 0. Calculate l.
-2, 1
Let g be (-30)/72*16/(-30). Sol