d derivative of w(p). Find q, given that k(q) = 0.
-1, 0, 1
Let k(g) be the first derivative of g**6/810 - 10*g**3 - 14. Let d(a) be the third derivative of k(a). Factor d(r).
4*r**2/9
Let d = 34/27 + -161/135. Let w(j) be the first derivative of 0*j**5 + 0*j**2 + 1/10*j**4 - d*j**6 + 0*j + 3 + 0*j**3. Solve w(l) = 0.
-1, 0, 1
Solve 8*i**2 + 32/3 + 76/3*i**3 - 8/3*i**4 - 4*i**5 - 112/3*i = 0 for i.
-2, 1/3, 1, 2
Let p(s) be the third derivative of 1/2184*s**8 - 1/390*s**6 + 0 + 0*s**3 + 0*s**7 + 0*s**5 + 0*s + 1/156*s**4 - 14*s**2. Factor p(d).
2*d*(d - 1)**2*(d + 1)**2/13
Solve 369/7*h**2 + 0 + 30*h**3 - 9/7*h**4 + 150/7*h = 0 for h.
-1, -2/3, 0, 25
Suppose 14*s - 9*s + 215 = 0. Let l = s - -45. Determine h, given that 0 + 1/4*h + 3*h**3 + 3/4*h**5 - 3/2*h**l - 5/2*h**4 = 0.
0, 1/3, 1
Factor 40*v**4 + 51447*v**2 - 16805 + 203*v**4 + 19505 + 23940*v - 7182*v**3.
3*(v - 15)**2*(9*v + 2)**2
Let h be (2 + 126/(-81))*6/4. Let j be (-6)/15 - 2/(-5). What is t in 0 - 4/3*t**5 + 10/3*t**4 - 4/3*t**2 + j*t - h*t**3 = 0?
-1/2, 0, 1, 2
Let 307*d + 3 - 15*d + 4*d**2 - 3 = 0. Calculate d.
-73, 0
Let 232/7*j - 3364/7 - 4/7*j**2 = 0. Calculate j.
29
Let b = 61/50 + -18/25. Let q(d) be the second derivative of -b*d**2 + 1/48*d**4 + 0 + 7*d + 1/8*d**3. Factor q(t).
(t - 1)*(t + 4)/4
Let d(n) = n + 10. Let x be d(-7). Let p be ((4/(-10))/((-35)/150)*-7)/(-2). Factor -129/2*j + 567/2*j**4 - 891/2*j**x + 513/2*j**2 + p.
3*(3*j - 1)**3*(7*j - 4)/2
Let l be -2*4/(-16) + (-38)/(-4). Suppose l = -3*b - 4*c, 0 = -2*b - 3*c + c - 4. Solve -2/15*z**5 - 8/15*z**3 + 4/15*z**b - 8/15*z**4 + 4/15 + 2/3*z = 0 for z.
-2, -1, 1
Factor 4/3*n**3 - 8*n**2 + 4*n + 40/3.
4*(n - 5)*(n - 2)*(n + 1)/3
Let w(p) be the second derivative of -3/10*p**5 + p**3 + 1/4*p**4 + 0 + 2*p - 1/10*p**6 + 0*p**2. Factor w(c).
-3*c*(c - 1)*(c + 1)*(c + 2)
Let f(j) be the second derivative of 2*j**7/105 + j**6/15 + j**5/15 + 9*j**2 - 12*j. Let x(c) be the first derivative of f(c). Factor x(k).
4*k**2*(k + 1)**2
Let u(w) = -w**3 - 7*w**2 + 6*w - 8. Let v be u(-8). Let y = 11 - v. Let 3*j**5 + 16*j**3 - 5*j**4 - 3*j**4 - 10*j**y - j = 0. Calculate j.
-1/3, 0, 1
Let -897/4*x**2 - 196 - 406*x - 29/2*x**3 - 1/4*x**4 = 0. Calculate x.
-28, -1
Suppose 4*m - 4*u = 0, 0 = 2*u - 6 - 0. Factor 13*q - m*q**2 + q - 3*q + 7*q.
-3*q*(q - 6)
Let y = 1/28 - -53/84. Let g(v) be the first derivative of -y*v**3 + 0*v - 2 + 2/3*v**2 + 1/6*v**4. Determine s, given that g(s) = 0.
0, 1, 2
Factor 0*g**2 - 124 + 3*g**2 + 103 + 18*g.
3*(g - 1)*(g + 7)
Let q(u) be the third derivative of u**7/525 - u**6/20 + 23*u**5/50 - 97*u**4/60 + 14*u**3/5 + 875*u**2. What is g in q(g) = 0?
1, 6, 7
Let b = 2 + 4. Suppose -q - 8 = -2*u - b*q, u - q - 4 = 0. Factor -5*y**3 + 9*y**2 - 2*y**3 + y**u - 3*y - 2*y**3 + 2*y**4.
3*y*(y - 1)**3
Let p = -3347/5 - -673. Let v be (-130)/(-78) + 125/51 + 4/(-34). Let p*t**v - 39/5*t**3 + 0 + 36/5*t**2 - 12/5*t - 3/5*t**5 = 0. Calculate t.
0, 1, 2
Let t(g) be the second derivative of g**5/40 - 15*g**4/8 + 29*g**3/4 - 43*g**2/4 - 798*g. Factor t(q).
(q - 43)*(q - 1)**2/2
Suppose -s = -2*p + 2 - 1, -4*p - 5*s + 9 = 0. Factor p + 3*d**2 + 10 + 3 + 12*d - 2.
3*(d + 2)**2
Let d be (12/48)/((-3)/(-6)). Let v(l) be the first derivative of -3/8*l**4 + 0*l - d*l**2 - 11 - 7/6*l**3. Let v(g) = 0. What is g?
-2, -1/3, 0
Let y(b) = -b**2 - 2 + 3 + 0*b**2. Let f(n) = 4*n**2 + 18*n - 86. Let l(o) = 2*f(o) + 10*y(o). Factor l(u).
-2*(u - 9)**2
Let o be 826/(-14455) + (-88)/(-70). Suppose 18/5*w**2 + 12/5*w + o*w**3 + 0 = 0. What is w?
-2, -1, 0
Let p be (-4 - 49/(-14))*1*34. Let t = 17 + p. Factor -1/3*c**2 + t*c + 1/3*c**3 + 0.
c**2*(c - 1)/3
Let w(a) be the second derivative of -3*a**5/40 - 19*a**4/24 - 11*a**3/6 + 6*a**2 - a + 91. Factor w(n).
-(n + 3)*(n + 4)*(3*n - 2)/2
Suppose 0*x + 12 = -4*x - 4*p, 0 = -x + 3*p - 11. Let o be (x/(-20))/((-14)/(-8)). Find n such that -1/7 + o*n**2 - 1/7*n + 1/7*n**3 = 0.
-1, 1
Let a(j) be the first derivative of -605*j**4/4 + 3245*j**3/3 - 560*j**2 + 100*j + 123. Let a(v) = 0. What is v?
2/11, 5
Let d(t) be the first derivative of -78/5*t**3 - 2/5*t**5 - 2 + 81/5*t**2 + 108/5*t + 43/10*t**4. Factor d(w).
-2*(w - 3)**3*(5*w + 2)/5
Let z(q) be the third derivative of -q**7/35 + 151*q**6/40 + 77*q**5/20 - 19*q**4/2 + 3*q**2 + 31*q. Solve z(r) = 0 for r.
-1, 0, 1/2, 76
Suppose -8*r + 24 - 8 = 0. Suppose -d - 3*d = 16, -r*d - 8 = 4*h. Solve 0*a**2 + 2/5*a**5 + 2/5*a**3 + 4/5*a**4 + h + 0*a = 0.
-1, 0
Let m(q) be the second derivative of 5/6*q**4 + 9*q + 5/2*q**2 + 5/42*q**7 + 1/2*q**5 + 0 - 1/2*q**6 - 5/2*q**3. Let m(x) = 0. What is x?
-1, 1
Suppose 40*w - 37*w = -18. Let n be w/(-9)*45/10. Factor -1/4*p**n - 1/2*p + 0 - 3/4*p**2.
-p*(p + 1)*(p + 2)/4
Let c(z) be the second derivative of z**6/20 - 33*z**5/40 + 33*z**4/8 - 5*z**3/4 - 75*z**2/2 - 35*z - 8. Solve c(d) = 0.
-1, 2, 5
Let p be 8/(-12)*3 + 5. Determine a so that -16*a - 4*a - 1 - p*a**2 - 11 + 5*a = 0.
-4, -1
Let j(m) = 4*m**3 + 22*m**2 - 6*m - 84. Let q(p) = p**2 + p - 2. Let c(f) = j(f) - 6*q(f). Find i, given that c(i) = 0.
-3, 2
Let b be 782/1173*3/42*6. Determine v, given that b*v + 0 - 2/7*v**2 = 0.
0, 1
Let q(u) be the third derivative of u**5/180 - u**4/6 - 67*u**2 + 2. Suppose q(t) = 0. What is t?
0, 12
Let b(m) be the third derivative of 3/20*m**5 + 1/12*m**4 - 37*m**2 + 0 + 0*m**3 + 0*m. Factor b(r).
r*(9*r + 2)
Let x(o) be the third derivative of 2 - 1/75*o**5 + 0*o**3 + 1/15*o**4 + 1/210*o**7 - 1/100*o**6 + 5*o**2 - 1/1680*o**8 + 0*o. Solve x(t) = 0.
-1, 0, 2
Factor 8/3 - 1/3*m**3 - 4*m + 2*m**2.
-(m - 2)**3/3
Let w(y) be the second derivative of -3*y**5/40 - y**4/2 - y**3 + 2*y + 44. Factor w(z).
-3*z*(z + 2)**2/2
Let l(r) be the first derivative of 0*r - 11 - 1/15*r**6 - r**3 - 4*r**2 - 11/30*r**5 - 5/6*r**4. Let n(o) be the second derivative of l(o). Factor n(s).
-2*(s + 1)**2*(4*s + 3)
Let g = 202 + -196. Let x(b) be the second derivative of 0*b**2 - 3/20*b**5 - 1/5*b**g + b - 1/14*b**7 + 0*b**3 + 0*b**4 + 0. Factor x(o).
-3*o**3*(o + 1)**2
Factor 17 - 9 + l**2 - 24.
(l - 4)*(l + 4)
Let o(k) be the first derivative of -k**4/46 + 2*k**3/69 + 5*k**2/23 + 6*k/23 + 137. Find d such that o(d) = 0.
-1, 3
Let u(a) = 3*a - 41. Let n(d) = -d + 20. Let g(c) = 5*n(c) + 2*u(c). Let q be g(-15). Determine i so that -2/5*i**2 - 1/5*i**q + 0 - 1/5*i = 0.
-1, 0
Let x(c) = -8*c**2 - 138*c - 136. Let k(a) = -17*a**2 - 277*a - 274. Let m(b) = 3*k(b) - 7*x(b). Factor m(d).
5*(d + 1)*(d + 26)
Factor 30*w**2 - 2*w - 10*w**2 + 27*w - 5*w**3.
-5*w*(w - 5)*(w + 1)
Factor -4*h**2 - 20*h**2 + 2*h**5 - 3*h**4 - 4*h**3 + 12*h**4 - h**4 + 18*h.
2*h*(h - 1)**2*(h + 3)**2
Suppose -2*z = 4*m - 2, -11 = 11*m - 13*m + z. Factor 0*s**2 + 7/5*s - 1/5*s**m - 6/5.
-(s - 2)*(s - 1)*(s + 3)/5
Let s be 45/60*(-36)/3 - (24 + -35). Factor -24/7*r**s - 100/7 - 2/7*r**3 - 90/7*r.
-2*(r + 2)*(r + 5)**2/7
Suppose -91*p + 89*p = -8. Suppose 0*v - p*v = 4*o, 0 = 2*o. Factor 2/3*r**2 + v*r - 2/3.
2*(r - 1)*(r + 1)/3
What is w in 4/7*w**3 + 480/7*w + 576/7 - 92/7*w**2 = 0?
-1, 12
Let b be (-31)/(-390) + 4/26. Let d(y) be the second derivative of 0*y**2 + b*y**6 + 0 + 11/12*y**4 + 1/3*y**3 + 4/5*y**5 + 3*y. Factor d(w).
w*(w + 1)**2*(7*w + 2)
Let i(x) be the first derivative of x**6/24 - 3*x**5/20 + x**4/16 + x**3/4 - x**2/4 - 225. Determine b so that i(b) = 0.
-1, 0, 1, 2
Suppose -k + 4*g - 5 = -29, -g = -2*k + 13. Factor -1/7*t**k + 0*t**3 + 0*t**2 + 0*t + 0.
-t**4/7
Determine s, given that -10*s**3 - 5 + 9*s**2 + 17*s**2 + 23*s**2 + 10*s + 5*s**4 - 49*s**2 = 0.
-1, 1
Factor 0 - 2/9*l + 2/9*l**5 + 0*l**3 - 4/9*l**4 + 4/9*l**2.
2*l*(l - 1)**3*(l + 1)/9
Let v(a) be the third derivative of -a**6/120 + a**5/60 - a**4/24 + 52*a**2. Let l(h) = -6*h**3 - 14*h**2 - 4*h. Let f(r) = -l(r) + 4*v(r). Factor f(n).
2*n**2*(n + 9)
Let f(q) be the first derivative of -2*q**5/5 - 4*q**4 + 38*q**3/3 - 10*q**2 - 66. Let f(j) = 0. What is j?
-10, 0, 1
Let d be ((-1)/2)/(10/(-40)). Factor 39*t**d + t**4 + 3*t**4 - 55*t**2.
4*t**2*(t - 2)*(t + 2)
Let z be -19 + (-16 - (-1422)/36). Solve -25/2*q**4 - z*q**5 - 3/2*q**2 - 21/2*q**3 + 0 + q = 0 for q.
-1, 0, 2/9
Suppose 1/3*z**2 - 10/3*z - 11/3 = 0. Calculate z.
-1, 11
Let t(j) = j**2 + 8*j + 17. Let f be t(-4). Let p be 5/25 - f/