derivative of -1/6*x**r + 1/4*x**4 + 1/10*x**5 + 0*x + 1 - 1/2*x**2. Factor a(p).
p*(p - 1)*(p + 1)*(p + 2)/2
Let t(y) be the first derivative of 0*y**2 - 46 - 2/33*y**3 + 0*y. Factor t(r).
-2*r**2/11
Let k(x) be the third derivative of 7*x**6/90 + 8*x**5/45 - 13*x**4/18 - 4*x**3/9 + 921*x**2. What is a in k(a) = 0?
-2, -1/7, 1
Let q(g) be the first derivative of -g**4/9 - 16*g**3/9 + 62*g**2/9 + 56*g/3 + 567. Let q(l) = 0. Calculate l.
-14, -1, 3
Let q(l) be the first derivative of -8*l**3 + 10*l**2 - 23 - 2 + 528*l**4 - 527*l**4. Suppose q(t) = 0. What is t?
0, 1, 5
Let b = -4273 + 4273. Factor n**2 + b + 2/5*n.
n*(5*n + 2)/5
Let p(h) = -h**4 + 2*h**2 + h + 1. Let a(k) = -3*k**4 + 36*k**3 - 66*k**2 + 31*k - 13. Let y(w) = -a(w) - 5*p(w). Find d, given that y(d) = 0.
1/2, 1, 2
Let l be (5/2*1/20)/1. Solve l*h**2 - 1/4*h + 1/8 = 0 for h.
1
Let b(h) be the second derivative of h**10/45360 - h**9/7560 + h**7/945 + 5*h**4/2 + 28*h. Let t(s) be the third derivative of b(s). Factor t(w).
2*w**2*(w - 2)**2*(w + 1)/3
Suppose 3*h + 4*c + 3 + 10 = 0, -3*c - 16 = -4*h. Let q be -1*h*(-144)/20. Find d, given that q*d**3 + 324/5*d + 243/5 + 162/5*d**2 + 3/5*d**4 = 0.
-3
Let r be 3/(-8) + (-18815)/(-1704). Let o be 16/6 + 3/9. Factor r*x - 19/3*x**2 + 5/6*x**o + 16/3.
(x - 4)**2*(5*x + 2)/6
Let v(a) be the second derivative of a**4/42 - 17*a**3/21 - 197*a. Factor v(s).
2*s*(s - 17)/7
Let f(s) be the second derivative of -s**7/420 + s**6/90 + s**5/60 - s**4/6 + 3*s**3/2 + 52*s. Let m(k) be the second derivative of f(k). Factor m(v).
-2*(v - 2)*(v - 1)*(v + 1)
Let v(a) be the third derivative of 17*a**7/210 - a**6/8 - 19*a**5/60 + 5*a**4/8 + a**3/3 + 3*a**2 + 12*a. Determine w, given that v(w) = 0.
-1, -2/17, 1
Let y(r) be the second derivative of 0*r**2 + 1 - 1/48*r**4 - 1/20*r**5 + 1/120*r**6 - 4*r + 1/6*r**3. Find b, given that y(b) = 0.
-1, 0, 1, 4
Let l(s) be the second derivative of -s**7/147 - 2*s**6/105 + 2*s**5/35 + 4*s**4/21 - s + 28. Find p such that l(p) = 0.
-2, 0, 2
Let l = -29 + 31. Factor 13*h - 16 + 4*h**l + 9*h - 22*h.
4*(h - 2)*(h + 2)
Factor 5*m**2 + 24*m**5 + m**2 - 4*m**3 + m**3 - 6*m**4 + 0*m**3 - 21*m**5.
3*m**2*(m - 2)*(m - 1)*(m + 1)
Let v = 1149/2 - 574. Let m = -55/2 + 28. Find j, given that -j + m + v*j**2 = 0.
1
Let p(n) be the third derivative of -n**7/140 - n**6/40 + 3*n**5/40 + n**4/4 - n**3 + 24*n**2. Solve p(f) = 0 for f.
-2, 1
Let w = 1007/490 + -123/98. Find v such that w*v**3 + 0 + 12/5*v**4 - 8/5*v + 4/5*v**5 - 12/5*v**2 = 0.
-2, -1, 0, 1
Suppose -18*m + 9*m + 36 = 0. Factor 0 + 3/2*a + 0*a**3 - 3/4*a**m + 9/4*a**2.
-3*a*(a - 2)*(a + 1)**2/4
Let -488*u + 10*u**2 + 249*u + 247*u = 0. Calculate u.
-4/5, 0
Suppose -3*a - 16 = -5*o, -4*o + 3*a + 18 = -2*a. Factor 4*l**3 + 3*l + 7*l**2 - 2*l**o - 10*l - 2.
(l - 1)*(l + 2)*(4*l + 1)
Let 3/2*j**3 + 54 - 87/2*j**2 - 3/2*j**5 + 15/2*j**4 + 18*j = 0. Calculate j.
-2, -1, 2, 3
Let y be 4 - (1 + (2 + -1)/(-1)). Find k such that 9 - 15*k**2 + 25*k - 19 + 0*k**4 + 5*k**y - 5*k**3 = 0.
-2, 1
Let a(v) = 1. Let n(j) be the first derivative of 9*j**4/4 + 2*j**3 - 10*j**2 + 4*j + 37. Let y(g) = -4*a(g) - n(g). Factor y(i).
-(i + 2)*(3*i - 2)**2
Let r(w) be the third derivative of -11/20*w**5 + 0 + 2/5*w**6 + 0*w + 1/4*w**4 - 1/10*w**7 + 0*w**3 + 18*w**2. Factor r(g).
-3*g*(g - 1)**2*(7*g - 2)
Suppose -43*c + 0*c = 2*c. Let a(l) be the third derivative of -1/90*l**6 + 4/9*l**3 + 1/6*l**4 + 0*l**5 + 0*l + c + 3*l**2. Determine p so that a(p) = 0.
-1, 2
Let l = -12603/7 - -1809. Suppose 4*t**4 - l*t**2 - 12/7*t**5 + 16/7 + 4*t**3 - 32/7*t = 0. Calculate t.
-1, 1/3, 2
Let g(f) = 2*f**2 + f + 2. Let t(l) = 2*l**2 + 35*l - 12. Let n(a) = -4*g(a) + 2*t(a). What is k in n(k) = 0?
1/2, 16
Let y = 7141/30 - 238. Let n(t) be the third derivative of 1/36*t**4 + 0 + 4*t**2 + 1/60*t**6 + 0*t + 0*t**3 - 1/315*t**7 - y*t**5. What is a in n(a) = 0?
0, 1
Let t(u) = -3 + 2 - 2*u - 5 - 13*u**2 + 9. Let a(z) = -66*z**2 - 9*z + 15. Let w(r) = -4*a(r) + 21*t(r). Determine d so that w(d) = 0.
-1, 1/3
Solve -20/3*t**2 - 14/3*t**3 + 2/3*t**4 + 80 + 152/3*t = 0 for t.
-2, 5, 6
Let f(c) be the third derivative of -1/10*c**6 + 4/15*c**5 + 0*c + 3*c**2 - 2/105*c**7 + 0*c**3 + 0 + 0*c**4. Factor f(n).
-4*n**2*(n - 1)*(n + 4)
Suppose 2 = -n - 9. Let c be -2 + -1 - (7 + n). Factor -4 + c + 0 - 3*w**2 + 6*w.
-3*(w - 1)**2
Let m(s) = 3*s**2 - 4*s + 4. Let x(u) = -4*u**2 + 4*u - 4. Let g(w) = w**3 - 8*w**2 + 5*w + 17. Let d be g(7). Let q(o) = d*m(o) + 2*x(o). Factor q(i).
(i - 2)**2
Let w(m) be the second derivative of -4*m**2 + 5*m**5 - 4/15*m**6 - 16/21*m**7 + 2/3*m**3 + 22/3*m**4 + 0 - 47*m. Solve w(c) = 0 for c.
-1, -1/2, 1/4, 2
Let v(y) be the third derivative of -y**6/360 + y**5/30 + y**4/8 - 7*y**3/9 - y**2 + 23*y. Suppose v(r) = 0. Calculate r.
-2, 1, 7
Suppose 0 = -4*u - 2*y - 119 - 613, -2*u - 2*y = 362. Let d = u - -188. Solve -14*l**2 - 4/7 - 4/7*l**d + 144/7*l**4 - 38/7*l = 0.
-1/2, -1/4, -2/9, 1
Let w(t) be the third derivative of -7*t**2 + 1/60*t**5 + 1/720*t**6 + 0*t + 2/9*t**3 + 1/12*t**4 + 0. Factor w(d).
(d + 2)**3/6
Let y(a) be the third derivative of 5/12*a**4 + 0*a - 5/24*a**6 + 0*a**3 + 0 + 7/12*a**5 - 2/21*a**7 + 13*a**2. Solve y(v) = 0 for v.
-2, -1/4, 0, 1
Let j(d) be the third derivative of d**7/1260 - d**6/36 + 5*d**5/12 - d**4 - 28*d**2. Let u(h) be the second derivative of j(h). Factor u(c).
2*(c - 5)**2
Let y be 170 - (-25)/(-9 - -4). Solve -150*q**2 + 5*q**3 + q - 15*q**4 - 11*q + 5*q**5 + y*q**2 = 0.
-1, 0, 1, 2
Let f(v) be the first derivative of -5*v**3/3 - 205*v**2/2 - 200*v + 147. Factor f(b).
-5*(b + 1)*(b + 40)
Suppose 0 = -2334*w + 2340*w - 12. Let t(m) be the third derivative of 0 - 1/10*m**4 - 2/5*m**3 - 1/100*m**5 + 3*m**w + 0*m. Solve t(h) = 0.
-2
Solve 100/3 + 1/3*k**2 - 52/3*k = 0 for k.
2, 50
Let l(k) be the third derivative of k**5/20 + 63*k**4/4 + 3969*k**3/2 - 98*k**2. Suppose l(f) = 0. Calculate f.
-63
Let z(p) be the first derivative of p**4/4 + 9*p**3 - p**2/2 - 27*p + 147. Factor z(h).
(h - 1)*(h + 1)*(h + 27)
Suppose 265 = 5*w + 14*c - 18*c, 5*w - 2*c = 255. Let v be w/63 + (-16)/36. Factor -v*z**3 + 0*z + 1/9*z**2 + 1/3*z**4 + 0 - 1/9*z**5.
-z**2*(z - 1)**3/9
Determine d, given that 40*d**2 - 3 - 22*d**2 + 23 - 22*d**2 + 79*d = 0.
-1/4, 20
Let b = -56 - -60. Determine i, given that -2*i**3 + 160*i**2 - 80 + 62*i**3 - 8*i**4 - 27*i**b - 240*i = 0.
-2, -2/7, 2
Let m be 30/90*12/2. Solve 1/3*t**m - 1/3 - 1/3*t + 1/3*t**3 = 0.
-1, 1
Let w(u) be the second derivative of u**6/30 - 3*u**5/140 - u**4/12 + u**3/14 - 54*u. What is g in w(g) = 0?
-1, 0, 3/7, 1
Let b(w) be the third derivative of w**7/2940 - w**6/315 + w**5/420 + w**4/14 - 37*w**3/6 - 34*w**2. Let t(a) be the first derivative of b(a). Factor t(c).
2*(c - 3)*(c - 2)*(c + 1)/7
Let g be (-1)/7 - (-29)/7. Let s(l) be the second derivative of 0 + 1/120*l**6 + 0*l**3 - 2*l - 1/80*l**5 - 1/24*l**g + 0*l**2. Factor s(h).
h**2*(h - 2)*(h + 1)/4
Let j = 900 - 900. Let w(g) be the third derivative of 0*g - 1/6*g**4 + 1/15*g**5 - 2/3*g**3 + j + 5*g**2 + 1/30*g**6. Find v such that w(v) = 0.
-1, 1
Factor -867*o - 17*o**2 - 1/9*o**3 - 14739.
-(o + 51)**3/9
Let k(y) be the second derivative of -y**6/540 + 5*y**5/72 - y**4/6 - 37*y**3/6 - 4*y. Let q(n) be the second derivative of k(n). Solve q(l) = 0 for l.
1/2, 12
Let u(q) = 998*q + 998. Let f be u(-1). Determine x so that 0*x**2 - 2/9*x + 2/9*x**3 + f = 0.
-1, 0, 1
Let a be (2/14)/(((-720)/(-84))/15). Factor 0 - a*i**2 - 1/4*i.
-i*(i + 1)/4
Let o(w) be the second derivative of -w**7/210 + w**6/45 - w**5/30 - w**4/6 + 2*w**3/3 - 26*w. Let z(r) be the third derivative of o(r). Solve z(l) = 0 for l.
1/3, 1
Suppose 3*n - 4 = 8. Factor -10 - n*q**2 + 6 - 4*q + 4.
-4*q*(q + 1)
Let t(g) be the second derivative of g + 1/120*g**6 + 0*g**4 - 1/40*g**5 + 1/2*g**3 + 0*g**2 + 0. Let r(o) be the second derivative of t(o). Factor r(p).
3*p*(p - 1)
Let d(u) be the third derivative of u**9/15120 + u**8/5040 - 3*u**5/20 - u**2. Let n(s) be the third derivative of d(s). Factor n(g).
4*g**2*(g + 1)
Suppose 17 + 25 = -2*b. Let z(a) = -33*a**3 - 9*a**2 + 48*a - 69. Let s(y) = -8*y**3 - 2*y**2 + 12*y - 17. Let g(p) = b*s(p) + 5*z(p). Factor g(t).
3*(t - 2)*(t - 1)*(t + 2)
Suppose 0 = o - 4 - 0