rst derivative of -b**7/420 + b**6/180 - 3*b**3 - 16. Let s(q) be the third derivative of m(q). Factor s(d).
-2*d**2*(d - 1)
Let n(w) be the third derivative of -w**5/180 - w**4/24 + w**3 - 233*w**2 - w. Let n(b) = 0. What is b?
-6, 3
Let r(b) be the first derivative of 4*b**6/15 - 11*b**5/5 + 7*b**4 - 32*b**3/3 + 8*b**2 + 9*b + 2. Let h(n) be the first derivative of r(n). Factor h(o).
4*(o - 2)**2*(o - 1)*(2*o - 1)
Let a = -1558 + 1560. Factor 18/7*b**a + 27/7*b + 0 + 3/7*b**3.
3*b*(b + 3)**2/7
Let v(x) be the third derivative of 3*x**7/175 + 4*x**6/25 + 79*x**5/150 + 13*x**4/15 + 4*x**3/5 - 4*x**2 - 4*x. Determine o so that v(o) = 0.
-3, -1, -2/3
Let x(q) = 2*q**4 - 4*q**3 + 4*q**4 - 5 + 3*q**2 - 3*q**4 + 4*q + 3. Let d(u) = u**4 + 1. Let r(i) = -2*d(i) + x(i). Factor r(w).
(w - 2)**2*(w - 1)*(w + 1)
Let i(w) be the third derivative of -w**6/900 - w**5/300 + w**4/30 + 11*w**3/3 + 27*w**2. Let f(r) be the first derivative of i(r). What is t in f(t) = 0?
-2, 1
Let a(b) be the first derivative of b**7/14 - b**6/5 + 3*b**5/20 - 32*b - 12. Let j(w) be the first derivative of a(w). Factor j(m).
3*m**3*(m - 1)**2
Let i = -500 - -24001/48. Let b(y) be the second derivative of 2*y + i*y**4 + 0*y**2 + 0 + 0*y**3. Solve b(n) = 0 for n.
0
Let c(o) be the second derivative of 1/10*o**6 + 7/2*o**3 + 23*o + 3/4*o**5 + 9/4*o**4 + 3*o**2 + 0. Determine n so that c(n) = 0.
-2, -1
Let i = 1019/3 + -330. Let o = 31/3 - i. Suppose -1/3*y**2 - o*y + 0 = 0. Calculate y.
-2, 0
Let u(i) = 8*i**2 - 28*i - 30. Let w(n) = n**2 - n - 1. Let g(p) = u(p) - 6*w(p). Suppose g(o) = 0. Calculate o.
-1, 12
Let q = 9/5 + -7/5. Find u, given that 0*u + q*u**3 + 0 - 2/5*u**5 - 4/5*u**2 + 4/5*u**4 = 0.
-1, 0, 1, 2
Suppose 5*u - 19 - 6 = 0. Factor 40*g**4 - g**2 - 2 - 42*g**4 + u*g**2.
-2*(g - 1)**2*(g + 1)**2
Let b(n) = -4*n**2 + 15*n + 7. Let a(i) = -2*i**2 + 14*i + 8. Let k(u) = -6*a(u) + 4*b(u). Factor k(p).
-4*(p + 1)*(p + 5)
Factor 33*a + 3/4*a**2 + 363.
3*(a + 22)**2/4
Let z be ((-125)/(-1875))/((-2)/(-20)). What is x in 0 + 4/3*x - z*x**2 = 0?
0, 2
What is u in 38*u**3 - 20*u**2 - 32*u - 596*u**4 + 588*u**4 + 28 + 2*u**3 - 2*u**5 - 6*u = 0?
-7, -1, 1, 2
Let q be -64 - -3*(-1)/3. Let l be 26/q - 24/(-10). Factor 2/3*s - 2/9 - 4/9*s**l.
-2*(s - 1)*(2*s - 1)/9
Solve 27/5 - 1/5*f**2 + 6/5*f = 0 for f.
-3, 9
Let a(h) be the third derivative of -1/210*h**5 + 0 - 21*h**2 + 0*h**4 + 0*h**7 + 1/2352*h**8 + 0*h**3 + 0*h - 1/280*h**6. Factor a(f).
f**2*(f - 2)*(f + 1)**2/7
Let x(w) = -2*w + 30. Let k be x(14). Factor 3*n - 2*n**k + 3*n - 10*n + 16.
-2*(n - 2)*(n + 4)
Factor -31*b**2 - 12*b - 1 + 4*b**3 + 50*b**2 + 1 - 11*b**2.
4*b*(b - 1)*(b + 3)
Let i(g) be the third derivative of -g**9/15120 + g**7/420 + g**6/90 + g**5/4 - 6*g**2. Let f(s) be the third derivative of i(s). Factor f(t).
-4*(t - 2)*(t + 1)**2
Suppose 4*a - 112 = 80. Let c be 32/70 + a/120. Suppose c*z**3 - 6/7*z + 3/7 + 0*z**2 - 3/7*z**4 = 0. What is z?
-1, 1
Let m(o) be the second derivative of -o**7/56 + o**6/10 - 9*o**5/40 + o**4/4 - o**3/8 + 118*o. Suppose m(l) = 0. Calculate l.
0, 1
Let d(w) be the third derivative of -w**6/720 - 29*w**5/360 - 7*w**4/36 + w**2 - 294*w. Find p such that d(p) = 0.
-28, -1, 0
Let 0 + 0*a**2 + 1/2*a**3 - 1/2*a = 0. Calculate a.
-1, 0, 1
Let v = -247 + 112. Let u = v + 949/7. Let 4/7*s**2 + u*s**3 - 4/7 - 4/7*s = 0. What is s?
-1, 1
Solve 11/4*q**2 - 11/4*q**4 - 1/4*q**3 + 3/2*q**5 - 5/4*q + 0 = 0.
-1, 0, 5/6, 1
Let p(w) be the first derivative of -w**4/14 - 26*w**3/21 - 55*w**2/7 - 150*w/7 + 630. Solve p(s) = 0 for s.
-5, -3
Factor -45/2 + 1/2*z**3 + 39/2*z - 11/2*z**2.
(z - 5)*(z - 3)**2/2
Let m(u) be the third derivative of -u**8/47040 + u**7/5880 - u**5/210 - u**4/6 - 32*u**2. Let l(o) be the second derivative of m(o). Factor l(z).
-(z - 2)**2*(z + 1)/7
Suppose 7*m = 4*m. Suppose p - 8 = -3*b, 0 = -m*b + 2*b + 2*p. Find s such that -3*s**2 + 4*s**2 - 3*s + 3*s**3 + 3*s**b - 4*s**2 = 0.
-1, 0, 1
Let t be -2*((-591)/985 - (-3)/(-10)). Find h, given that 1/5*h**2 + 2*h + t = 0.
-9, -1
Let t(b) be the third derivative of b**6/120 - 2*b**5/15 + 5*b**4/8 + 489*b**2. Find s, given that t(s) = 0.
0, 3, 5
Let p(t) be the third derivative of -t**7/105 - t**6/15 + 4*t**4/3 + 16*t**3/3 - 21*t**2. Solve p(r) = 0 for r.
-2, 2
Let t be (-4)/14*(-5 - (-14)/(-7)). Factor 4/5*u**3 + 2/15*u**4 + 8/5*u + 26/15*u**t + 8/15.
2*(u + 1)**2*(u + 2)**2/15
Let m(w) be the second derivative of -5*w**6/4 - 39*w**5/8 - 3*w**4/4 + 16*w**3 + 24*w**2 - 175*w. What is b in m(b) = 0?
-2, -4/5, 1
Suppose 0*l - 30 = 5*l. Let i = l - -9. Let -2*q**5 + 4*q**3 + 9 + 16*q**2 + 14*q - 8 + i - 4*q**4 = 0. Calculate q.
-1, 2
Suppose 5*c + d = 777, 4*d - 47 = -2*c + 253. Factor 287 + 54*p - 200 + 3*p**2 + c.
3*(p + 9)**2
Let m be (165/110)/((-85)/(-88) + -1). Let r be (-12)/3 + m/(-10). Suppose -4/5 + r*h + 2/5*h**2 = 0. What is h?
-2, 1
Let c(h) = -h**2 + 9*h - 4. Let q be c(8). Factor -11*u + q*u**3 - 5*u**2 - u + 8 + 5*u**2.
4*(u - 1)**2*(u + 2)
Suppose -3*o + 5*w - 10*w + 35 = 0, 4*o - 5*w + 35 = 0. Find x such that -3/2*x**3 + o - 3/2*x**2 - 1/2*x**4 - 1/2*x = 0.
-1, 0
Let m(r) be the second derivative of -r**5/30 + 11*r**4/60 - 2*r**3/5 + 21*r**2 - 3*r. Let c(j) be the first derivative of m(j). Factor c(n).
-2*(n - 1)*(5*n - 6)/5
Let h(u) be the third derivative of u**7/70 + u**6/10 + u**5/20 - 3*u**4/4 + 91*u**2. Factor h(x).
3*x*(x - 1)*(x + 2)*(x + 3)
Let s(a) be the first derivative of -a**4/8 - a**3/2 - 3*a**2/4 - 27*a + 2. Let f(n) be the first derivative of s(n). Factor f(p).
-3*(p + 1)**2/2
Suppose -3*f + 17 = 2*m - 7*m, -2*m - 11 = 3*f. Let p be ((-3)/12)/(2 + m). Factor -1/8*x**4 + p*x**5 - 1/4*x - 3/8*x**3 + 0 + 5/8*x**2.
x*(x - 1)**3*(x + 2)/8
Let u(c) = 20*c**2 - 67*c - 44. Let p(s) = 7*s**2 - 23*s - 14. Let i(n) = -17*p(n) + 6*u(n). Factor i(j).
(j - 13)*(j + 2)
Suppose 2*l + 3*l = 0. Solve 4*p**3 - 2*p + 2 + l*p**3 + 0 - 2*p**3 - 2*p**2 = 0.
-1, 1
Let g(f) be the third derivative of 1/80*f**5 + 0*f - 1/32*f**4 + 0 - 1/4*f**3 + 18*f**2. Solve g(k) = 0.
-1, 2
Suppose 30 = 57*r - 42*r. Let v(u) be the first derivative of 1/2*u**4 + 3 + 2*u - 2/3*u**3 - u**r. Factor v(l).
2*(l - 1)**2*(l + 1)
Factor 0 + 2*t + 1/3*t**2.
t*(t + 6)/3
Let x(b) = -12*b**3 - 50*b**2 - 36*b + 20. Let n(p) = -p**3 - 2*p**2 - p + 1. Let v(i) = 4*n(i) + x(i). Suppose v(y) = 0. What is y?
-2, 3/8
Let m = 86 - 121. Let v = m - -35. Factor -2/3 + v*c**2 - 1/3*c**3 + c.
-(c - 1)**2*(c + 2)/3
Factor 326*m + 19 + 38*m**2 + 73*m - 71 + 91*m.
2*(m + 13)*(19*m - 2)
Let w be (0 - -1)*152/57. Let 2/9 - 16/9*t**3 - 4/3*t + w*t**2 = 0. Calculate t.
1/2
Let f(a) = -a**2 - 3*a - 10. Let j be f(-4). Let p = 18 + j. Find i such that 0*i - 2/11*i**p + 4/11*i**2 + 2/11*i**3 + 0 = 0.
-1, 0, 2
Let t(c) be the second derivative of -c**6/10 + 9*c**5/20 - 3*c**4/4 + c**3/2 + 218*c. Factor t(p).
-3*p*(p - 1)**3
Suppose 9*v - 14*v + 200 = 0. Let y be (-24)/110 - (-16)/v. Factor 0*j + 0 - y*j**3 + 2/11*j**2.
-2*j**2*(j - 1)/11
Factor 0*p + 0 + 2/13*p**4 + 8/13*p**3 + 6/13*p**2.
2*p**2*(p + 1)*(p + 3)/13
What is f in 0 - 5/12*f + 1/12*f**3 - 1/3*f**2 = 0?
-1, 0, 5
Suppose w - 102 = -99. Let q(j) = -3*j + 1. Let f be q(-1). Factor 0*z - 14*z**f + 20*z**4 + 2*z - 7*z**4 + w*z**2.
-z*(z - 2)*(z + 1)**2
Let a(s) = 8*s**2 - 28*s + 72. Let b(i) = -7*i**2 + 29*i - 72. Let p(m) = -4*a(m) - 5*b(m). Suppose p(q) = 0. What is q?
3, 8
Suppose 15*s + 3 - 3 = 0. Let v(a) be the first derivative of 0*a + 1/12*a**3 + 3/16*a**4 + s*a**2 - 2 + 1/10*a**5. Factor v(g).
g**2*(g + 1)*(2*g + 1)/4
Let s be -2 + 5 + (-11 - -3). Let h = 0 - s. Suppose -1/4*j**h - 3/4*j**4 + 1/4 + 1/2*j**2 - 1/2*j**3 + 3/4*j = 0. What is j?
-1, 1
Let b(m) be the second derivative of m**4/4 + 3*m**3/2 - 60*m**2 - 76*m. What is c in b(c) = 0?
-8, 5
Find s such that 1099*s**4 - 8*s**3 + 72 - 1101*s**4 + 10*s**2 + 78*s - 6*s = 0.
-3, -2, 3
Let k(b) be the first derivative of -b**6/3 + 2*b**4 + 4*b**3/3 - 3*b**2 - 4*b - 67. Suppose k(x) = 0. What is x?
-1, 1, 2
Let l(t) be the third derivative of -t**8/1344 - 13*t**7/840 - t**6/48 + 11*t**5/30 + 5*t**2. Let h(a) be the third derivative of l(a). Solve h(j) = 0.
-5, -1/5
Let k(z) be the third derivative of -z**6/600 + 13*z**5/300 - 2*z**4/15 - 32*z**3/5 - 39