) be the third derivative of -n**9/14 - n**8/40 + n**7/63 + n**6/135 + n**3 - 3*n**2. Let m(i) be the first derivative of f(i). What is t in m(t) = 0?
-2/9, 0, 1/4
Factor 8 - 81*i**2 - 69*i**2 + 12*i + 154*i**2.
4*(i + 1)*(i + 2)
Let -40*f**3 - 12 - 18*f**2 + 36*f**5 + 46*f - 99*f**5 + 24*f**5 + 33*f**5 - 2*f**2 + 32*f**4 = 0. What is f?
-1, 1/3, 1, 2, 3
Factor -56169/5 - 474/5*k - 1/5*k**2.
-(k + 237)**2/5
Let g(w) be the third derivative of -w**7/504 + w**6/120 - w**5/120 - w**4/72 - 37*w**3/6 - 24*w**2. Let i(c) be the first derivative of g(c). Factor i(u).
-(u - 1)**2*(5*u + 1)/3
Let m(w) be the first derivative of 1/18*w**4 - 2/9*w**2 - 2/15*w**5 + 2/9*w**3 + 0*w + 4 + 1/27*w**6. Determine o, given that m(o) = 0.
-1, 0, 1, 2
Let t(o) be the second derivative of -o**4/24 + 100*o**3/3 - 10000*o**2 + 478*o. Factor t(f).
-(f - 200)**2/2
Factor 132*p**2 - 2*p**5 + 8*p**4 - 294 + 2*p**4 + 60*p**3 + 70*p - 307 - 32*p**2 + 619.
-2*(p - 9)*(p + 1)**4
Find w, given that -2/3*w**4 - 8/3*w + 10/9*w**3 + 0 + 32/9*w**2 = 0.
-2, 0, 2/3, 3
Let o(i) be the third derivative of -7/96*i**4 - 1/480*i**6 + 0*i + 1/48*i**5 + 2*i**2 - 1 + 1/8*i**3. Let o(w) = 0. Calculate w.
1, 3
Let g(l) be the first derivative of l**4/18 + 142*l**3/27 + 1295*l**2/9 + 2450*l/9 + 343. What is w in g(w) = 0?
-35, -1
Let b(w) = 2*w**4 - 2*w**3 + 4*w**2 + 4*w - 4. Suppose 101 - 106 = 5*g. Let c(m) = -m**3 + m**2 + m - 1. Let v(j) = g*b(j) + 4*c(j). Factor v(d).
-2*d**3*(d + 1)
Factor -54/7*n - 729/7 - 1/7*n**2.
-(n + 27)**2/7
Let v(i) = -120*i**4 + 10*i**3 - 10*i**2 - 10*i. Let c be -8 - -1 - (2 + -3). Let u(m) = -11*m**4 + m**3 - m**2 - m. Let l(k) = c*v(k) + 65*u(k). Factor l(w).
5*w*(w - 1)*(w + 1)**2
Let r(u) = u**2 + 3*u + 1. Let a be r(1). Factor 6*i + 6*i + a*i**2 + 18*i - 10*i + 15.
5*(i + 1)*(i + 3)
Let k be (-1)/(8 - (-369)/(-45)). Let m(u) be the third derivative of 0*u + 0 - 4*u**2 + 1/8*u**4 + 3/4*u**3 + 1/120*u**k. Find o such that m(o) = 0.
-3
Let u be (10/18)/((-1575)/108 + 15). Determine r, given that 1/3*r**2 - 4/3*r - 1/3*r**4 + u*r**3 + 0 = 0.
-1, 0, 1, 4
Let c(z) be the second derivative of -z**6/168 + 3*z**5/20 - 2*z**4/7 - 4*z**3/3 - 34*z. Let l(t) be the second derivative of c(t). Let l(g) = 0. Calculate g.
2/5, 8
Suppose 2*z + 136 = 148. Let b(o) = 17*o - 102. Let l be b(z). Solve l - 2/9*v**3 + 0*v - 2/9*v**2 = 0 for v.
-1, 0
Let q(g) = -4*g**2 - 2556*g + 2552. Let s(d) = -3*d**2 - 1703*d + 1701. Let b(f) = 5*q(f) - 8*s(f). What is i in b(i) = 0?
-212, 1
Let l(f) = 3*f**2 + 20*f - 3. Let d be l(-7). Let k(t) be the third derivative of -6*t**2 - 1/60*t**5 + 0*t**3 - 1/24*t**d + 0 + 0*t. Factor k(z).
-z*(z + 1)
Let k(p) be the third derivative of p**7/147 + p**6/140 - p**5/42 - p**4/28 + 197*p**2. Determine s, given that k(s) = 0.
-1, -3/5, 0, 1
Let t(p) be the first derivative of 9*p**5/5 - 5*p**4/2 + 2*p**3 + p**2 - 2*p + 37. Let x(b) = 2*b**4 - b**4 - 2*b**4. Let l(i) = -t(i) - 5*x(i). Factor l(s).
-2*(s - 1)**3*(2*s + 1)
Find a such that 30*a**2 - 41*a**3 + 27*a**2 + 409154 - 17*a**4 + a**5 - 409154 = 0.
-3, 0, 1, 19
Suppose w - 8 = 5*z + 2, 3*w = -4*z - 8. Suppose -i - 2*q = w, -3*q - q = -i. Factor 0*u + i - 16/5*u**4 + 4/5*u**2 - 2/5*u**3 - 2*u**5.
-2*u**2*(u + 1)**2*(5*u - 2)/5
Suppose 0 = 2*q - 16 - 2. Suppose 5*s**3 - 20*s**3 - 3*s**5 + 6*s**2 + q + 12*s**4 - 9 = 0. Calculate s.
0, 1, 2
Find i, given that -7*i + 1081*i**2 - 1077*i**2 - 32 - i = 0.
-2, 4
Let q be (-18)/(-63)*((-7)/2)/((-25)/10). Factor q*y + 2/5*y**2 + 0.
2*y*(y + 1)/5
Let v be (-3)/4 + (-2145)/660 - -7. Determine q, given that 3/8*q**2 - 3/8*q**v + 0*q + 0 = 0.
0, 1
Let s(g) = g**2 + 3*g + 5. Let p be s(-3). Let n(j) be the second derivative of 4*j**4 + 2*j**3 + 21/20*j**p + 0 + 4*j + 0*j**2. Solve n(o) = 0 for o.
-2, -2/7, 0
Let m(v) be the second derivative of 0*v**3 + 0 - 1/9*v**6 + 0*v**2 + 15*v + 8/15*v**5 - 2/9*v**4 - 25/63*v**7. Find s, given that m(s) = 0.
-1, 0, 2/5
Suppose 256*t + 39 = 269*t. Let a(c) be the first derivative of -6 - 18/5*c + 6/5*c**2 - 2/15*c**t. Factor a(d).
-2*(d - 3)**2/5
Suppose -4*a - 1 + 9 = 0. Factor -49*s**2 + 95*s**a - 8*s + 4*s**3 - 42*s**2.
4*s*(s - 1)*(s + 2)
Factor 3/4*l**2 - 5/4*l**3 + 0 + 1/4*l**4 + 0*l + 1/4*l**5.
l**2*(l - 1)**2*(l + 3)/4
Let s(d) be the second derivative of -15*d**7/98 + 44*d**6/35 - 459*d**5/140 + 17*d**4/7 + 6*d**3/7 + 348*d. Find p, given that s(p) = 0.
-2/15, 0, 1, 2, 3
Let c(f) be the second derivative of f**6/75 + 2*f**5/25 + f**4/15 - 4*f**3/15 - 3*f**2/5 + f + 5. Let c(s) = 0. Calculate s.
-3, -1, 1
Let q(z) be the third derivative of -z**7/210 - z**4/24 + z**3/6 + 2*z**2 - 21*z. Let c(i) = i**4 - 12*i**3 + 5*i - 5. Let k(o) = -c(o) - 5*q(o). Factor k(l).
4*l**3*(l + 3)
Suppose 36*c**2 + 1284*c**3 + 34*c**4 - 1152*c**3 + 77*c**4 - c**5 + 16*c**5 = 0. What is c?
-6, -1, -2/5, 0
Let s be (8/16)/(3/15). Let w = 23 + -19. Let -5/2*t**2 - 5/4*t**w - 1/4*t**5 - 5/4*t - s*t**3 - 1/4 = 0. What is t?
-1
Factor -17*f**3 + 2*f**5 - f**5 - 2*f**4 + 18*f**3.
f**3*(f - 1)**2
Let r(c) be the first derivative of c**3/2 + 9*c**2/4 - 6*c - 186. Suppose r(j) = 0. Calculate j.
-4, 1
Let r be ((-8)/3)/(5*9/(-270)*4). Let 2/3*n**2 - r - 2/3*n = 0. What is n?
-2, 3
Let b(d) = d**4 + 24*d**3 + 191*d**2 + 511*d. Let s(m) = -m**2 - m. Let c(j) = 3*b(j) - 3*s(j). Find a such that c(a) = 0.
-8, 0
Let u be (1 - 4) + 9 + -2. Suppose -2*c - 8 = -4*n, -1 + 0 = -3*n + u*c. Suppose -6*k + 4*k - 4*k + 9*k**2 - 3*k**n = 0. Calculate k.
0, 1, 2
Let a(q) be the first derivative of -3*q**5/10 - 9*q**4/4 + 3*q**3/8 + 51*q**2/16 - 9*q/4 - 414. Suppose a(g) = 0. Calculate g.
-6, -1, 1/2
Let b = -3148 - -9454/3. Factor -b*l + 1/3*l**2 - 11/3.
(l - 11)*(l + 1)/3
Let s(v) be the second derivative of 13*v + 0*v**2 + 4/15*v**6 + 0 + 3/5*v**5 - 2/21*v**7 - 8/3*v**3 - 4/3*v**4. Solve s(i) = 0 for i.
-1, 0, 2
Let t(z) be the second derivative of -z**5/120 + z**4/36 + z**3/36 - z**2/6 + 16*z. Let t(n) = 0. What is n?
-1, 1, 2
Let h(m) be the second derivative of m**7/21 + 2*m**6/5 - m**5/5 - 2*m**4 + m**3/3 + 6*m**2 + 3*m - 90. Suppose h(l) = 0. Calculate l.
-6, -1, 1
Let f(z) be the second derivative of -z**5/4 + 5*z**4/6 + 5*z**3/6 - 5*z**2 + 369*z. Determine o, given that f(o) = 0.
-1, 1, 2
Let k(v) = 76*v**3 + 100*v**2 + 32*v. Let c(s) = -7*s**3 - 4*s**2 - 6*s**2 + 3*s - 6*s + s**2. Let x(r) = 32*c(r) + 3*k(r). Factor x(u).
4*u**2*(u + 3)
Suppose -4*f + 22 = 4*k - 2*k, 5*f + 5 = 4*k. Determine v so that 5*v**3 - 8*v**2 - v**3 + 0*v**f = 0.
0, 2
What is r in 1/4*r**2 + 21/4*r + 0 = 0?
-21, 0
Factor -12*c - 2*c**2 + 143 - 67 - 44.
-2*(c - 2)*(c + 8)
Let w(x) be the second derivative of x**6/75 + 17*x**5/100 + 7*x**4/20 - x**3/30 - 7*x**2/10 + 117*x. Factor w(c).
(c + 1)**2*(c + 7)*(2*c - 1)/5
Let w(f) be the third derivative of f**10/756000 - f**9/151200 + 23*f**5/60 - 31*f**2. Let v(g) be the third derivative of w(g). Determine k so that v(k) = 0.
0, 2
Let t be -4 + -2*28/(-8). Factor 6 - 3*w**2 - 7*w + t*w + 0*w + w.
-3*(w - 1)*(w + 2)
Factor 38 + 126*s**2 - 24 - 3*s**3 + 261*s + 118.
-3*(s - 44)*(s + 1)**2
Suppose 35319*i = 35324*i. What is u in -3/2*u**2 + 3/4*u**3 + 3/2*u**4 - 3/4*u**5 + i*u + 0 = 0?
-1, 0, 1, 2
Suppose 14*a - 6 = 11*a. Suppose 5*c + 21 = 3*x, 0 = 3*x + 2*x - a*c - 16. Determine r so that -2/3*r**x + 0 + 4/3*r**3 - 4/3*r + 2/3*r**4 = 0.
-2, -1, 0, 1
Let o = -3967/3 - -1323. Determine b, given that -o*b**2 + 0 + 0*b + 1/6*b**4 - 1/2*b**5 + 2*b**3 = 0.
-2, 0, 1/3, 2
Let v(u) = 8*u**2 + 3*u - 4. Let o(c) = c**2 + c - 1. Let i(g) = 14*o(g) - 2*v(g). Factor i(d).
-2*(d - 3)*(d - 1)
Let s(h) be the first derivative of -3 - h**2 + 0*h + 1/3*h**3. Let s(d) = 0. What is d?
0, 2
Let m be (-10)/(-45) - (1 - (-86)/(-18)). Find k, given that -m*k**2 + 5*k - 10 - 10*k**3 - 10*k**4 + 10*k**2 + 14*k**2 + 5*k**5 = 0.
-1, 1, 2
Let p(w) be the first derivative of 2*w**4 + 4/15*w**5 - 17 + 16/3*w**3 + 4*w + 20/3*w**2. Factor p(u).
4*(u + 1)**3*(u + 3)/3
Let f(a) be the second derivative of a**4/42 - 62*a**3/21 + 961*a**2/7 + 5*a - 8. Solve f(y) = 0.
31
Suppose -9*w = 60 - 78. Factor 0*u + 1/6*u**w - 1/6.
(u - 1)*(u + 1)/6
Let j(z) = z**2 + 17*z + 33. Let t(g) = -16*g - 34. Let m(h) = -4*j(h) - 6*t(h). What is o in m(o) = 0?
-2, 9
Suppose -y + 4*x - 8*x -