et t(x) be the third derivative of -2 + 18*x**2 - 3/5*x**3 - 1/60*x**5 + 0*x + 47/120*x**4. Determine i so that t(i) = 0.
2/5, 9
Let i(j) be the first derivative of j**4/4 + 5*j**3/3 + j**2 - 8*j - 214. Let i(f) = 0. What is f?
-4, -2, 1
Suppose -1 = 3*q - 2*y - 20, y - 7 = -4*q. Let -5*h**q + 2*h**2 + 13*h**2 - 8*h - 2*h = 0. Calculate h.
0, 1, 2
Suppose 102/5*a**2 + 14/5*a**3 + 24/5 + 112/5*a = 0. What is a?
-6, -1, -2/7
Let y(a) = -6*a**4 - 10*a**3 + 6*a**2 + 6*a + 4. Let f = 21 - 28. Let p(h) = -11*h**4 - 19*h**3 + 11*h**2 + 12*h + 7. Let s(c) = f*y(c) + 4*p(c). Factor s(z).
-2*z*(z - 1)*(z + 1)*(z + 3)
Suppose -3 = 2*i - 2*m + 1, 16 = 2*i + 2*m. Let a be (-2)/14 - ((-45)/7)/i. Factor 4/3*b**a + 5/3*b + 1/3*b**3 + 2/3.
(b + 1)**2*(b + 2)/3
Let w(s) be the second derivative of -1/2*s**3 + 0 + 0*s**2 - 2*s + 1/12*s**4. Factor w(n).
n*(n - 3)
Let y(x) = x + 7. Let j(q) = 1. Let m(w) = -3*j(w) + y(w). Let r be m(5). What is b in 16*b**3 - 2 + 4*b**4 + 12*b**2 - 5 - 16*b - r = 0?
-2, -1, 1
Let m(c) be the third derivative of -1/120*c**5 + 0*c**3 + 0*c + 1/240*c**6 + 12*c**2 - 1/48*c**4 + 1/420*c**7 + 0. Factor m(a).
a*(a - 1)*(a + 1)**2/2
Suppose 0 = -218*c + 763 - 109. Factor -5/2 + 1/2*j**c - 9/2*j - 3/2*j**2.
(j - 5)*(j + 1)**2/2
Determine k, given that 13*k**3 - 36*k + 19*k**2 - 187 - k**4 + 403 - 61*k**2 = 0.
-2, 3, 6
Let b = -2041/9 - -227. Let t(r) = -4*r + 16. Let f be t(4). Determine i, given that f*i**2 + 0 + b*i - 2/9*i**3 = 0.
-1, 0, 1
Let k(m) be the third derivative of -m**6/8 - 5*m**5/12 + 95*m**4/24 - 55*m**3/6 - 568*m**2. Determine s, given that k(s) = 0.
-11/3, 1
Let v(d) be the first derivative of -d**3/18 - 2*d**2/3 + 10*d/3 - 526. Let v(w) = 0. Calculate w.
-10, 2
Let a(b) be the first derivative of -1 + 0*b**2 - 1/18*b**3 - 1/24*b**4 + 0*b. Let a(p) = 0. What is p?
-1, 0
Suppose 13*w + 8 = 15*w. Factor 10*d**2 - 5*d - 5*d**3 + 4*d**3 - w*d**3 + 0*d**3.
-5*d*(d - 1)**2
Suppose -38*s + 142 = 33*s. Factor -36/7*i + 2/7*i**s + 162/7.
2*(i - 9)**2/7
Let p(h) be the first derivative of -h**6/16 - 3*h**5/5 - 63*h**4/32 - 11*h**3/4 - 3*h**2/2 - 178. Find z such that p(z) = 0.
-4, -2, -1, 0
Let i be (-2)/(-7) + 52/14. Let q be ((-1)/5)/(-4 + 276/68) + 5. Factor 0*g + 4*g**i + 0 - q*g**2 - 12/5*g**3.
4*g**2*(g - 1)*(5*g + 2)/5
Let y(s) = s**2 - 4*s + 2. Let z be y(4). Let v = -485 + 489. Let 4*i**z + 12*i - v - 2*i**2 + i**2 + 13 = 0. What is i?
-3, -1
Let c be (1/1 + 0)*(-2 + 1). Let w be 2/8 - ((-1)/(-4))/c. Factor 31/2*n**2 + 0*n**4 + 27/4*n**5 - 19/4*n - 18*n**3 + w.
(n - 1)*(n + 2)*(3*n - 1)**3/4
Let r = -55 + 58. Let j(u) = 23*u**2 - 51*u + 16. Let b(q) = -q**2 + q. Let p(o) = r*b(o) + j(o). Factor p(g).
4*(g - 2)*(5*g - 2)
Let f(l) be the second derivative of -5*l**4/12 + 85*l**3/2 - l - 136. Solve f(j) = 0.
0, 51
Let s(v) = 4*v**3 - 9*v**2 - 4*v + 9. Let w(l) = 13*l**3 + 10*l**3 + 3 - 22*l**3 - 3*l**2 - l. Let j(q) = -2*s(q) + 7*w(q). Factor j(y).
-(y - 1)*(y + 1)*(y + 3)
Let h(w) be the first derivative of 18*w**5/85 + 55*w**4/17 + 304*w**3/17 + 672*w**2/17 + 256*w/17 + 748. Find r such that h(r) = 0.
-4, -2/9
Let j be (-13)/(4160/24)*(2 + -6). Let y(c) be the second derivative of j*c**5 + 2*c - 3/25*c**6 - 7/30*c**4 + 1/15*c**3 + 0*c**2 + 0. Factor y(i).
-2*i*(i - 1)*(3*i - 1)**2/5
Suppose 4*f - 201 = 3. Let d be (-5)/(-30) - f/(-18). Solve -3 + 3*c**2 + 0*c**2 - 3*c**d - 3*c + 6*c = 0 for c.
-1, 1
Let p(x) be the first derivative of -x**6/80 + x**4/16 + 2*x**2 - 1. Let v(o) be the second derivative of p(o). Factor v(b).
-3*b*(b - 1)*(b + 1)/2
Let y(z) be the third derivative of -z**5/30 + 5*z**4/3 - 17*z**3 - 647*z**2. Find m such that y(m) = 0.
3, 17
Let j be (-3)/(160/(-55) + 3). Let w = -31 - j. Factor 48*y**3 + 5*y**w - 5*y**4 - 48*y**3.
-5*y**2*(y - 1)*(y + 1)
Suppose -16/7*t**4 + 6/7*t**5 - 104/7*t**2 - 24/7*t - 102/7*t**3 + 0 = 0. What is t?
-2, -1, -1/3, 0, 6
Let u(l) be the first derivative of -l**7/42 + l**6/15 + l**5/20 - l**4/6 + 7*l + 19. Let a(h) be the first derivative of u(h). Solve a(m) = 0 for m.
-1, 0, 1, 2
Let h(c) be the second derivative of c**7/280 + c**6/30 + 14*c**3/3 - 10*c. Let k(y) be the second derivative of h(y). Let k(q) = 0. What is q?
-4, 0
Let a be ((-15)/6 - 0)*(-4)/5. Determine z, given that -z**3 + 8 - 8*z**a + 4*z + 0*z**3 + 0*z**3 - 3*z**3 = 0.
-2, -1, 1
Let k(o) be the second derivative of o**6/6 - o**5/4 - 5*o**4/4 + 25*o**3/6 - 5*o**2 + 151*o + 1. Determine q, given that k(q) = 0.
-2, 1
Let t(l) = -5*l**4 - 73*l**3 - 394*l**2 - 312*l + 804. Let a(r) = -10*r**4 - 143*r**3 - 789*r**2 - 622*r + 1609. Let z(q) = -4*a(q) + 9*t(q). Solve z(i) = 0.
-10, -4, 1
Let b be (-9)/6*(-8)/18. Let j be (33/44)/(81/72). Factor -b*p**3 + j*p**2 + 2/3*p - 2/3.
-2*(p - 1)**2*(p + 1)/3
Let c be 48/4*((-9)/(-6))/3. Suppose 2*a + 3*g = 6, -4*a - c = 4*g - 14. Factor 1/3*h**2 + a + 0*h.
h**2/3
Let q(c) = -4*c**2 + 13*c + 40. Let l(h) = -3*h**2 + 13*h + 38. Let a(p) = 5*l(p) - 4*q(p). Solve a(t) = 0 for t.
-10, -3
Let t(z) be the third derivative of z**8/504 - 4*z**7/315 - 11*z**6/180 - z**5/15 - z**2 - 3. Factor t(w).
2*w**2*(w - 6)*(w + 1)**2/3
Let a be (2 + 4/(-192)*98)/(-3). Let c(g) be the second derivative of a*g**4 + 0 - 1/12*g**2 + 5*g + 1/120*g**5 - 1/36*g**3. Factor c(d).
(d - 1)*(d + 1)**2/6
Let a be (-1)/(-4)*3 + (-3105)/(-900). Determine m, given that -a*m - 6/5 + 6/5*m**2 + 21/5*m**3 = 0.
-1, -2/7, 1
Let t(j) be the first derivative of -j**4/20 - j**3/15 + 8*j**2/5 + 16*j/5 - 170. Let t(b) = 0. Calculate b.
-4, -1, 4
Suppose -o - 4*z = -23, 7*z - 8*z - 7 = -4*o. Let x(u) be the second derivative of 7*u + 1/70*u**5 + 0*u**o + 0*u**4 + 0*u**2 + 0. Solve x(j) = 0 for j.
0
Let y(q) be the first derivative of 0*q**2 + 5 + 9/28*q**4 + 0*q - 12/35*q**5 + 1/7*q**3. Factor y(i).
-3*i**2*(i - 1)*(4*i + 1)/7
Let f(t) be the first derivative of 0*t + 1/3*t**3 - t**2 + 19. Factor f(x).
x*(x - 2)
Let i(z) be the third derivative of 0*z + 1/300*z**5 + 0*z**4 - 1/210*z**7 - 5*z**2 - 1/560*z**8 - 1/600*z**6 + 0*z**3 + 0. Factor i(v).
-v**2*(v + 1)**2*(3*v - 1)/5
Let c be 4/38 - (-3 - (-316)/114). Factor 0 + c*j**2 - 4/3*j.
j*(j - 4)/3
Let i(u) = -u**3 - 2*u**2 - u - 1. Let q(y) = 21*y**3 + 14*y**2 - 11*y + 7. Let z(d) = -22*i(d) - 2*q(d). Factor z(t).
-4*(t - 2)*(t + 1)*(5*t + 1)
Let k(j) be the third derivative of 0*j + 0 - 1/150*j**5 + 5*j**2 - 16/15*j**3 - 2/15*j**4. Factor k(m).
-2*(m + 4)**2/5
Suppose 24/7*v**2 + 12/7 - 4/7*v**4 + 0*v**3 + 32/7*v = 0. What is v?
-1, 3
Let k be -5*21/9 + (-3)/9. Let n be -3*2*14/k. Factor z - n*z**3 + 0 + 3/2*z**2.
-z*(2*z - 1)*(7*z + 2)/2
Suppose 2/9*f**2 - 104/9*f + 1352/9 = 0. Calculate f.
26
Suppose -z + 4*z = 6. Let m be z/15 + 84/720. Solve -1/2*r**4 - 1/2 - m*r**5 - 1/4*r + r**2 + 1/2*r**3 = 0 for r.
-2, -1, 1
Let s = -6/25 - -99/100. Factor 3/4*g**2 + 3/4*g + 0 - 3/4*g**3 - s*g**4.
-3*g*(g - 1)*(g + 1)**2/4
Let c = -120078/5 - -24016. Factor -c*q - 1/2*q**2 + 1/10.
-(q + 1)*(5*q - 1)/10
Let i be (-6)/27 - -11*2/18. Let q be 1*(-3)/(-9)*i. Factor q*d**3 - d - 2/3 + 0*d**2.
(d - 2)*(d + 1)**2/3
Let s(h) be the first derivative of -h**6/225 - h**5/150 + h**4/90 + h**3/45 + 2*h - 10. Let w(r) be the first derivative of s(r). Solve w(u) = 0.
-1, 0, 1
Let l = -2896/231 - -140/11. Let i(o) be the second derivative of -6*o + l*o**3 - 4/7*o**2 - 1/42*o**4 + 0. Factor i(c).
-2*(c - 2)**2/7
Factor 25/4*l**3 + 0 + 256*l - 80*l**2.
l*(5*l - 32)**2/4
Let u(y) be the second derivative of -2*y**6/75 - 4*y**5/25 - y**4/3 - 4*y**3/15 - 2*y - 65. Let u(d) = 0. What is d?
-2, -1, 0
Suppose -2*k = -64 + 54. Let n(j) be the second derivative of 1/5*j**k - 5*j - 1/3*j**3 - 1/21*j**7 + 0 + 2/15*j**6 - 2/3*j**4 + 2*j**2. What is l in n(l) = 0?
-1, 1, 2
Let t = 19/65 + -11/260. Let y(c) be the first derivative of -c + 1/3*c**3 - t*c**2 + 1/8*c**4 - 7. Factor y(k).
(k - 1)*(k + 1)*(k + 2)/2
Let w(c) = -201*c + 30 - 217*c + 402*c + c**3 - 13*c**2. Let r be w(14). Find k, given that r*k + 0 - 8/3*k**3 + 2/3*k**2 = 0.
-3/4, 0, 1
Let u(y) = 11*y + 7*y**2 + 6 + 6*y**2 - 14 - 26*y**2 + 5*y**2. Let r = 0 - -4. Let s(m) = m**2 - m + 1. Let x(z) = r*u(z) + 36*s(z). Factor x(o).
4*(o + 1)**2
Let q(u) be the second derivative of -9*u - 3/16*u**4 + 13/24*u**3 - 2/15*u**6 - 1/2*u**5 + 0 - 1/4*u**2.