**4 - 2. Factor t(s).
2*s*(s + 1)**3
Let f(r) be the first derivative of r**9/1008 + r**8/140 + 3*r**7/140 + r**6/30 + r**5/40 + 5*r**3/3 - 7. Let d(k) be the third derivative of f(k). Factor d(u).
3*u*(u + 1)**4
Suppose -2*o - 4*d = -8, o - 6 = -o - 3*d. Let j(h) be the third derivative of o*h - h**2 + 1/36*h**4 - 1/180*h**6 + 1/90*h**5 - 1/9*h**3 + 0. Factor j(z).
-2*(z - 1)**2*(z + 1)/3
Let b(j) be the third derivative of j**6/900 + j**5/50 + 3*j**4/20 + 3*j**3/5 + 3*j**2. Solve b(w) = 0.
-3
Let k(l) be the second derivative of -l**5/10 + 2*l**4/3 - 5*l**3/3 + 2*l**2 + 27*l. Find y, given that k(y) = 0.
1, 2
Factor 3/7*x**5 + 0*x**3 + 0 - 6/7*x**4 - 3/7*x + 6/7*x**2.
3*x*(x - 1)**3*(x + 1)/7
What is y in -1/6*y**5 - y**4 - 1/3 - 7/3*y**3 - 8/3*y**2 - 3/2*y = 0?
-2, -1
Let p = 19 + -113/6. Let j(s) be the third derivative of 0*s**3 + p*s**4 + 2*s**2 + 1/105*s**7 + 0*s**6 + 0 + 0*s - 1/10*s**5. What is k in j(k) = 0?
-2, 0, 1
Let g(t) = -t**3 + 4*t**2 + 8*t - 7. Let y be g(5). Suppose -h + 5*k + y = 2*k, 0 = 5*h + 2*k - 6. Factor -11/4*c + 1/2 - c**3 + 13/4*c**h.
-(c - 2)*(c - 1)*(4*c - 1)/4
Let p(u) be the third derivative of 1/168*u**8 - 1/3*u**3 - 1/105*u**7 + 0 + 1/12*u**4 + 2*u**2 + 1/15*u**5 - 1/30*u**6 + 0*u. Find y such that p(y) = 0.
-1, 1
Let b be 0 + 20/35 + (-6)/(-210). Solve 27/5 + b*g**2 + 18/5*g = 0.
-3
Suppose -4*n - 7 = 4*o - 3, -n - 9 = -3*o. Let d(r) be the third derivative of 1/120*r**5 + 0*r**4 + 0 - 1/240*r**6 + 0*r**3 + r**o + 0*r. Solve d(y) = 0 for y.
0, 1
Let p(i) be the second derivative of 7*i**5/80 + i**4/3 + i**3/6 + 4*i. What is f in p(f) = 0?
-2, -2/7, 0
Let r = 1817/15 - 121. Let q(i) be the first derivative of -r*i**3 + 1/10*i**2 + 0*i + 1/20*i**4 - 1. Determine z so that q(z) = 0.
0, 1
Let l(u) be the second derivative of 1/30*u**4 - 2/15*u**3 + 0 - 2*u + 0*u**2. Factor l(z).
2*z*(z - 2)/5
Let q(h) be the second derivative of -h**5/170 - 2*h**4/51 - 5*h**3/51 - 2*h**2/17 - 65*h. Determine f, given that q(f) = 0.
-2, -1
Suppose 0 = -2*h + 3*j - 9, 3*h - 3 = -2*j + 16. Find n such that h*n - 9*n**2 - 6 + 2*n + 10*n = 0.
2/3, 1
Let x(g) be the second derivative of -g**7/21 + g**6/15 + g**5/10 - g**4/6 - 14*g. Factor x(a).
-2*a**2*(a - 1)**2*(a + 1)
Let i(p) be the second derivative of p**7/105 + 4*p**6/75 + 3*p**5/25 + 2*p**4/15 + p**3/15 - 7*p. Suppose i(k) = 0. Calculate k.
-1, 0
Let z(q) be the second derivative of -3*q**5/10 + 33*q**4/4 - 72*q**3 + 96*q**2 + 15*q - 1. Factor z(s).
-3*(s - 8)**2*(2*s - 1)
Let c(d) = -d**2 - 8*d - 8. Let o be c(-8). Let t(h) = h + 8. Let g be t(o). Solve g*r + 0 + 2/7*r**2 = 0.
0
Let t(n) be the first derivative of 1/4*n**4 + 2*n**2 - 4/3*n**3 + 6 + 0*n. Suppose t(s) = 0. Calculate s.
0, 2
Let a be 14*4 + -4 + 0. Factor 169*z - 140*z**2 - 32 - 18*z**4 - 132*z**3 + 7*z - a*z**2 - 2*z**2.
-2*(z + 4)**2*(3*z - 1)**2
Factor 3*m + m + 0*m**3 - 4*m**3.
-4*m*(m - 1)*(m + 1)
Let p(v) be the third derivative of -v**7/70 + v**6/10 - 3*v**5/20 - v**4/2 + 2*v**3 - 3*v**2. What is y in p(y) = 0?
-1, 1, 2
Suppose 0*r + 5*y = -5*r + 115, 2*r - 3*y = 31. Factor -16 + r + 3*h**2 - 4*h - 2*h**2.
(h - 2)**2
Let g(n) be the first derivative of 5*n**4/4 - 20*n**3/3 + 25*n**2/2 - 10*n + 11. Factor g(v).
5*(v - 2)*(v - 1)**2
Let r(q) = 4*q**2 + 8*q + 7. Let l(n) = -23*n**2 - 48*n - 42. Let k(g) = -6*l(g) - 34*r(g). Factor k(h).
2*(h + 1)*(h + 7)
Factor 0 - 2/9*t**2 + 2/3*t.
-2*t*(t - 3)/9
Factor 1/2*u**3 - 1/4*u**5 + 0*u**2 + 0 - 1/4*u**4 + 0*u.
-u**3*(u - 1)*(u + 2)/4
Suppose 0 = 4*b - 2*b - 22. Let x(q) = 17*q**2 + 23*q + 17. Let z(h) = -6*h**2 - 8*h - 6. Let u be -6*4/6*-1. Let c(g) = b*z(g) + u*x(g). What is d in c(d) = 0?
-1
Factor 3 + 35*v**2 + 44*v + 157*v**2 + 5*v - v.
3*(8*v + 1)**2
What is t in 7 + 2 - 5 + 4*t**2 - 8*t = 0?
1
Let y(l) = -2*l**3 + 18*l**2 + 18*l + 20. Let x be y(10). Solve 8/5*v**2 + 0*v + 16/5*v**3 + 2*v**4 + x + 2/5*v**5 = 0 for v.
-2, -1, 0
Let o = 47/26 + -4/13. Factor 15/2*l**4 + 3/2 + 15*l**2 + 15*l**3 + o*l**5 + 15/2*l.
3*(l + 1)**5/2
Let j(f) = f**2 + 2*f + 1. Let c be j(-3). Let p(y) be the third derivative of -1/180*y**5 + 0 - y**2 + 0*y - 2/9*y**3 + 1/18*y**c. Factor p(k).
-(k - 2)**2/3
Let p(h) = 31*h - 19. Let o be p(-11). Let z = o + 1094/3. Factor -10/3*g + 4/3 - z*g**2.
-2*(g + 1)*(7*g - 2)/3
Let n be 4/(-6)*3/(-1). Solve -n*f**3 + 8*f - 5*f - f = 0.
-1, 0, 1
Let k(h) = h - 2. Let b be k(-2). Let l be 9 + (-2 - (b - -2)). Suppose -6 + l + d**2 - 5 - d = 0. What is d?
-1, 2
Let d(b) = -b + 1. Let l be d(-4). Factor -5*q - q**3 - 5*q - 3*q**4 - q**l + 3*q**2 + 12*q.
-q*(q - 1)*(q + 1)**2*(q + 2)
Let o(n) = n**2 + 5*n - 2. Let c be o(-6). Suppose c*b = -5*d - 0*d, 35 = 5*d - 3*b. Factor 2/5*f**d + 6/5*f**3 + 4/5*f**2 + 0*f + 0.
2*f**2*(f + 1)*(f + 2)/5
Let d(n) be the first derivative of -6*n**5/5 - n**4/2 + 10*n**3/3 + n**2 - 4*n + 25. Suppose d(r) = 0. Calculate r.
-1, 2/3, 1
What is j in 1/2*j**3 + 1/2*j**2 + 0*j + 0 = 0?
-1, 0
Let r = -236256 - -2130097/9. Let w = -421 + r. Factor -w - 10/9*u**2 - 14/9*u.
-2*(u + 1)*(5*u + 2)/9
Let x(r) be the third derivative of -r**7/42 - r**6/12 + r**5/12 + 5*r**4/12 + 15*r**2. Suppose x(c) = 0. What is c?
-2, -1, 0, 1
Let q be 4 + 0 - (-12 - -12). Let f(n) be the second derivative of 0*n**2 + 0*n**3 + 1/15*n**q + 1/50*n**5 - n + 0. Factor f(y).
2*y**2*(y + 2)/5
Suppose 8*y - 6 = 5*y. Let d(i) be the first derivative of 1/2*i**y + 1/4*i**4 - 2/3*i**3 + 3 + 0*i. Find o, given that d(o) = 0.
0, 1
Let n(x) be the third derivative of -x**9/90720 + x**8/30240 + x**5/20 - 3*x**2. Let u(p) be the third derivative of n(p). Solve u(o) = 0 for o.
0, 1
Let m(f) be the first derivative of -3*f**4/7 - 17*f**3/7 - 30*f**2/7 - 12*f/7 + 3. Factor m(k).
-3*(k + 2)**2*(4*k + 1)/7
Let l be ((-8)/(-10))/((-2)/(-5)). Determine y, given that -5 + 3*y + 12*y**2 + l + 0 + 24*y**2 = 0.
-1/3, 1/4
Factor -2/7*p - 2/7*p**2 + 4/7.
-2*(p - 1)*(p + 2)/7
Let y(l) be the second derivative of l**6/10 - l**5/5 + l**4/12 - 14*l. Factor y(v).
v**2*(v - 1)*(3*v - 1)
Let x(f) be the third derivative of -f**6/24 + f**5/2 - 15*f**4/8 + 19*f**2. Factor x(w).
-5*w*(w - 3)**2
Suppose 8/7 + 0*q**2 + 12/7*q - 4/7*q**3 = 0. What is q?
-1, 2
Let n = 14 - 10. Suppose 0 = -3*z - 3*g - 9, z - 4 = n*z + 2*g. Factor 0*j**3 - 2*j - j**3 + j + 2*j**z.
-j*(j - 1)**2
Suppose -3*o + 6*o + 81 = 0. Let i = -27 - o. Factor 0*x + 0 + 2/7*x**3 - 2/7*x**5 + 0*x**2 + i*x**4.
-2*x**3*(x - 1)*(x + 1)/7
Let j(h) be the third derivative of h**6/24 - h**5/6 - 2*h**2 + 25. Factor j(b).
5*b**2*(b - 2)
Let p(i) = -2*i - 6. Let m be p(-4). Let n(k) be the first derivative of 1 - 8/3*k - 2/9*k**3 + 4/3*k**m. Let n(t) = 0. Calculate t.
2
Let n = 14 + 18. Let -5 - 16*m + 18*m**5 - 34*m**5 + n*m**3 + 8*m**2 - 4*m**4 + 1 = 0. What is m?
-1, -1/4, 1
Let i(o) be the first derivative of o**7/84 + o**6/20 + 3*o**5/40 + o**4/24 + 4*o + 3. Let m(b) be the first derivative of i(b). Factor m(c).
c**2*(c + 1)**3/2
Let p(g) be the second derivative of -g**8/4200 - g**7/1050 - g**6/900 - 2*g**3/3 + 2*g. Let o(b) be the second derivative of p(b). Solve o(j) = 0.
-1, 0
Let v(b) be the third derivative of -b**6/60 + b**3/6 + b**2. Let q be v(-1). Suppose 9*g + 0*g**2 - q - 3*g**2 - 5 + 2 = 0. What is g?
1, 2
Let n(l) be the third derivative of 2*l**2 + 1/105*l**7 + 0*l**3 - 1/15*l**6 + 2/15*l**5 + 0 + 0*l**4 + 0*l. Let n(r) = 0. What is r?
0, 2
Let s be (30/12)/(1/(-2)). Let h = -5 - s. Factor -3*p**4 + h*p**3 - 8*p + 8*p**2 + p**4 - 4*p**3 + 6*p**3.
-2*p*(p - 2)*(p - 1)*(p + 2)
Let h(b) = -2*b**5 + 9*b**4 - 6*b**3 + 2*b**2 - 3*b + 3. Let o(n) = n**4 - n + 1. Let x(v) = -h(v) + 3*o(v). Factor x(r).
2*r**2*(r - 1)**3
Factor -6*l**4 - 3*l**3 - 18*l**2 - 3*l**5 + 18*l**2.
-3*l**3*(l + 1)**2
Let g be -3 + -3*10/(-9). Let v(j) be the first derivative of 1/9*j**3 + 1/12*j**4 - 1 - 1/6*j**2 - g*j. Factor v(k).
(k - 1)*(k + 1)**2/3
Factor 12*x + 3*x**2 - 21 + 3 - 5*x**2.
-2*(x - 3)**2
Let c(b) be the second derivative of 2*b**7/21 - 3*b**5/5 - 2*b**4/3 - 4*b. Factor c(q).
4*q**2*(q - 2)*(q + 1)**2
Let c be ((-2)/4)/((-1)/6). Let d(r) be the first derivative of 0*r + 2/5*r**5 - 3/10*r**4 + 0*r**2 - 4/15*r**c + 2. Factor d(m).
2*m**2*(m - 1)*(5*m + 2)/5
Suppose 0 - 1/6*p**2 + 1/6*p**3 + 0*p = 0. Calculate p.
0, 1
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