6
Let y(j) be the first derivative of j**7/840 + j**6/160 + j**5/240 - j**4/32 - j**3/12 - 15*j**2/2 - 26. Let s(w) be the second derivative of y(w). Factor s(c).
(c - 1)*(c + 1)**2*(c + 2)/4
Let j(l) = -10*l**2 + 3 - 3 + 5. Let r be ((-24)/21)/4 - 185/(-35). Let g(q) = q**3 - q**2 + 1. Let o(s) = r*g(s) - j(s). Factor o(v).
5*v**2*(v + 1)
Let c(y) be the first derivative of -49*y**3/15 - 28*y**2/5 - 16*y/5 - 290. What is a in c(a) = 0?
-4/7
Suppose 16 = -5*a + 1. Let m = -1 - a. Factor -7*u + 3*u + 22*u**m + 0*u.
2*u*(11*u - 2)
Let p(t) be the third derivative of -t**7/42 + 11*t**6/24 - 13*t**5/6 + 10*t**4/3 - 264*t**2. Factor p(i).
-5*i*(i - 8)*(i - 2)*(i - 1)
Let f = -28393/15 - -1893. Let 4/15 - 4/15*m**2 - 2/15*m**3 + f*m = 0. Calculate m.
-2, -1, 1
Let n(s) be the first derivative of -7*s**8/24 + 6*s**7/5 - 109*s**6/60 + 6*s**5/5 - s**4/3 - s**2 + 6. Let t(d) be the second derivative of n(d). Factor t(i).
-2*i*(i - 1)**2*(7*i - 2)**2
Let h(t) = -2*t. Let z(r) = -5*r**2 - 36*r - 40. Let x(w) = 3*h(w) - z(w). Determine b, given that x(b) = 0.
-4, -2
Determine h so that -3/4*h + 15/8*h**2 + 3/4*h**3 + 0 - 15/8*h**4 = 0.
-1, 0, 2/5, 1
Let a be 10/(-8)*11/(-110). Let r(i) be the first derivative of -2 - 1/3*i**3 + 0*i + a*i**2. Suppose r(g) = 0. What is g?
0, 1/4
Let s be 2*(-12)/(-10) - 12/(-20). Factor -7*y**2 + 6 + y**3 + 8*y + 10 + 0*y**3 + 0*y**s.
(y - 4)**2*(y + 1)
Let o = -81 - -83. Let i = -240 + 728/3. Suppose -i*x**3 - 4/3*x**o - 2/3*x**4 + 2 + 8/3*x = 0. Calculate x.
-3, -1, 1
Let p(a) be the second derivative of -a**6/540 - a**5/60 + a**4/9 - 7*a**3/6 + 6*a. Let j(q) be the second derivative of p(q). Factor j(z).
-2*(z - 1)*(z + 4)/3
Let c(o) be the second derivative of o**6/6 + 7*o**5/4 - 5*o**4/4 - 275*o**3/6 + 125*o**2 + 2*o + 166. Factor c(k).
5*(k - 2)*(k - 1)*(k + 5)**2
Find k such that -10/3*k**4 - 90*k**2 + 68*k**3 + 0 + 76/3*k = 0.
0, 2/5, 1, 19
Let g(j) be the second derivative of j**8/26880 - j**7/1008 + 5*j**6/576 + 25*j**4/6 + 7*j - 1. Let f(y) be the third derivative of g(y). Factor f(v).
v*(v - 5)**2/4
Let r be 44/14*(-62678)/(-444). Factor -r + 1/3*u**3 - 11*u**2 + 121*u.
(u - 11)**3/3
Let x(m) = 2*m - 9. Let s be x(4). Let r be 21/28 + s/2. Factor -1/4*y + 1/2*y**2 + 0 - r*y**3.
-y*(y - 1)**2/4
Let p(f) be the second derivative of -147*f**6/50 - 21*f**5/25 + 437*f**4/60 + 14*f**3/5 + 2*f**2/5 - 3*f - 5. Suppose p(x) = 0. What is x?
-1, -2/21, 1
Let 1/4*r**5 - 1/4 - 3/4*r - 1/2*r**2 + 1/2*r**3 + 3/4*r**4 = 0. Calculate r.
-1, 1
Factor -12/7*i**3 - 2/7*i**4 - 24/7*i**2 - 6/7 - 20/7*i.
-2*(i + 1)**3*(i + 3)/7
Let y be 1*-1*(-10)/(-25) + (-4)/(-10). Factor -2*m**3 + 0*m - 4/7*m**2 + y.
-2*m**2*(7*m + 2)/7
Suppose 0 = 7*j - 59 - 11. Solve -4*u - 29*u**2 + 26*u**2 + j*u - 3 = 0 for u.
1
Suppose -74 = 5*q - 359. Suppose -26*p = -24*p - 24. Factor -48*u + 18*u**2 + 38*u**2 + 19*u**2 + p + 21*u**4 - 3*u**5 - q*u**3.
-3*(u - 2)**2*(u - 1)**3
Solve 0*i - 2/5*i**3 + 0*i**2 + 2/5*i**4 + 0 = 0 for i.
0, 1
Factor h**3 + 43/5*h + 7/5 + 41/5*h**2.
(h + 1)*(h + 7)*(5*h + 1)/5
Let o(j) be the first derivative of j**7/840 - j**6/180 - 14*j**3/3 + 14. Let h(r) be the third derivative of o(r). Factor h(p).
p**2*(p - 2)
Let f(i) be the first derivative of 6*i**5/5 - i**4/2 - 6*i**3 + 9*i**2 - 4*i + 141. Find z, given that f(z) = 0.
-2, 1/3, 1
Let c(v) be the first derivative of v**4 + 38*v**3/3 - 11*v**2 - 20*v + 74. Find f such that c(f) = 0.
-10, -1/2, 1
Let b(x) be the third derivative of 0 - 5/8*x**4 - 2*x**2 + 0*x - 5/3*x**3 + 1/24*x**6 + 0*x**5. Factor b(s).
5*(s - 2)*(s + 1)**2
Let q be 15*9/54 - (-3)/2. Factor 3*l**4 - 4*l**2 - 2*l**q - 5*l**4 + 20*l + 8*l**4 - 20*l**3.
4*l*(l - 5)*(l - 1)*(l + 1)
Let y(h) = -155*h**3 - 1070*h**2 - 1955*h - 970. Let l(d) = 9*d**3 + 63*d**2 + 115*d + 57. Let q(p) = -35*l(p) - 2*y(p). Factor q(t).
-5*(t + 1)**2*(t + 11)
Let g(r) be the third derivative of r**8/16800 + r**7/1575 + 5*r**4/8 - 26*r**2. Let h(x) be the second derivative of g(x). Find p such that h(p) = 0.
-4, 0
Let d(u) be the third derivative of u**8/560 + 2*u**7/25 + 49*u**6/50 - 127*u**2 - 2. Let d(r) = 0. What is r?
-14, 0
Suppose 0 = w + 28 - 53. Let l be ((-5)/w)/(2 + (-14)/6). What is f in 0*f + 2/5*f**2 + l*f**3 + 0 + 1/5*f**4 = 0?
-2, -1, 0
Let y(i) be the second derivative of 1/80*i**6 + 0*i**3 - 2*i + 0*i**2 - 3/160*i**5 - 3 - 1/16*i**4. Factor y(a).
3*a**2*(a - 2)*(a + 1)/8
Let y(p) be the second derivative of p**7/126 - p**6/18 + p**5/30 + 5*p**4/9 - 4*p**3/3 + 4*p. Determine v, given that y(v) = 0.
-2, 0, 2, 3
Let s(w) = w**3 + 7*w**2 - 7*w + 10. Let c be s(-8). Let v**c + 5*v**3 - 2*v**2 - 5*v**2 + 3*v**4 - 8*v**3 = 0. Calculate v.
-1, 0, 2
Let y be (-30)/10 - (-3)/((-3)/(-16)). Factor y*k + 21*k**2 - 6 + k**3 - 13*k**2 - 16*k**2.
(k - 6)*(k - 1)**2
Let b(j) = 334*j**4 + 792*j**3 + 546*j**2 + 120*j + 4. Let w(r) = r**4 - 3*r**3 + 2*r**2 + 1. Let m(t) = b(t) + 4*w(t). Solve m(l) = 0.
-1, -2/13
Factor 42/5 + 1/5*z**2 + 13/5*z.
(z + 6)*(z + 7)/5
Let g = -80 + 167. Suppose -h + 90 = g. Let -3*w**4 - 12/5*w - 9/5*w**h + 0 + 36/5*w**2 = 0. Calculate w.
-2, 0, 2/5, 1
Let k(i) = 3*i**3 - i. Let f(n) = -16*n**3 - 40*n**2 + 78*n. Let b(v) = -2*f(v) - 12*k(v). Factor b(m).
-4*m*(m - 18)*(m - 2)
Let p(j) be the first derivative of j**7/70 + 27*j**2/2 + 21. Let l(a) be the second derivative of p(a). Factor l(w).
3*w**4
Let n(z) be the third derivative of 0*z**3 + 0*z**4 + 1/8*z**6 + 0*z + 0 - 2/21*z**7 + 1/12*z**5 + z**2. Solve n(f) = 0 for f.
-1/4, 0, 1
Let m(c) = -4*c**2 - 38*c - 100. Let d(g) = -16*g**2 - 151*g - 400. Let h(j) = -2*d(j) + 9*m(j). Factor h(k).
-4*(k + 5)**2
Let n(f) be the first derivative of 35*f**6/18 + 44*f**5/3 - 155*f**4/4 + 130*f**3/9 + 40*f**2/3 - 503. What is a in n(a) = 0?
-8, -2/7, 0, 1
Let y(b) be the first derivative of 5*b**8/336 + b**7/42 + 5*b**2 - 2*b - 29. Let z(o) be the second derivative of y(o). Factor z(p).
5*p**4*(p + 1)
Suppose 5*b + 8 = 6*b. Factor -5*c**3 + 3*c**4 + 12*c**2 - b*c - c**4 - 5*c**4 + 7*c**3.
-c*(c - 2)*(c + 2)*(3*c - 2)
Factor 275*u**4 + 2*u**5 + 0*u**5 - 265*u**4.
2*u**4*(u + 5)
Suppose 4 = -15*s + 49. Factor -1/3*m**s + 1/3*m + 1/3*m**2 - 1/3.
-(m - 1)**2*(m + 1)/3
Let n(v) be the first derivative of -4*v**3/3 - 14*v**2 - 40*v + 63. Find q, given that n(q) = 0.
-5, -2
Let m = -43/10549 + 1687793/727881. Let z = m - -3/161. Let 5/3*t**3 + z*t + 1/3*t**4 + 3*t**2 + 2/3 = 0. What is t?
-2, -1
Let v(o) be the third derivative of -o**5/180 + 37*o**4/72 - o**2 + 43. Find x, given that v(x) = 0.
0, 37
Let w(f) = -f**2 + 23*f + 82. Let v be w(29). Let y be v*(-6)/72 - 7. Find d, given that 2/3*d**3 - y*d - 1/3*d**2 + 0 + 1/3*d**4 = 0.
-2, -1, 0, 1
Let a(o) = 0*o**2 - 2*o**2 + 3*o**2 + 9 + 7*o. Let c be a(-6). Let -4*q + 7*q**2 - q - 3*q + 10*q**3 - 16 - 11*q**c = 0. Calculate q.
-1, 4
Let w(q) be the third derivative of q**8/30240 + q**7/7560 - 4*q**5/15 - 3*q**2. Let g(r) be the third derivative of w(r). Factor g(m).
2*m*(m + 1)/3
Let o(i) = i**3 - 3*i**2 + 8*i - 6. Let j be o(4). Let y = j - 37. Suppose 0 + 0*b**2 - b**3 + 0*b + 1/2*b**y + 1/2*b**4 = 0. What is b?
-2, 0, 1
Let l be -3*(-2)/(-15)*(-10 + (20 - 11)). Solve -l*p + 2/5 + 2/5*p**3 - 2/5*p**2 = 0.
-1, 1
Let c(v) be the first derivative of -v**8/2520 + v**6/180 + v**5/90 - 20*v**3/3 + 5. Let b(h) be the third derivative of c(h). Factor b(s).
-2*s*(s - 2)*(s + 1)**2/3
Factor 18*o**2 - 2*o**3 - 21*o + 31*o**3 - 26*o**3.
3*o*(o - 1)*(o + 7)
Let t = 2 + 6. Let u(c) = -6*c**2 - 2 - 3*c - 5*c**3 - c + t*c. Let x(o) = -5*o**3 - 5*o**2 + 4*o - 3. Let a(h) = -3*u(h) + 2*x(h). Suppose a(s) = 0. What is s?
-2, 0, 2/5
Let j(f) be the second derivative of f**6/10 - 3*f**5/10 - f**4 + 4*f**3 - 2*f - 67. Factor j(q).
3*q*(q - 2)**2*(q + 2)
Let a = 22202 + -22200. Suppose -12/17 + 2/17*h + 2/17*h**a = 0. What is h?
-3, 2
Let k(y) be the first derivative of -1/2*y**2 + 1/4*y**4 - 2*y + 2 + 2/3*y**3. Factor k(q).
(q - 1)*(q + 1)*(q + 2)
Let n(r) be the first derivative of r**4/4 - 4*r**3/3 + 2*r**2 - 2*r + 8. Let c be n(3). What is w in 4*w - 7 - c - 2*w**2 - 12*w = 0?
-2
Let v(a) be the first derivative of 5*a**3/3 + 25*a**2/2 + 20*a + 5. Determine g so that v(g) = 0.
-4, -1
Suppose -4/3*o + 8/3*o**2 + 0 - 2/3*o**4 - o**3 + 1/3*o**5