6. Determine r so that k(r) = 0.
0, 1, 3
Let u(y) be the second derivative of 3*y**5/20 + 11*y**4/4 + 7*y**3 - 120*y**2 - 154*y + 10. Factor u(s).
3*(s - 2)*(s + 5)*(s + 8)
Let h be ((-4 - -2) + 4)*(-22)/(-4). Suppose -15*o + 116 = -h*o. Suppose -2*w + 6*w**2 + o - 64 + 29 + 2*w**3 = 0. What is w?
-3, -1, 1
Let v(u) be the first derivative of 5*u**6/3 + 18*u**5/5 - 25*u**4/2 - 30*u**3 + 20*u**2 + 72*u + 509. Suppose v(s) = 0. What is s?
-2, -9/5, -1, 1, 2
Let k(w) = -w**2 - 260*w - 513. Let j be k(-2). Let u(h) be the second derivative of -3/4*h**4 + 3/20*h**5 + h + 0*h**2 + h**j + 0. Factor u(b).
3*b*(b - 2)*(b - 1)
Let z = -118 - -122. Suppose -z = -7*o + 6*o. What is x in 22*x**5 - 6*x**o + 19*x**4 - 7*x**5 - 2*x**3 = 0?
-1, 0, 2/15
Let 0*o - 2/5*o**3 - 1/5*o**4 + 0*o**2 + 1/5*o**5 + 0 = 0. What is o?
-1, 0, 2
Let j be (-165)/(-198)*(-6)/(-27)*6. Let f(c) be the first derivative of 14/9*c**2 - j*c**3 - 2/3*c + 19. Determine g, given that f(g) = 0.
1/3, 3/5
Let m be (5 + (-14)/42)*(-5 + 72/14). Solve 1/3 + 1/3*c**2 - m*c = 0.
1
Let f = -38710 - -38713. Find c such that -3*c**f + 3/2*c**2 + 9/4*c + 3/4*c**5 + 0*c**4 - 3/2 = 0.
-2, -1, 1
Suppose -2*x - 159*x - 114*x = 0. Factor x*y + 20*y**4 + 0 + 5/2*y**5 + 45*y**2 + 105/2*y**3.
5*y**2*(y + 2)*(y + 3)**2/2
Let i be ((-2 + 1)*-2 + (-8 - -5))*-4. Let s(d) be the second derivative of -16*d**2 + 4*d**3 - 16*d + 0 - 1/3*d**i. What is x in s(x) = 0?
2, 4
Let h(a) = -4*a**3 - 96*a**2 + 21*a + 504. Let c be h(-24). What is d in 2/3*d**2 + 1/3*d**3 + 0*d + c = 0?
-2, 0
Let k(h) be the third derivative of 0*h**4 + 0*h**3 + 0*h + 0 - 1/1365*h**7 + 1/195*h**6 + 48*h**2 - 1/130*h**5. Suppose k(j) = 0. Calculate j.
0, 1, 3
Let z(k) be the second derivative of 1/80*k**5 + 2*k + 0*k**4 - 21 + 0*k**2 + 0*k**3 - 1/60*k**6 + 1/168*k**7. Solve z(t) = 0 for t.
0, 1
Let w(o) = o**3 - 14*o**2 + 11*o + 50. Let q be w(13). Let 1 - 4 - 7 - 4*y**2 - 10 - q*y = 0. Calculate y.
-5, -1
Suppose -8/7*x**2 + 6 + 1/7*x**3 + 1/7*x = 0. What is x?
-2, 3, 7
Let u be 0*((-238)/(-252) - 1). Solve 2/5*r**2 + 0*r**3 + 0 + u*r - 2/5*r**4 = 0 for r.
-1, 0, 1
Let f(k) be the second derivative of -k**4/3 + 52*k**3/3 - 50*k**2 - 729*k + 2. Factor f(i).
-4*(i - 25)*(i - 1)
Let r(j) be the first derivative of -2*j**3/3 + 51*j**2 - 196*j + 342. Let r(f) = 0. Calculate f.
2, 49
Find u such that -1/7*u**2 - 632/7*u - 631/7 = 0.
-631, -1
Let f(v) be the second derivative of 2*v**7/231 + 71*v**6/110 + 2753*v**5/220 - 747*v**4/44 - 243*v**3/22 + v + 514. Suppose f(o) = 0. Calculate o.
-27, -1/4, 0, 1
Suppose 11*y + 168 = 7*y. Let w = 46 + y. Determine x, given that 2*x - 10*x - 6*x**2 - 61*x**4 + 62*x**w - 3 = 0.
-1, 3
Let s be 1/(-23) - (-44562)/(-49266)*-17. Factor x**2 - s*x + 5.
(x - 15)*(3*x - 1)/3
Let i(b) be the second derivative of -b**5/8 - 155*b**4/6 - 205*b**3/4 + 2344*b. Factor i(w).
-5*w*(w + 1)*(w + 123)/2
Let z = 321 + -316. Let m be -4 + -2 - (-560)/72. Factor -2/3*h + 0 - 4/3*h**3 + 2/9*h**z + 0*h**4 + m*h**2.
2*h*(h - 1)**3*(h + 3)/9
Let z = 1837 - 1821. Suppose -38*i + z*i = -44. Determine v so that 0 - 1/5*v**i + 0*v = 0.
0
Suppose 8 = 5*y - 2. Let p = -188 - -191. Factor 11*b**y - 19*b - b**3 - 3*b**2 + p*b.
-b*(b - 4)**2
Let l be ((-2)/42)/((-5)/18*99/165). Let d(y) be the first derivative of 29 + 3/7*y + 1/21*y**3 + l*y**2. Factor d(t).
(t + 1)*(t + 3)/7
Let w(x) be the third derivative of x**6/24 - 5*x**5/12 - 20*x**4/3 - 30*x**3 + 2306*x**2. Factor w(v).
5*(v - 9)*(v + 2)**2
Factor -92/3*t - 88/3 - 4/3*t**2.
-4*(t + 1)*(t + 22)/3
Let b(s) be the third derivative of -25*s**8/112 - 43*s**7/21 - 53*s**6/24 + 31*s**5/2 - 15*s**4 - s**2 - 145*s. Solve b(p) = 0.
-4, -3, 0, 3/5, 2/3
Let q = -3031425/7 + 433067. Solve -48/7*l**3 + 4/7*l**4 + q*l**2 + 0 + 0*l = 0 for l.
0, 1, 11
Find m such that -1/2*m**2 + 1/6*m**4 - 10 + m**3 - 26/3*m = 0.
-5, -2, 3
Let q(u) = -46*u + 142. Let p(h) = h**3 - 7*h**2 + 25*h - 111. Let v be p(6). Let m be q(v). Solve -6/11*j**3 + 0*j - 4/11*j**2 - 2/11*j**m + 0 = 0.
-2, -1, 0
Let o(n) be the first derivative of -n**5 + 3/4*n**4 + 0*n + 5*n**2 - 1/6*n**6 + 17/3*n**3 + 43. Find d such that o(d) = 0.
-5, -1, 0, 2
Let z(c) be the third derivative of -c**5/270 - 65*c**4/108 + 350*c**3/27 - 1377*c**2. Determine p, given that z(p) = 0.
-70, 5
Factor 0 + 21/4*v**3 + 1/2*v**4 + 21/2*v**2 + 4*v.
v*(v + 2)*(v + 8)*(2*v + 1)/4
Suppose 0 = -3*d + 1532 + 484. Determine f, given that -2*f**5 + d*f**4 - 676*f**4 + 144 + 52*f**3 - 192*f - 2*f**5 + 4*f**2 = 0.
-3, 1, 2
Let i(s) = -8*s + 5*s - 3 + 2 + 2*s. Let l be i(-6). Suppose 3*c**l - 23*c + 23*c - 3*c**3 = 0. Calculate c.
-1, 0, 1
Let c be (-1)/(-2)*1*6. Suppose c*g - 7 - 3 = a, -4*a - g = -12. Factor -3 + z**3 + 7*z**2 - 4*z**a + 7*z - 16*z + 8*z.
(z - 1)*(z + 1)*(z + 3)
Let z = 4339/3 - 1445. Let c(f) be the first derivative of -4/3*f - 18 + 31/9*f**3 + 7/12*f**4 + z*f**2 - 4/5*f**5. What is l in c(l) = 0?
-1, -2/3, 1/4, 2
Factor 705*c**2 + 1767*c**2 + 5*c**3 + 43*c**2 + 852845*c + 1615*c**2.
5*c*(c + 413)**2
Let m(f) = f**2 + 10*f + 29. Let h be m(-6). Factor -4*x**3 - 10*x - 35*x**2 - 37*x**3 - 4*x**3 - 5*x**h - 25*x**4.
-5*x*(x + 1)**3*(x + 2)
Let z(k) be the third derivative of -k**5/540 - 379*k**4/216 + 127*k**3/9 - k**2 - 7*k - 5. Let z(o) = 0. What is o?
-381, 2
Let w(l) = l**3 + 3*l**2 - 6*l + 2. Let u(s) = 46*s**3 + 2474*s**2 - 332*s + 20. Let q(x) = -u(x) + 10*w(x). Factor q(c).
-4*c*(c + 68)*(9*c - 1)
Let q be 23/5 + -2 + -2. Let c = -65601 + 65604. Factor 1/5*s**4 + 0 + 0*s**2 - q*s**c + 4/5*s.
s*(s - 2)**2*(s + 1)/5
Let l be 12/(-28) - (-85)/35. Factor -o**l + 4 + 4 - 133*o + 131*o.
-(o - 2)*(o + 4)
Let o(w) be the second derivative of -w**5/20 + 7*w**4/4 - 10*w**3/3 + w**2 + w - 6. Let c be o(20). Factor -6*h**c + 31*h**2 - 16*h**2 + 9*h**3 - 6*h**4 - 6*h.
-3*h*(h - 2)*(h + 1)*(2*h - 1)
Let b(f) = 2*f**2 - 4218*f - 16901. Let m be b(-4). Suppose -19/3*x - 1/3*x**4 - 26/3*x**2 - 14/3*x**m + 1/3*x**5 - 5/3 = 0. What is x?
-1, 5
Factor 1/6*k**4 + 5/6*k - 5/6*k**3 + 1/2*k**2 - 2/3.
(k - 4)*(k - 1)**2*(k + 1)/6
Let b = 358192/7 + -51170. Let -6/7 - b*o**3 + 2/7*o + 6/7*o**2 = 0. What is o?
-1, 1, 3
Let g(t) be the second derivative of -64/5*t**5 + 0 + 0*t**2 - 16/15*t**6 - 1/42*t**7 + 40*t + 0*t**3 + 0*t**4. Solve g(f) = 0 for f.
-16, 0
Let h = 262344 - 262341. Find u, given that 69/4*u**h + 0 + 3*u + 15*u**2 + 21/4*u**4 = 0.
-2, -1, -2/7, 0
Let x(i) = 5*i**2 - 128*i + 986. Let s(z) = -2*z - 1. Let j(n) = n**2 + 33*n + 26. Let l be j(-32). Let q(m) = l*s(m) - x(m). Factor q(k).
-5*(k - 14)**2
Let f = 223321/4 + -55825. Factor 0*o + 0*o**2 + 0 - 3/4*o**4 - f*o**3.
-3*o**3*(o + 7)/4
Suppose 9*r + 15 = 4*r - 4*c, 2*c + 6 = -2*r. Let q be -1 - (2 + 76)/r. Let -q*z - 5*z**2 + 2 - 2 + 0 = 0. Calculate z.
-5, 0
Let j(g) be the second derivative of 8*g**4/3 + 122*g**3/3 - 198*g**2 - 3*g - 152. Let j(s) = 0. What is s?
-9, 11/8
Let d(x) be the second derivative of 7*x**7/15 - 77*x**6/25 + 137*x**5/25 - 9*x**4/5 - 7*x**3/3 - 3*x**2/5 + 412*x + 7. What is m in d(m) = 0?
-1/7, 1, 3
Let j(i) = -33*i**2 + 232*i - 1027. Let a(r) = 1070*r**2 - 7425*r + 32865. Let b(k) = -2*a(k) - 65*j(k). Factor b(g).
5*(g - 41)*(g - 5)
Suppose 16 + 52/5*p**2 - 128/5*p - 4/5*p**3 = 0. What is p?
1, 2, 10
Let o = 4609 + -59975/13. Let r = o - -129/26. Factor 0 + r*a**3 - 1/2*a - 1/2*a**2 + 1/2*a**4.
a*(a - 1)*(a + 1)**2/2
Let q be 2 - (-3)/(4 - 1). Suppose 0*m + 2*b - 2 = -2*m, q = 4*m + 5*b. Factor 4*d**2 - 6*d**2 - d**m + 10*d + d**2 + 12.
-2*(d - 6)*(d + 1)
Determine u, given that -202*u**2 + 1/3*u**3 + 30603*u + 0 = 0.
0, 303
Let q(x) be the second derivative of -x**5/5 + 37*x**4/3 - 24*x**3 + x - 2527. Suppose q(h) = 0. Calculate h.
0, 1, 36
Suppose -20 - 10 = -10*l. Let -2*m**2 - 2*m**5 - 33*m**4 - 5*m**3 + 17*m**4 + 18*m**4 + 7*m**l = 0. Calculate m.
-1, 0, 1
Let j(r) be the first derivative of 5/96*r**4 + 8 - 1/240*r**5 + 0*r - 7/2*r**2 - 1/4*r**3. Let m(w) be the second derivative of j(w). Factor m(c).
-(c - 3)*(c - 2)/4
Suppose 16 = -i + 3*x, 4*i - 4*x = -x - 10. Determine l, given that 0 - 7/3*l**i - 1/3*l**4 + 5/3*l**3 + l = 0.
0, 1, 3
Suppose 4*u + f - 13 - 54 = 0, -2*u - 5*f = -11. Let q be (2 + u/(-10))/((-4)/(-60)). Factor 0*j + 2/11*j**q + 0 - 2/11*j**2.
2*j**2*(