ird derivative of -r**6/30 + 7*r**5/15 - 5*r**4/2 + 6*r**3 + r**2 + 210*r. Determine n so that y(n) = 0.
1, 3
Suppose -4*w + 3*r + 137 = 0, -4*w = -0*w - 2*r - 138. What is s in 39500 - 39500 + s**2 - w*s = 0?
0, 35
Determine l, given that 170*l**2 + 29 - 21*l**3 - 66*l + 220*l**2 - 150*l - 29 = 0.
0, 4/7, 18
Let z(j) be the first derivative of -41/6*j**3 - 24 + 8*j**2 - 2*j + 13/8*j**4. Factor z(y).
(y - 2)*(y - 1)*(13*y - 2)/2
Let b(w) be the second derivative of w**7/252 - w**6/10 + 59*w**5/120 - 7*w**4/12 + 30*w - 48. Let b(c) = 0. Calculate c.
0, 1, 3, 14
Let d(x) be the first derivative of -x**4/8 - 2*x**3 + 49*x**2/4 + 30*x - 1397. Factor d(v).
-(v - 4)*(v + 1)*(v + 15)/2
Let z(s) be the second derivative of 1/105*s**6 + 153*s + 16/21*s**3 + 0*s**2 + 0 + 4/35*s**5 + 10/21*s**4. Factor z(y).
2*y*(y + 2)**2*(y + 4)/7
Let q(w) be the third derivative of -w**7/210 - 7*w**6/120 + 3*w**4/2 - 1633*w**2. Factor q(i).
-i*(i - 2)*(i + 3)*(i + 6)
Let k(v) = -5*v**2 + 42*v - 439. Let r(q) = q + 1. Let l(u) = 2*u**2 - 5*u - 6. Let x(w) = l(w) + 5*r(w). Let b(h) = k(h) + 2*x(h). Factor b(a).
-(a - 21)**2
Factor -240/7 - 317/7*m - 76/7*m**2 + 1/7*m**3.
(m - 80)*(m + 1)*(m + 3)/7
Let h(i) be the second derivative of -i**8/1344 - 5*i**7/504 - 71*i**4/12 - 88*i. Let l(r) be the third derivative of h(r). Solve l(p) = 0.
-5, 0
Suppose 0 = 113*u - 2896 + 1088. Let t(k) be the second derivative of 0*k**2 - u*k + 5/6*k**4 + 0 + 1/4*k**5 + 5/6*k**3. Find q, given that t(q) = 0.
-1, 0
Let j(w) be the third derivative of -w**6/1260 + 4*w**5/21 - 400*w**4/21 - 49*w**3/2 + 3*w**2 + 46. Let g(o) be the first derivative of j(o). Factor g(v).
-2*(v - 40)**2/7
Factor -192/5*j**2 + 4794/5*j - 8836/5 + 2/5*j**3.
2*(j - 47)**2*(j - 2)/5
Let j = 1430894/3 - 476918. What is h in 980/3 + 5/3*h**2 + j*h = 0?
-14
Let i(a) = -a**3 + 5*a**2 - 5*a. Let x be i(3). Find d, given that 14*d + 24*d**2 + 26*d**2 - 2*d**5 - 10*d**4 - 12*d**x - 67*d**2 + 6 + 21*d**2 = 0.
-3, -1, 1
Factor -33/2 - 1/4*l**2 - 25/4*l.
-(l + 3)*(l + 22)/4
Factor 0*s - 128/11*s**3 + 0 - 2/11*s**4 + 0*s**2.
-2*s**3*(s + 64)/11
Let d be ((-10)/20)/((5/(-6))/5). Let -6*b**d - b**3 - 22*b**4 + 23*b**4 = 0. What is b?
0, 7
Let s = -3892/5 + 27294/35. Factor s*d**2 - 3/7*d**3 + 2/7 - 9/7*d.
-(d - 2)*(d - 1)*(3*d - 1)/7
Let d = 2239/70 + -28827/910. Suppose d*y + 2/13*y**2 - 2/13*y**3 + 0 = 0. What is y?
-1, 0, 2
Let f = -4630/77 - -25306/385. Find z, given that 4/5*z**3 - 2 + f*z - 24/5*z**2 + 2/5*z**4 = 0.
-5, 1
Let o(z) be the first derivative of z**6/210 - z**5/28 + z**4/14 + 2*z**3/21 - 4*z**2/7 + 80*z - 65. Let f(x) be the first derivative of o(x). Factor f(q).
(q - 2)**3*(q + 1)/7
Let g(j) be the third derivative of -1/630*j**7 + 13*j + j**2 + 1/180*j**5 - 1/360*j**6 + 1/72*j**4 + 0*j**3 + 0. Factor g(q).
-q*(q - 1)*(q + 1)**2/3
Let a = 2/19997 + 1379687/1059841. Let f = a + 5/159. Factor -8/3 - 20/3*v - f*v**2 + 8/3*v**3.
4*(v - 2)*(v + 1)*(2*v + 1)/3
Let v(m) be the second derivative of m**7/16380 + 11*m**6/936 + m**4/12 - m**3/3 - 110*m + 1. Let z(t) be the third derivative of v(t). Factor z(k).
2*k*(k + 55)/13
Let q(w) be the second derivative of -5*w**4/12 + 115*w**3/3 - 600*w**2 + 2*w - 3175. Determine o, given that q(o) = 0.
6, 40
Factor 1/12*x**5 + 1/3*x + 13/12*x**3 - 1/2*x**4 - x**2 + 0.
x*(x - 2)**2*(x - 1)**2/12
Let n(x) = x**3 + 21*x**2 - 25*x + 3. Let l(c) = -8 - 13*c + 53*c + 0 - 2*c**3 - 52*c**2 + 22*c. Let h = -1 + -11. Let g(v) = h*n(v) - 5*l(v). Factor g(m).
-2*(m - 2)*(m - 1)**2
Factor 2/3*t**3 + 310/3*t - 650/3 - 46/3*t**2.
2*(t - 13)*(t - 5)**2/3
Suppose 0 = 9*o - 761 - 814. Let k be (-150)/o - 276/(-224). Determine c so that -3/2*c**4 - 3/4*c**3 - k*c + 3/2*c**2 + 0 + 9/8*c**5 = 0.
-1, 0, 1/3, 1
Let x = -12/192881 + 2700370/578643. Factor -x*n**4 - 8*n**3 - 2*n**2 + 0 + 4/3*n.
-2*n*(n + 1)**2*(7*n - 2)/3
Let n(b) = b**3 + 13*b**2 - 620*b - 8848. Let g be n(-15). Factor 16/5*q**g - 24/5*q**3 + 0 - 1/5*q**5 + 0*q + 9/5*q**4.
-q**2*(q - 4)**2*(q - 1)/5
Let b be (-6 - 449/2)*2. Let a = 5073/11 + b. Find p such that -6/11*p**3 - 2/11*p - 6/11*p**2 + 0 - a*p**4 = 0.
-1, 0
Factor 219/2*u - 3/2*u**2 + 225.
-3*(u - 75)*(u + 2)/2
Let a(f) = 5*f**2 + 30*f - 4. Let l be a(-10). Factor 19*b**3 + 648 - 15*b**3 + 664*b - l*b + 80*b**2.
4*(b + 2)*(b + 9)**2
Let h be ((-18)/(-8))/((-1269)/(-1128)). Let u be -2*(4/3 + -2). Factor -2/3*d**h - 2*d - u.
-2*(d + 1)*(d + 2)/3
Let s(i) = i**4 + i**3 - 14*i**2 + i + 1. Let p(b) = -3*b**4 + 81*b**3 - 10*b**2 - 79*b + 1. Let g(k) = p(k) - s(k). Factor g(w).
-4*w*(w - 20)*(w - 1)*(w + 1)
Let q(m) = m**4 - m**2 + 1. Let c(j) = 12*j**4 + 6 + 1 + 7 - 6*j**2. Let z(w) = 2*c(w) - 28*q(w). Factor z(l).
-4*l**2*(l - 2)*(l + 2)
Let d(o) be the first derivative of -o**7/147 + o**6/21 - 2*o**5/35 + 2*o + 72. Let h(v) be the first derivative of d(v). What is i in h(i) = 0?
0, 1, 4
Factor 3801*k + 17*k**3 - 518*k**2 - 119*k**3 + 849*k**2 + 2*k**4 + 357*k + 807*k**2 + 2916.
2*(k - 27)**2*(k + 1)*(k + 2)
Let u(q) be the second derivative of 1/84*q**6 + 0 + 3/35*q**5 - 8/21*q**3 + 1/7*q**4 - 2*q**2 + 11*q. Let d(i) be the first derivative of u(i). Factor d(w).
2*(w + 2)**2*(5*w - 2)/7
Let i = -333389/30 + 11113. Let r(c) be the third derivative of 0 + 0*c - 23*c**2 + i*c**5 + 2*c**3 + 5/12*c**4. Factor r(k).
2*(k + 2)*(k + 3)
Let m(c) = -c**3 + 5*c**2 - 2*c + 14. Let r be m(5). Factor 7*d**2 - 5*d**3 + 4*d**4 + 5*d - 6 + d**4 - 7*d**4 - 2*d**r + 3*d**4.
-(d - 1)**2*(d + 1)*(d + 6)
Let o(k) = -4*k**2 + 2*k + 1. Let i(w) = 9*w**2 - 5*w - 4. Let z(q) = -i(q) - 2*o(q). Determine p, given that z(p) = 0.
-1, 2
What is h in 518*h**3 + 895*h - 469*h**3 + 56*h**2 + 451*h**2 - 1148 - 302 - h**4 = 0?
-5, 1, 58
Let t be (5 + 5 - -7) + -15. Let x(p) be the first derivative of 17/8*p**4 + 0*p**2 - 15 - 5/12*p**6 - 3/10*p**5 - t*p + 19/6*p**3. Let x(w) = 0. Calculate w.
-1, 2/5, 2
Let h = -7227/16 + 50621/112. Factor 8/7 + 10/7*m**2 + h*m**3 + 16/7*m.
2*(m + 1)*(m + 2)**2/7
Let c(r) be the first derivative of 2*r**5/25 + 9*r**4/10 - 16*r**3/3 - 48*r**2/5 + 1554. Solve c(y) = 0 for y.
-12, -1, 0, 4
Let s(a) = a. Let g be (70/(-15) + 4)/(2/(-3)). Let m(f) be the first derivative of -4*f**3/3 + 9*f**2 - 16*f - 2. Let r(o) = g*m(o) - 2*s(o). Factor r(u).
-4*(u - 2)**2
Solve 75/2*t**2 + 800*t**5 + 0 - 2040*t**4 + 1745/2*t**3 - 45*t = 0.
-1/5, 0, 3/8, 2
Let s be 9 - (31350/105)/38. Factor -80/7*h**4 + 0 + 36/7*h**5 - s*h**2 + 52/7*h**3 + 0*h.
4*h**2*(h - 1)**2*(9*h - 2)/7
Find a, given that 68*a - 402 + 402 - 246*a**2 - 3*a**3 + 181*a = 0.
-83, 0, 1
Let c = 742 + -740. Factor 8*k**3 + 165*k - 32*k**c - 12 - 237*k - 24 + 4*k**4.
4*(k - 3)*(k + 1)**2*(k + 3)
Let -386887206 - 3609/2*j**2 + 3/4*j**3 + 1447209*j = 0. What is j?
802
Let b(c) be the second derivative of c**7/1470 + c**6/126 - c**5/15 + 65*c**3/3 - 126*c. Let q(u) be the second derivative of b(u). Let q(z) = 0. What is z?
-7, 0, 2
Let 7*i**2 + 55*i**3 - 11*i**2 + 1420*i**5 - 8*i**2 - 29*i**4 - 1416*i**5 = 0. Calculate i.
0, 1/4, 3, 4
Let v = -7221/5 + 1467. Find t, given that 2/5*t**3 + v*t - 12*t**2 - 56/5 = 0.
1, 28
Let o(x) be the second derivative of x**5/70 - 23*x**4/42 + 124*x**3/21 - 192*x**2/7 + 141*x + 5. Suppose o(n) = 0. What is n?
3, 4, 16
Let a(u) = -5*u + 19. Let b be a(-5). Let q = -39 + b. Determine m, given that -q*m**3 - m - 5*m**4 + 5*m**2 + 8*m - 2*m = 0.
-1, 0, 1
Suppose u = x - 6*x - 677, 4*x + 5*u = -550. Let p be (-4)/10*x/216. Factor -p*m**2 + 1/4 + m**3 - m.
(m - 1)*(m + 1)*(4*m - 1)/4
Let h be 5/((-10)/(-66)) - 18/18. Factor 8*j**2 - h - 21*j**2 + 36*j + 9*j**2.
-4*(j - 8)*(j - 1)
Let h = 15647/30 + -3115/6. Let i(a) be the second derivative of h*a**5 + 7/3*a**4 + 0*a**2 + 19*a + 0 - 7/30*a**6 + 2/3*a**3 - 7/24*a**7. Solve i(v) = 0 for v.
-2, -2/7, 0, 2
Suppose 3*u + u - 36358 = 2*d, 3*u - 27273 = 3*d. Suppose -30751 = -3*x - u. Suppose -36*k**2 - 28*k**3 - 8*k - x + 7221 = 0. Calculate k.
-1, -2/7, 0
Let h = -3450/209 + 34394/1881. Determine g, given that 4/3*g**2 + 10/3*g + h - 2/9*g**3 = 0.
-1, 8
Find q such that -242*q**4 + 7*q**5 - 156*q**2 + 266*q**4 - 21*q**3 - 10*q**5 + 132*q + 240 = 0.
-2, -1, 2, 4, 5
Let b = 1010857/404342 + -1/202171. Let 3/8*j**3 - 7/4*j**2 + b*j - 1 = 0. Calculate j.
2/3, 2
Let j