.
-4*(q - 2)*(q + 4)
Let q(t) be the second derivative of t**7/168 - t**6/10 + 9*t**5/80 + 45*t**4/8 - 27*t**3/2 - 243*t**2 - 87*t. Factor q(i).
(i - 6)**3*(i + 3)**2/4
Factor 48*p**2 + 165 + 332*p + 4*p**2 + 21*p**2 + 4*p**3 + 47*p**2 + 51.
4*(p + 1)*(p + 2)*(p + 27)
Let i(j) be the third derivative of -j**8/420 - 4*j**7/315 + j**6/60 + 3*j**5/10 + j**4/2 + 9*j**2. Let p(k) be the second derivative of i(k). Factor p(l).
-4*(l - 1)*(2*l + 3)**2
Let h(i) = 7*i**2 + 74*i + 200. Let b(t) = t**2 + 2*t. Let l(a) = 2*b(a) - h(a). Factor l(r).
-5*(r + 4)*(r + 10)
Suppose -5*j + 3*r + 26 = -r, -3*j + 2*r + 16 = 0. Solve -j*k**3 - 12*k**4 - 8*k**4 + 11*k**4 - 3*k**5 = 0.
-2, -1, 0
Let q(a) be the third derivative of -a**8/26880 - a**7/5040 - a**6/2880 + 3*a**4/8 + 6*a**2. Let k(v) be the second derivative of q(v). Factor k(n).
-n*(n + 1)**2/4
Let o(n) = -13*n**3 + 13*n. Let y(a) = -81*a + 7*a**3 + 23*a + 25*a + 26*a. Let b(j) = 6*o(j) + 11*y(j). Factor b(r).
-r*(r - 1)*(r + 1)
Let r(l) = -l**3 - 326*l**2 - 7052*l - 6721. Let i(w) = 6*w**3 + 1632*w**2 + 35260*w + 33606. Let s(y) = -3*i(y) - 14*r(y). Find n, given that s(n) = 0.
-41, -1
Factor -21*q**3 + 83*q**2 + 25*q**3 - 99*q**2 + 12*q.
4*q*(q - 3)*(q - 1)
Let t(z) = -z**3 - 2*z**2 + 1. Let q(n) = -5*n**4 + 25*n**3 + 35*n**2 - 10*n - 15. Let k(j) = q(j) + 15*t(j). Solve k(p) = 0 for p.
-1, 0, 1, 2
Suppose -7*i + 17 + 11 = 0. Let a be (-13 - -14)/(i + -1). Factor -a*o + 1/3*o**4 + 0 + o**2 - o**3.
o*(o - 1)**3/3
Let k(v) = -v**3 + 19*v**2 + 53*v - 658. Let c be k(20). Factor -6/5*h - 1/5*h**c - 9/5.
-(h + 3)**2/5
Factor 0 + 0*v**2 - 24/19*v**3 + 0*v + 2/19*v**5 - 2/19*v**4.
2*v**3*(v - 4)*(v + 3)/19
Let p(v) be the third derivative of v**7/105 + 5*v**6/12 + 4*v**5/5 - 200*v**2. Suppose p(t) = 0. Calculate t.
-24, -1, 0
Let g(o) be the second derivative of 0 + 32/3*o**3 + 25/3*o**4 + 19/5*o**5 + 8*o**2 + 2/21*o**7 + 9*o + 14/15*o**6. Suppose g(v) = 0. What is v?
-2, -1
Let r(q) be the third derivative of -q**6/60 + q**5/3 + 9*q**4/4 - 12*q**3 - 11*q**2 - 7*q. Factor r(w).
-2*(w - 12)*(w - 1)*(w + 3)
Factor 1/2*f**2 + 2*f + 3/2.
(f + 1)*(f + 3)/2
Let j(h) be the second derivative of h**5/25 - 5*h**4/3 - 52*h**3/15 - 16*h + 2. Find i, given that j(i) = 0.
-1, 0, 26
Let c(n) be the first derivative of n**5/25 + 29*n**4/20 + 224*n**3/15 + 98*n**2/5 + 123. Factor c(s).
s*(s + 1)*(s + 14)**2/5
Factor 45 + 808*n - 808*n - 5*n**2.
-5*(n - 3)*(n + 3)
Factor -3*f**3 - 33*f**2 - 21*f**2 + 10*f**2 + 5*f**3.
2*f**2*(f - 22)
Let h(l) be the first derivative of -l**3/18 + 31*l**2/3 - 1922*l/3 - 2. What is v in h(v) = 0?
62
Suppose 5*i = 3*i - 6, 2*j - 33 = -3*i. Suppose j = 7*z - 0*z. Let 5*t**3 - 4*t**3 - 5*t**2 - 9 + 24*t + 7*t**z - 17*t**2 - t**4 = 0. Calculate t.
1, 3
Factor -926100 + 26208*g**2 + 1256/5*g**3 + 4/5*g**4 + 899640*g.
4*(g - 1)*(g + 105)**3/5
Let w(u) = 4*u**2 + 20*u + 100. Let y(c) = 40*c + 12 + 7*c**2 + 0*c**2 + 188. Let z(o) = -5*w(o) + 3*y(o). Solve z(s) = 0.
-10
Let m be ((-34)/(-30) - 1)/((-149)/(-1788)). Let i(c) be the first derivative of -m*c**5 - 2 + 0*c**3 + 2/3*c**6 + 0*c**2 + c**4 + 0*c. Factor i(a).
4*a**3*(a - 1)**2
Let g(j) be the third derivative of 11*j**2 + 1/192*j**4 - 1/480*j**5 + 0*j**3 + 0*j + 0. Find m, given that g(m) = 0.
0, 1
Factor 121/4*i**3 - 4 + 45*i - 132*i**2.
(i - 4)*(11*i - 2)**2/4
Let t(l) = -41*l**3 - 289*l**2 - 243*l + 15. Let p(n) = -120*n**3 - 866*n**2 - 728*n + 46. Let d(z) = -5*p(z) + 14*t(z). Find r, given that d(r) = 0.
-10, -1, 1/13
Let -68*n + 92*n + 32 - 21*n**3 - 28*n**2 - 4*n**3 + n**3 - 4*n**4 = 0. Calculate n.
-4, -2, -1, 1
Let c(j) be the second derivative of 5*j**4/12 + 5*j**3 - 152*j. What is p in c(p) = 0?
-6, 0
Let v = 51 - 48. Factor 3*z**2 - v*z**2 + 8*z - z**2 + 3*z**2.
2*z*(z + 4)
Let w = 13 - 11. Let f be -2 + 1 - (-8 + 4). Solve -7*a**4 - 4*a**3 + 2*a + 7*a**w + 4*a**f - 5*a**3 + 3*a**3 = 0 for a.
-1, -2/7, 0, 1
Let w(c) be the third derivative of -1/1344*c**8 - 1/24*c**4 - 1/140*c**7 + 0*c**3 - 13/480*c**6 - 27*c**2 - 1/20*c**5 + 0 + 0*c. Factor w(r).
-r*(r + 1)**2*(r + 2)**2/4
Let w(n) = -n**2 - 4*n + 6. Let p be w(-4). Suppose 16*d - p = 13*d. Find j, given that 1 - 2*j**2 - 2*j + 8*j**2 - 5*j**d = 0.
1
Let s be 5*(-76)/(-28) + -13. Factor -s*v**3 + 0 - 4/7*v**4 + 4/7*v**2 + 4/7*v.
-4*v*(v - 1)*(v + 1)**2/7
Factor 1/4*d**3 - 71/4*d - 17/2*d**2 - 9.
(d - 36)*(d + 1)**2/4
Let x(d) be the second derivative of -d**4/3 + 18*d**3 - 252*d**2 - 25*d + 10. Let x(p) = 0. Calculate p.
6, 21
Let u = 492 - 492. Let u - 4/9*o**2 - 2/9*o**3 - 2/9*o = 0. Calculate o.
-1, 0
Let m(s) be the second derivative of 0 - 2*s + 0*s**4 + 0*s**3 + 0*s**2 + 1/70*s**5. Let m(l) = 0. What is l?
0
Let z be 589/95 - 2/10. Factor -3*q + 14*q + 15*q - z*q - 15 - 5*q**2.
-5*(q - 3)*(q - 1)
Let g(m) be the second derivative of m**7/1890 + m**6/270 + 23*m**4/12 + 10*m. Let w(t) be the third derivative of g(t). Let w(i) = 0. What is i?
-2, 0
Let v(y) be the second derivative of -y**6/420 + y**5/35 - y**4/7 + 8*y**3/21 + 29*y**2/2 + 25*y. Let w(f) be the first derivative of v(f). Factor w(s).
-2*(s - 2)**3/7
Let k be -14 + 25 + (-1326)/130. Find n such that 2/5*n**2 + 1/5*n**4 - k*n**3 + 4/5*n - 3/5 = 0.
-1, 1, 3
Suppose s - 2*j = -53, 0*s + 4*s - 3*j = -192. Let v = s + 66. Factor 6*u - 7*u**2 - v*u**4 - 6*u**3 - 3 + 3 + 28*u**2.
-3*u*(u - 1)*(u + 1)*(7*u + 2)
Solve 2601 + 1/4*t**2 + 51*t = 0.
-102
Suppose 0 = 2*k + f - 8, 2*k - 5*f = -0*f - 16. Factor 0*s**2 - s**2 + 6*s - 3*s**2 + 6*s**k.
2*s*(s + 3)
Let k(x) = -16*x**3 + 797*x**2 - 1264*x - 427. Let r(b) = 17*b**3 - 796*b**2 + 1268*b + 428. Let z(j) = -4*k(j) - 5*r(j). Suppose z(a) = 0. What is a?
-2/7, 2, 36
Let w(h) be the first derivative of -4*h**3 + 23/18*h**4 + 4*h**2 - 16/9*h + 10 + 8/15*h**5 - 1/3*h**6. Let w(q) = 0. Calculate q.
-2, 2/3, 1
Let v(q) be the second derivative of -q**9/10080 + q**8/4480 - q**4 - 2*q. Let p(c) be the third derivative of v(c). Factor p(x).
-3*x**3*(x - 1)/2
Let m(o) = -210*o**2 + 1485*o + 405. Let u(y) = 15*y**2 - 106*y - 29. Let d(q) = 2*q**2 + 14*q - 3. Let r be d(4). Let k(x) = r*u(x) + 6*m(x). Factor k(h).
5*(h - 7)*(3*h + 1)
Let o = 215 - 415/2. Let x(z) be the first derivative of 20*z**3 - 6 + o*z**4 + 20*z**2 + z**5 + 0*z. Factor x(k).
5*k*(k + 2)**3
Let h(f) be the third derivative of f**7/2520 - f**6/270 + f**5/72 - f**4/36 - 2*f**3/3 + 3*f**2. Let z(g) be the first derivative of h(g). Factor z(r).
(r - 2)*(r - 1)**2/3
Let c = 2175/7 + -2172/7. Solve 0*s - c*s**2 + 0 = 0.
0
Let i(b) = 55*b**3 + 90*b**2 - 140*b - 300. Suppose -3*n - n = -80. Let a(r) = 8*r**3 + 13*r**2 - 20*r - 43. Let s(w) = n*a(w) - 3*i(w). Factor s(q).
-5*(q - 2)*(q + 2)**2
Suppose -33*j + 9*j**3 - 387*j**4 + 24*j**3 - 36 + 384*j**4 + 39*j**2 = 0. Calculate j.
-1, 1, 12
Let p(g) = g**3 - 33*g**2 - 5*g + 165. Let m be p(33). Factor -1/9*s**4 + 0 + 0*s**2 - 2/9*s**3 + m*s.
-s**3*(s + 2)/9
What is t in -24/11 - 26/11*t**2 - 1/11*t**3 - 49/11*t = 0?
-24, -1
Determine x, given that -119 + 91 - 3*x**2 - 4*x**2 - 3*x**2 + 74*x = 0.
2/5, 7
Let c(j) be the second derivative of -j**6/15 + 2*j**5/5 + 5*j**4/6 - 12*j**3 + 36*j**2 + 59*j. Suppose c(g) = 0. Calculate g.
-3, 2, 3
Factor -4*u**2 - 34*u - 45*u - 89*u - 1764.
-4*(u + 21)**2
Let n(v) be the third derivative of -v**5/60 + 19*v**4/8 + 301*v**2. Factor n(b).
-b*(b - 57)
Let s(l) = -5*l**4 - 77*l**3 + 8*l**2 + 86*l. Let q(o) = -10*o**4 - 155*o**3 + 15*o**2 + 170*o. Let x(n) = -3*q(n) + 5*s(n). Factor x(b).
5*b*(b - 1)*(b + 1)*(b + 16)
Let q(i) be the third derivative of -i**9/16632 - i**8/4620 - i**7/4620 - i**3/3 - 17*i**2. Let g(z) be the first derivative of q(z). Factor g(t).
-2*t**3*(t + 1)**2/11
Let v(c) be the third derivative of -c**6/540 - c**5/18 - 110*c**2 - 1. Determine l, given that v(l) = 0.
-15, 0
Let h = -294011/26966 + 619/97. Let j = -3/139 - h. Solve -d - j*d**2 - 7/2*d**3 + 0 = 0 for d.
-1, -2/7, 0
Factor 33/4*h**2 + 87/4*h - 9.
3*(h + 3)*(11*h - 4)/4
Determine u so that 8/5*u + 3 + 1/5*u**2 = 0.
-5, -3
Let i(l) be the third derivative of -l**8/84 + 2*l**7/105 + 2*l**6/15 - 4*l**5/15 + 29*l**2. Solve i(r) = 0.
-2, 0, 1, 2
Let u(q) = 21 - 7*q - q**3 - 14 - 7*q**3 - 5*q**3 - 7*q**2. Let c = 4 + -7. Let a(t) = -6*t**3 - 3*t**2 - 3*t + 3. Let 