*m**3/12 - 17*m**2/2 - 65*m. Find k such that x(k) = 0.
-34, -1
Find h such that 16*h**3 + 4/5*h**4 + 396/5*h**2 - 80 - 16*h = 0.
-10, -1, 1
Let j(h) be the third derivative of -h**5/300 - h**4/12 - 5*h**3/6 + 2*h**2 + 57. Factor j(n).
-(n + 5)**2/5
Let b be (88/(-770))/((-5)/25). Factor -b*s**2 - 4/7*s + 8/7.
-4*(s - 1)*(s + 2)/7
Factor 18/5*k**3 - 112/5 + 344/5*k - 276/5*k**2.
2*(k - 14)*(3*k - 2)**2/5
Let v be 28/35*(-30)/(-12). Let x = 169/12 + -40/3. Determine b so that b**3 - x*b**4 - 1/4*b**v + 0*b + 0 = 0.
0, 1/3, 1
Let i be (78/27 + -4)/(70/(-42)). Determine c so that -80/3*c - 32/3 - 22*c**2 - i*c**4 - 20/3*c**3 = 0.
-4, -1
Factor 46/5*c + 28/5 + 4*c**2 + 2/5*c**3.
2*(c + 1)*(c + 2)*(c + 7)/5
Let q = 79/45 - 14/9. Let a(t) be the second derivative of q*t**2 - 2/15*t**3 - t + 1/30*t**4 + 0. Factor a(r).
2*(r - 1)**2/5
Suppose -15 - 33 = -6*n. Factor 2*k**2 - 471*k + 475*k - 5*k**3 - n + 4*k**3.
-(k - 2)**2*(k + 2)
Factor -17/2*a - 1/6*a**4 + 65/6*a**2 + 0 - 13/6*a**3.
-a*(a - 3)*(a - 1)*(a + 17)/6
Let i(s) be the third derivative of -s**5/12 - 115*s**4/24 - 35*s**3 + 78*s**2. What is x in i(x) = 0?
-21, -2
Solve 132/13*r**2 + 296/13*r - 2/13*r**4 + 14/13*r**3 + 16 = 0 for r.
-2, 13
Let g = -20 + 34. Let m(v) = -10*v**2 + 0*v**2 - 32*v - 6*v + g - 6*v. Let k(u) = 2*u**2 + 9*u - 3. Let s(y) = 28*k(y) + 6*m(y). Factor s(d).
-4*d*(d + 3)
Find q, given that -9 + 8/3*q**3 + 1/3*q**4 - 14/3*q**2 - 16*q = 0.
-9, -1, 3
Let x = -112968/13 - -8690. Determine t, given that x*t - 2/13*t**3 + 4/13*t**2 - 4/13 = 0.
-1, 1, 2
Let p(u) be the third derivative of u**8/4032 + u**7/336 - 3*u**5/20 + 47*u**2. Let b(h) be the third derivative of p(h). Determine r so that b(r) = 0.
-3, 0
Let x(j) be the second derivative of -35/3*j**3 + 2*j + 65/2*j**2 + 14 + 5/12*j**4. Let x(w) = 0. Calculate w.
1, 13
Let k(t) be the first derivative of -t**6 - 88*t**5/5 - 122*t**4 - 416*t**3 - 704*t**2 - 512*t + 155. Suppose k(f) = 0. What is f?
-4, -2, -2/3
Find x, given that 6 - 57*x**2 - 120*x - 14 - 2 - 2 = 0.
-2, -2/19
Suppose j + 8 = 3*j. Let o(n) = 3*n**2 - 3*n + 6. Let s(w) = 8*w**2 - 8*w + 17. Let i(g) = j*s(g) - 11*o(g). Find v such that i(v) = 0.
-1, 2
Suppose -7*j + 20 + 8 = 0. Suppose -v = j*l - 2, -v = 2*v + 4*l - 6. Factor -4/9*i + 14/3*i**3 - 2/9*i**v + 0.
2*i*(3*i - 1)*(7*i + 2)/9
Let o(l) = -l**2 + l + 1. Let u = -29 - -28. Let d(p) = 25*p**2 - 40*p - 35. Let v(b) = u*d(b) - 30*o(b). Factor v(q).
5*(q + 1)**2
Let q(s) be the first derivative of -s**7/168 - s**6/36 - 25*s**3/3 - 11. Let f(p) be the third derivative of q(p). Factor f(h).
-5*h**2*(h + 2)
Let z be (-1)/((-56)/(-16) - 4). Let o(a) be the third derivative of a**z + 0*a - 1/200*a**6 + 1/150*a**5 + 0*a**4 + 0*a**3 + 0. Factor o(i).
-i**2*(3*i - 2)/5
Factor -3*u**2 - 18*u**3 + 114267*u + 21*u**4 - 114267*u.
3*u**2*(u - 1)*(7*u + 1)
Let u(k) be the first derivative of k**4/4 - 7*k**3/3 - 3*k**2 - 16*k - 21. Let h be u(8). Factor h + 2/7*r + r**2 + 5/7*r**4 + 9/7*r**3 + 1/7*r**5.
r*(r + 1)**3*(r + 2)/7
Let w(v) be the first derivative of v**6/30 + 17*v**5/25 - 9*v**4/10 - 233. Factor w(f).
f**3*(f - 1)*(f + 18)/5
Let u(o) be the third derivative of o**7/280 + o**6/180 - 7*o**5/120 + o**4/12 + o**3/3 + 16*o**2. Let n(l) be the first derivative of u(l). Solve n(k) = 0.
-2, 1/3, 1
Let u(s) be the second derivative of s**6/135 - 8*s**5/45 + 17*s**4/18 - 4*s**3/3 - 270*s - 1. Factor u(m).
2*m*(m - 12)*(m - 3)*(m - 1)/9
Let n(a) be the third derivative of a**8/6720 + 31*a**5/60 - 4*a**2. Let q(j) be the third derivative of n(j). Factor q(p).
3*p**2
Factor 64/5*o**2 - 164/5*o - 4/5*o**3 + 104/5.
-4*(o - 13)*(o - 2)*(o - 1)/5
Let y(r) = -8*r**4 - r**3 + 4*r**2 - 9*r - 3. Let n(l) = 18*l**4 + 3*l**3 - 8*l**2 + 21*l + 7. Let q(v) = -3*n(v) - 7*y(v). Determine o so that q(o) = 0.
-1, 0, 2
Let v = 30517/483010 + 2/4391. Let x(t) be the second derivative of 0*t**2 - 4*t + 1/33*t**4 + 0 - v*t**5 + 1/33*t**6 + 0*t**3. Factor x(m).
2*m**2*(m - 1)*(5*m - 2)/11
Let c = 2984/4503 - -6/1501. Let p be 0 + 3/(-9)*-1. Let g - p*g**2 - c = 0. What is g?
1, 2
Let c(w) be the first derivative of -w**6/10 + 12*w**5/25 - 3*w**4/5 - 69. Let c(b) = 0. What is b?
0, 2
Let d(l) = 7*l**3 + l**2 - l - 7. Let j(t) = 5*t**3 + t**2 - 2*t - 6. Let r(p) = 4*d(p) - 6*j(p). Find y, given that r(y) = 0.
-2, -1, 2
Let w be (-18)/(-117) + 261/78. Factor -1/2*u**3 + 3/2 + 5/2*u**2 - w*u.
-(u - 3)*(u - 1)**2/2
Let y(l) be the second derivative of -l**6/480 - l**5/240 + l**4/48 - 33*l**2/2 - 11*l. Let g(r) be the first derivative of y(r). Factor g(t).
-t*(t - 1)*(t + 2)/4
Let v(w) = -w**3 + w**2 - w + 1. Let q(d) = -4*d**3 - 208*d**2 + 96*d - 16. Let z(g) = q(g) + 16*v(g). What is m in z(m) = 0?
-10, 0, 2/5
Suppose 11*s - 20*s = 54. Let v be (s/9 - (-1)/1)*0. Factor 1/6*u**2 + 1/6*u + v.
u*(u + 1)/6
Let n(q) be the third derivative of 1/150*q**5 - 2/15*q**3 + 0 + 0*q + 7*q**2 - 1/60*q**4. Factor n(t).
2*(t - 2)*(t + 1)/5
Let p(i) be the first derivative of i**5/60 - i**4/24 - 13*i**2/2 - 26. Let x(r) be the second derivative of p(r). Factor x(j).
j*(j - 1)
Factor -5*g + 2*g**3 - 38*g - 3*g**3 + 0*g + 5*g - 39*g**2.
-g*(g + 1)*(g + 38)
Factor -988/5*f - 2/5*f**2 - 122018/5.
-2*(f + 247)**2/5
Let y = 206 + -204. Let w(a) = 5*a**2 + a - 2. Let l be w(-2). Factor -6*b**y - l*b + 16*b - 3*b**3.
-3*b**2*(b + 2)
Let q be (-2)/(7134/(-7062) + 1). Let k = q - 196. Factor k*a**3 + 1/2*a + 1/2*a**2 + 1/6.
(a + 1)**3/6
Let i(u) be the third derivative of u**5/120 + 3*u**4/8 + 27*u**3/4 - 36*u**2. Let i(c) = 0. Calculate c.
-9
Let b = -3630/13 - -25488/91. What is q in 2/7*q**2 + b*q - 8/7 = 0?
-4, 1
Let -14/11*z**4 + 0*z**2 + 2/11*z**5 + 12/11*z**3 + 0 + 0*z = 0. What is z?
0, 1, 6
Let i be (-72)/(-34) - 5/(255/6). Factor -2/3 + 10/3*d**i - 16/3*d**4 - 2/3*d + 8/3*d**5 + 2/3*d**3.
2*(d - 1)**3*(2*d + 1)**2/3
Let d(t) be the first derivative of 3*t**5/25 + 6*t**4/5 + 6*t**3/5 - 12*t**2 + 15*t + 132. Factor d(u).
3*(u - 1)**2*(u + 5)**2/5
Let d(b) be the second derivative of -b**7/21 + b**6/10 + 7*b**5/20 - 3*b**4/4 - 5*b**3/6 + 3*b**2 + 127*b. Solve d(n) = 0.
-3/2, -1, 1, 2
Factor -135*h - 6 + 79*h - 816*h**2 - 86*h + 288*h**3.
2*(h - 3)*(12*h + 1)**2
Suppose -3*w = -5*u - 1301, -4*w = 3*u + 466 + 303. Let x = u - -259. Find z such that x - 4/11*z**2 + 0*z + 6/11*z**3 + 10/11*z**4 = 0.
-1, 0, 2/5
Let f = -898/7 - -3599/28. Determine d, given that f*d + 1/4*d**2 + 0 = 0.
-1, 0
Let f(m) be the second derivative of -12*m**2 - 14*m - m**4 + 22/3*m**3 + 0. What is s in f(s) = 0?
2/3, 3
Find v such that 12*v**2 - 4*v**4 - 306 + 306 + 8*v = 0.
-1, 0, 2
Suppose -15 = -3*v, -3*t - 4*v + 2*v + 43 = 0. Let k be 38/10 - t/(-55). Factor a + 3*a**3 - 12*a**3 + 4*a + k*a**3.
-5*a*(a - 1)*(a + 1)
Let l = 16 - 6. Let x = 14 - l. Factor -8*j**2 - 4*j**x + 0*j**4 - 6 + 6 - 12*j**3.
-4*j**2*(j + 1)*(j + 2)
Let n(h) = 3*h**3 + 14*h**2 + 34*h. Let k(z) = 0*z**3 - 7*z**3 - 101*z - 43*z**2 - 3*z**3. Let a(x) = -4*k(x) - 14*n(x). Factor a(w).
-2*w*(w + 6)**2
Let j(g) be the first derivative of 5*g**4/4 - 25*g**3/3 + 15*g**2/2 + 45*g + 196. Factor j(l).
5*(l - 3)**2*(l + 1)
Let h = -6 + 11. Let y(u) = 72*u + 1. Let x be y(h). Let 219*j**2 + 30 + 375*j**3 - 6 + 180*j - 130*j**2 + x*j**2 = 0. Calculate j.
-2/5
Suppose -14*q + 8*q + 12 = 0. Determine t so that -3 + 2 + 3*t**q + 10*t + 7 - t = 0.
-2, -1
Factor 1823*h**3 + 985*h**3 + 15876*h + 12096*h**2 + 44730*h**4 + 4*h**5 - 44538*h**4.
4*h*(h + 3)**2*(h + 21)**2
Let u(p) be the second derivative of 8*p**7/21 + 14*p**6/5 - 7*p**5/5 - 55*p**4/3 + 18*p**3 + 20*p**2 + 513*p. Let u(i) = 0. What is i?
-5, -2, -1/4, 1
Suppose 18*b - 4 = -0*b + 50. Suppose 25/4*w**4 + 2 - 55/4*w**b + 7*w - 3/2*w**2 = 0. What is w?
-2/5, 1, 2
Let l = 5 - 0. Suppose 3*r = -4*t + 6, -l*t + 0*t + 2*r = -19. Factor -o**2 - 3*o - 12*o**t - 8*o**2 - 4*o**2 - 2*o**2.
-3*o*(o + 1)*(4*o + 1)
Let w(u) be the first derivative of u**6/72 + 17*u**5/60 - 5*u**4/12 - u**3 + 488. Let w(c) = 0. Calculate c.
-18, -1, 0, 2
Let x(u) = -3*u**3 - 1. Let d(o) = 3*o**5 + 21*o**4 - 6*o**3 - 213*o**2 + 120*o + 303. Let p(y) = -d(y) - 3*x(y). Determine r, given that p(r) = 0.
-5, -1, 2
Let f be ((-504)/7)/9*(-1)/14. Determine x, given that -4/7*x**4 - 12/7*x - f*x**2 + 8/7 + 12/7*x