7*w - 40. Let k(m) = 3*a(m) + 25*t(m). Factor k(s).
-5*(s - 4)*(s + 1)*(81*s - 2)
Factor 7*u**2 - 66938 + 1020*u + 33239 + 33407.
(u + 146)*(7*u - 2)
Let r(j) be the second derivative of j**4/28 - 45*j**3/14 - 69*j**2/7 + 11*j - 50. Solve r(z) = 0 for z.
-1, 46
Suppose -28*h + 810 = 75*h + 59*h. Let c(o) be the third derivative of 0*o + 0*o**3 + 0*o**4 - 11*o**2 - 1/96*o**6 + 0 - 1/24*o**h. Solve c(l) = 0 for l.
-2, 0
Let i(s) be the first derivative of -17/3*s**3 - 33/2*s**2 + 1 - 16*s. Let g(l) = 4*l**2 + 8*l + 4. Let r(u) = 9*g(u) + 2*i(u). Solve r(w) = 0 for w.
-2, -1
Let k(h) = 5*h**3 + h**2 + h + 3. Let a(y) = 2*y**4 + 287*y**3 + 1091*y**2 + 1440*y + 500. Let g(w) = a(w) - 8*k(w). Factor g(d).
(d + 2)**2*(d + 119)*(2*d + 1)
Let y(r) be the first derivative of r**3/21 + 334*r**2/7 - 1012. Determine z so that y(z) = 0.
-668, 0
Factor 0 - 2/9*l**4 - 460/3*l - 1384/9*l**3 - 2762/9*l**2.
-2*l*(l + 1)**2*(l + 690)/9
Suppose 0 = 5*l - 2*d + 36, 3*l - 33*d + 22 = -32*d. Let r be 12/(-20) + -6*4/l. Let -r*y**4 - 4/5*y**2 - 2/5*y**5 + 16/5 - 22/5*y**3 + 24/5*y = 0. Calculate y.
-2, -1, 1
Let p(k) be the second derivative of -26*k**2 - 1/3*k**4 - 28/3*k**3 + 0 - 85*k. Factor p(t).
-4*(t + 1)*(t + 13)
Let v = 2646292/7 - 378040. Let h = 7 - 2. What is f in v*f**3 - 2*f - 6/7 + 10/7*f**4 - 4/7*f**2 + 2/7*f**h = 0?
-3, -1, 1
Let y(r) be the second derivative of r**6/100 + 71*r**5/50 - 677*r**4/120 + 97*r**3/30 - 7*r + 366. Determine d so that y(d) = 0.
-97, 0, 1/3, 2
Let f(j) = 37*j + 579. Let c be f(-13). Let d = c + -95. Suppose -3/2*r**2 + 11/8*r + 3/4 - 5/8*r**d = 0. Calculate r.
-3, -2/5, 1
Let l(g) be the second derivative of -g**5/180 - 11*g**4/72 + 15*g**2/2 - 48*g. Let z(n) be the first derivative of l(n). What is y in z(y) = 0?
-11, 0
Let z = -1165460 + 1165462. Determine n, given that -45/4 - 87/4*n - 39/4*n**z + 3/4*n**3 = 0.
-1, 15
Let o(z) = 2*z**2 + 112*z + 39. Let f(i) = 2*i**2 + 114*i + 52. Let w(p) = 3*f(p) - 4*o(p). Determine b, given that w(b) = 0.
-53, 0
Let h = -12 - -15. Suppose h*a - 3 = 0, a = u - 4 - 1. What is o in 43 - 98*o**2 - 71 + u*o**4 - 26*o**3 - 94*o + 0*o**4 = 0?
-1, -2/3, 7
Let v = 13844 - 13844. Factor -36/13*s**2 + v - 10/13*s**3 + 16/13*s.
-2*s*(s + 4)*(5*s - 2)/13
Let j be 7/(-10)*(855/(-105) + 7). Let t(m) = m**3 + 12*m**2 - 65*m - 14. Let i be t(-16). Factor j*b - 2/15*b**i - 2/3.
-2*(b - 5)*(b - 1)/15
Let y(n) be the second derivative of 7/54*n**3 + 0 + 5/6*n**2 - 14*n - 1/54*n**4. Factor y(j).
-(j - 5)*(2*j + 3)/9
Let k(z) = 8*z**2 - 3. Let h be k(1). Suppose 10 = 2*m - 2*n, 2*m + 5*n = 6*n + h. What is d in 0 + 0*d**3 + 0*d + m*d**2 + 2/5*d**4 = 0?
0
Let y(i) be the first derivative of -4*i**3/27 - 64*i**2/9 + 272*i/9 - 1029. Factor y(z).
-4*(z - 2)*(z + 34)/9
Factor -50*r**2 - 21296*r - 5368*r + 62*r**2 + 44435556 - 8*r**2.
4*(r - 3333)**2
Let c(l) be the second derivative of -2*l - 8/7*l**2 + 1/70*l**5 + 109 + 2/3*l**3 - 1/6*l**4. Factor c(z).
2*(z - 4)*(z - 2)*(z - 1)/7
Factor -3*h**5 - 8 - 23*h**4 - 533*h**3 - 500*h**3 - 69*h**2 + 974*h**3 - 38*h.
-(h + 1)**3*(h + 4)*(3*h + 2)
Suppose -4*q + 200 = 2*g, 5*q = -6*g + 4*g + 255. Let u be ((-10)/25)/((-2)/10). Factor -q*x - 5/2*x**u - 605/2.
-5*(x + 11)**2/2
Let m be (2/(-7) - (240/28)/(-2))*1. Let q(c) be the third derivative of -1/30*c**6 + 0*c**5 + 0 + 1/6*c**m - 8*c**2 + 0*c**3 + 0*c. Let q(w) = 0. What is w?
-1, 0, 1
Let g(y) be the third derivative of 1/36*y**4 + 1/315*y**7 + 2/9*y**3 - 7*y**2 + 0 - 1/30*y**5 - 3*y - 1/180*y**6. Determine i, given that g(i) = 0.
-1, 1, 2
Let m = -1/2537766 - -23202433/2537766. Factor 4/7*u**3 + m*u + 4*u**2 + 48/7.
4*(u + 2)**2*(u + 3)/7
Let v(f) = -f**3 + 6*f**2 - 5*f + 4. Let o be v(5). Suppose -13 = -5*p - 3*m, -p - o*m - 11 = -0*m. Factor -5*x + 4 - 4 + 3*x**5 - 8*x**p + 10*x**3.
-5*x*(x - 1)**2*(x + 1)**2
Let l be 1*1/21*450/(-20). Let x = l + 67/56. What is b in x*b**3 + 0 - 1/4*b - 3/8*b**2 + 3/8*b**4 + 1/8*b**5 = 0?
-2, -1, 0, 1
Let b be ((-1989)/26)/(1/(-6)). Let p = b + -456. Factor 18*m**3 + 0 + 9/2*m**2 + 21/2*m**4 - p*m.
3*m*(m + 1)**2*(7*m - 2)/2
Suppose -26450/7 + 15180*t - 107642/7*t**2 + 264*t**3 - 8/7*t**4 = 0. What is t?
1/2, 115
Suppose 308 + 332 = 8*m. Factor 27*v - 77*v**4 + m*v**4 - 81 - 12*v**3 + 33*v - 18*v**2 + 48*v.
3*(v - 3)**2*(v - 1)*(v + 3)
Let w be -1 - (2/(-5) - (-2296)/(-410)). Factor -5/8*v**4 + 1/4*v + 1/8*v**w + 9/8*v**3 - 7/8*v**2 + 0.
v*(v - 2)*(v - 1)**3/8
Let q be (-7)/((-35)/(-4))*-5. Factor -d**q + 16*d**2 - 4*d**5 + 0*d**5 - 6*d**4 - 5*d**4.
-4*d**2*(d - 1)*(d + 2)**2
Factor -80/3 - 122*w - 75*w**2 - 31/3*w**3.
-(w + 2)*(w + 5)*(31*w + 8)/3
Let c = 6076/5 - 1215. Let w = -123 - -123. Factor w + c*j**2 - 1/5*j.
j*(j - 1)/5
Let f(b) be the second derivative of -2 + 9/20*b**5 + 0*b**3 + 19/70*b**7 + 0*b**2 - 18/25*b**6 + 1/10*b**4 + 20*b. Factor f(m).
3*m**2*(m - 1)**2*(19*m + 2)/5
Factor -19509889/5 + 8834/5*p - 1/5*p**2.
-(p - 4417)**2/5
Let i(p) = -3*p**4 + 7*p**3 - 12*p**2 - 13*p + 21. Let b(q) = 7 + 1 - q**4 + 3*q**3 + 3 - q - 5*q - 1 - 6*q**2. Let o(h) = -5*b(h) + 2*i(h). Factor o(a).
-(a - 2)*(a - 1)*(a + 2)**2
Let m be 10/(80/28)*2. Factor -16 - x**2 - 3*x**2 - 4*x**2 + m*x**2 - 8*x.
-(x + 4)**2
Let t = -130 - -134. Suppose -4*l = -t*y, -4*l - 13*y + 8*y + 18 = 0. Factor -2*o + 1/11*o**l + 11.
(o - 11)**2/11
Let j be 0 - 1914/(-4) - 21/(-42). Let b = -479 + j. Determine s, given that 0*s - 1/6*s**2 + b = 0.
0
Let l(a) be the third derivative of a**6/160 + 11*a**5/20 + 437*a**4/32 - 529*a**3/4 - 12359*a**2. Suppose l(x) = 0. What is x?
-23, 2
Let i(k) be the second derivative of 49*k - 1/180*k**6 - 1/120*k**5 + 5/24*k**4 + 1 - 9/2*k**2 + 1/4*k**3. Solve i(t) = 0 for t.
-3, 2, 3
Let q(g) be the third derivative of g**7/630 - g**6/45 + 2*g**5/15 - g**4/4 - g**3/3 + 10*g**2. Let h(a) be the second derivative of q(a). Solve h(l) = 0.
2
Suppose 34*k - 35*k = 48. Let i = k + 96. Find x, given that -68*x**2 + 196*x**5 + i*x**4 + 18*x**4 + 4 - 20 - 292*x**3 + 18*x**4 + 96*x = 0.
-1, 2/7, 1
Let l = 3381 - 3375. Let u(z) be the second derivative of -3*z + 1/3*z**4 - 4/3*z**3 + 2/3*z**7 + 0 + 3*z**5 + 38/15*z**l + 0*z**2. Suppose u(c) = 0. What is c?
-1, 0, 2/7
Let g(d) be the first derivative of -16/3*d - 8/9*d**3 + 10/3*d**2 + 277 + 1/12*d**4. Factor g(y).
(y - 4)*(y - 2)**2/3
What is u in 92*u**5 - 110*u + 19*u**3 - 35*u**5 + 65*u**2 - 40*u - 33*u**5 - 25*u**5 - 5*u**4 = 0?
-5, 0, 2, 3
Let u = -1190 - -5954/5. Let j = 598/5 - 118. Find k, given that -u*k + j - 2/5*k**2 + 1/5*k**3 = 0.
-2, 2
Let u = -245 + 257. Let d = -12 + 15. Factor -2*f**2 + 7*f**2 + 3*f**3 + u - 17*f**2 - d*f.
3*(f - 4)*(f - 1)*(f + 1)
Let v(j) be the second derivative of j**7/315 + 8*j**6/75 + 7*j**5/50 - 23*j**4/45 - 2*j - 189. Find x, given that v(x) = 0.
-23, -2, 0, 1
Let f be (-2 + -572)*(-306)/357. Let w be ((-123)/f)/(1/(-6)). Factor 3/2 - w*t**2 - 3/4*t**3 + 3/4*t.
-3*(t - 1)*(t + 1)*(t + 2)/4
Suppose -225 = -4*m + v + 60, -2*m + 143 = -v. Suppose 18*q + m = 125. Factor 24/5*g - 16/5 - 9/5*g**2 + 1/5*g**q.
(g - 4)**2*(g - 1)/5
Let a(i) be the first derivative of -i**6/72 - i**5/12 + 25*i**4/8 + 2*i**3/3 - 47*i - 23. Let g(q) be the third derivative of a(q). Factor g(h).
-5*(h - 3)*(h + 5)
Let a be ((6 - 22) + 14)/(1684/6). Let w = a + 1269/842. Find u such that -w - 3/4*u**3 + 9/4*u + 0*u**2 = 0.
-2, 1
Let f be 5/10 + (-3 - 10/(-4)). Find u such that 7*u**2 - 160 - 28*u - 52*u - 3*u**2 + f*u**3 + 5*u**3 + 6*u**2 = 0.
-4, -2, 4
Let m(k) = -4*k**4 - 58*k**3 - 164*k**2 - 176*k - 51. Let w(o) = 12*o**4 + 175*o**3 + 494*o**2 + 527*o + 156. Let l(d) = 8*m(d) + 3*w(d). Factor l(y).
(y + 1)**2*(y + 12)*(4*y + 5)
Suppose -2408 = -6*i + 178. Factor -188*x**5 - 837*x**4 + 1065*x**3 - 12 + 61*x - 603*x**2 + 83*x + i*x**5.
3*(x - 1)**3*(9*x - 2)**2
Solve -504/5 + 231/5*j**2 + 3/5*j**4 + 48/5*j**3 + 222/5*j = 0.
-7, -6, -4, 1
Let z be 1 + 14 + -4 - (-24)/(-4). Let z*b**5 - b + 2192*b**3 - 2217*b**3 + b - 20*b**4 = 0. What is b?
-1, 0, 5
Determine w so that -55*w**2 - 97693*w**4 + 90*w**3 + 97684*w**4 + 439*w**2 - 3*w**5 + 288*w = 0.
-4, -1, 0, 6
Let g(v) be the second derivative of -v**5/15 + 3*v**4 - 34*v**3/3 - 67*v**2/2 - 110*v. Let c(r) be the first derivative of g(r). Determine t so that c(t) = 0.
1, 17