 p(u) be the second derivative of -7*u**5/6 + 37*u**4/18 - 2*u**3/9 - 1199*u. Factor p(k).
-2*k*(k - 1)*(35*k - 2)/3
Let o(d) = -2 + 28*d**2 + 13*d**2 - 5*d - 40*d**2. Let a be o(6). Determine u, given that 4/7*u - 2/7*u**2 + 0 + 2/7*u**a - 4/7*u**3 = 0.
-1, 0, 1, 2
Determine c, given that 93/4 + 3/4*c**3 + 87/4*c**2 - 183/4*c = 0.
-31, 1
Let m(f) be the first derivative of 11/5*f**3 - 21/10*f**2 - 12/5*f + 88. Factor m(z).
3*(z - 1)*(11*z + 4)/5
Let n(f) = 15*f**2 - 32*f - 184. Let u(j) = 7*j**2 - 15*j - 93. Let y(q) = -6*n(q) + 13*u(q). Let h be y(-9). Factor 0 - 9/2*d**2 - 3/2*d**3 - h*d.
-3*d*(d + 1)*(d + 2)/2
Suppose -330 = -9*v - 2*v. Suppose 5*d - 15*d + v = 0. Suppose -4/7*u**d + 12/7*u**2 + 16/7*u + 0 = 0. Calculate u.
-1, 0, 4
Let g(w) be the first derivative of 2*w**3/3 - 33*w**2 - 140*w - 1848. Factor g(u).
2*(u - 35)*(u + 2)
Let w be 28/4 + 276/(-40). Let p(y) be the first derivative of 20 + 1/6*y**3 + 0*y - w*y**5 + 1/4*y**2 - 1/8*y**4. Factor p(x).
-x*(x - 1)*(x + 1)**2/2
Let t(j) be the first derivative of -3/8*j**2 - 1/24*j**6 + 3/10*j**5 - 28 + 5/6*j**3 - 3/4*j**4 + 0*j. Solve t(m) = 0 for m.
0, 1, 3
Find t, given that -1/7*t**3 - 143/7*t - 24/7*t**2 + 0 = 0.
-13, -11, 0
Let t(d) = -d**3 - 2*d**2 + 6*d + 1. Let i(z) = 11*z**3 + 61*z**2 + 150*z - 10. Let r(k) = i(k) + 10*t(k). Let r(j) = 0. What is j?
-35, -6, 0
Let c(h) be the second derivative of -h**8/1344 - h**7/210 + h**6/160 + 3*h**5/40 - 79*h**2 - h + 164. Let m(j) be the first derivative of c(j). Factor m(b).
-b**2*(b - 2)*(b + 3)**2/4
Let v(x) be the first derivative of x**3/15 - 112*x**2 + 62720*x + 1698. Determine u, given that v(u) = 0.
560
Let i(o) be the second derivative of o**5/25 - 2482*o**4/15 + 617024*o**3/3 - 1230080*o**2 + 10*o - 33. Factor i(a).
4*(a - 1240)**2*(a - 2)/5
Factor 471*m + 1/2*m**2 + 941/2.
(m + 1)*(m + 941)/2
Suppose -3*j = h - 6, -3*j + 6 = -0*j + 5*h. Let r = -4491/2 - -103301/46. Suppose 6/23*n + r + 2/23*n**j = 0. What is n?
-2, -1
Let s be (102/(-170))/(3/(-5))*(12 - 12). Factor 1/4*u**3 - 1/12*u**5 + s*u**4 + 0*u - 1/6*u**2 + 0.
-u**2*(u - 1)**2*(u + 2)/12
Suppose 0 = 4*x - 499 - 141. Let j = x - 479/3. Factor 5/3*c**2 + 2/3*c + j*c**4 + 4/3*c**3 + 0.
c*(c + 1)**2*(c + 2)/3
Suppose -24 - 1/2*u**4 + 18*u**2 + 2*u + 9/2*u**3 = 0. Calculate u.
-2, 1, 12
Let x be ((-5)/70)/((-1875)/(-90) + -21). What is o in 0 + 18/7*o**3 + x*o**5 + 3/7*o - 12/7*o**2 - 12/7*o**4 = 0?
0, 1
Let l(d) be the second derivative of 5*d**4/9 - 4534*d**3/27 + 604*d**2/9 - d + 2025. Let l(f) = 0. What is f?
2/15, 151
Suppose 40*d - 23*d = 3 + 99. Let u(r) be the third derivative of -9*r**2 - 1/660*r**d + 0 + 0*r**3 + 1/330*r**5 + 0*r + 1/66*r**4. Factor u(q).
-2*q*(q - 2)*(q + 1)/11
Let x(p) be the first derivative of -2/5*p**5 - p**4 + 5 - 2/3*p**3 + 0*p**2 + 0*p. Let x(z) = 0. Calculate z.
-1, 0
Let f(c) be the first derivative of -5*c**3/3 + 895*c**2 - 160205*c - 671. Factor f(t).
-5*(t - 179)**2
Let g = 2455 - 2465. Let f be (-4)/g*-22*(-70)/231. Factor 0*a + f*a**2 + 2*a**4 + 0 + 20/3*a**3 - 3*a**5.
-a**2*(a - 2)*(3*a + 2)**2/3
Let p be ((-6)/60)/(129/(-430)). Let w(y) be the second derivative of -p*y**4 - 38*y + 0 - 8/3*y**3 - 8*y**2. Let w(j) = 0. Calculate j.
-2
Let o = -1393 + 1395. Let w(f) = -f**3 + 9*f**2 - 9*f + 10. Let l be w(8). Solve -6 + 0*y**o + 6 + 3*y**l + 6*y = 0 for y.
-2, 0
Let t(a) be the second derivative of a**6/225 - 19*a**5/150 - 31*a**4/15 + 188*a**3/9 - 200*a**2/3 + 7046*a. Determine w, given that t(w) = 0.
-10, 2, 25
Let j(p) be the first derivative of p**5/15 - 19*p**4/6 + 40*p**3 + 19*p**2/3 - 361*p/3 - 5455. Determine k, given that j(k) = 0.
-1, 1, 19
Let v be ((-45)/(-30))/((-4)/32 + (-35)/(-40)). Factor 2/5*m**4 - 2/5*m**v + 0*m + 2/5*m**5 + 0 - 2/5*m**3.
2*m**2*(m - 1)*(m + 1)**2/5
Let j(v) be the second derivative of v**6/90 + 5*v**5/12 - 121*v**4/36 - 4237*v**3/18 + 722*v**2 + 898*v + 3. Find w such that j(w) = 0.
-19, 1, 12
Find s, given that 261*s**2 + 990*s - 260*s**2 - 965*s = 0.
-25, 0
Suppose -3*b - 1417 - 3173 = 0. Let c = b + 1532. Suppose -c*l + 1/2*l**2 + 2 = 0. What is l?
2
Let i(j) be the second derivative of -j**9/68040 - j**8/5040 - j**7/945 - j**6/405 + 49*j**4/12 - j - 5. Let f(a) be the third derivative of i(a). Factor f(u).
-2*u*(u + 2)**3/9
Let q be (13 + (-17 - -5))*(-5)/(-1). Factor -15*m**5 - 9*m**3 + 1755*m + m**q + 1620 + 540*m**2 - 21*m**3 + 9*m**5 - 40*m**4.
-5*(m - 4)*(m + 3)**4
Let i(f) = f**3 - f**2 + 2*f + 90. Let p be i(0). Let g = p - 86. Suppose -3/5*r**5 + 0 + 6/5*r + 3*r**2 + 9/5*r**3 - 3/5*r**g = 0. What is r?
-1, 0, 2
Suppose -76 = 100*r - 138*r. Let d(g) be the second derivative of 1/4*g**4 + 3*g**r - 8*g - 3/2*g**3 + 0. Factor d(y).
3*(y - 2)*(y - 1)
Factor -46*n - 27*n - n - 620 - n**2 - 55*n.
-(n + 5)*(n + 124)
Let g(n) be the second derivative of 0*n**2 - 2 + 7/66*n**4 + 2/11*n**3 + 1/110*n**5 - 8*n. Factor g(s).
2*s*(s + 1)*(s + 6)/11
Determine p, given that 510/7*p + 450/7 + 2/7*p**3 + 62/7*p**2 = 0.
-15, -1
Let v be (558/837)/((-1)/2*(-9 - -1)). Let c be 9 + (-98)/10 - 58/(-60). Solve -u**3 + 8/3 + c*u**4 + 4*u + v*u**2 = 0 for u.
-1, 4
Let a(n) be the second derivative of -3/17*n**3 + 285*n - 1/102*n**4 - 20/17*n**2 + 0. Let a(x) = 0. What is x?
-5, -4
Let 0 - 1/10*d**4 - 34/5*d - 7*d**3 - 137/10*d**2 = 0. What is d?
-68, -1, 0
Factor -1/5*z**5 + 24/5*z**4 + 0*z + 0 + 0*z**2 + 117*z**3.
-z**3*(z - 39)*(z + 15)/5
Factor 141957*g**2 - 70974*g**2 + 13811220 + 16620*g - 70978*g**2.
5*(g + 1662)**2
Let j(g) be the third derivative of -g**7/1260 + 9*g**6/20 - 2187*g**5/20 + 5*g**4/8 + 21*g**2 + 8. Let b(i) be the second derivative of j(i). Factor b(l).
-2*(l - 81)**2
Factor -2/3*t**2 - 28/3*t + 48.
-2*(t - 4)*(t + 18)/3
Let j(x) be the third derivative of -2*x**7/21 + 493*x**6/30 - 4254*x**5/5 + 4896*x**4 + 9216*x**3 + 4*x**2 + 335. Suppose j(w) = 0. What is w?
-2/5, 3, 48
Let l(i) = 3*i**3 + 3*i**2 - 3*i + 1. Let a(o) = -7*o**3 - 6*o**2 + 9*o - 2. Let w(y) = -2*a(y) - 5*l(y). Let w(u) = 0. What is u?
-1
Let h be (4125/(-6600))/(5/(-12)) + (-5)/6. Factor h*o + 1/3*o**2 + 0.
o*(o + 2)/3
Let d(z) be the second derivative of -z**8/1344 - z**7/120 - z**6/30 - z**5/20 + 11*z**2 - 11*z. Let p(u) be the first derivative of d(u). Solve p(h) = 0 for h.
-3, -2, 0
Let o(v) = 14*v**2 + 976*v - 1634. Let i(b) = -5*b**2 - 331*b + 546. Let x(z) = 11*i(z) + 4*o(z). Solve x(c) = 0.
-265, 2
Let a(m) be the third derivative of m**6/24 - 137*m**5/60 - 59*m**4/6 + 58*m**3/3 - 780*m**2. What is i in a(i) = 0?
-2, 2/5, 29
Let h(s) be the second derivative of 24025/4*s**4 + 0 + 310*s**3 + 6*s**2 + 57*s. Factor h(f).
3*(155*f + 2)**2
Suppose 2*s = 5*k - 9, k + 0*s - 5 = 2*s. Let o be k + 1 + 1 - (-108 + 107). Factor 4/7*q**o + 32/7*q**3 + 72/7*q**2 + 64/7*q + 20/7.
4*(q + 1)**3*(q + 5)/7
Suppose -104*h = -100*h - 68. Suppose 16*a**3 - 3*a**2 + 12*a + 2*a**4 - h*a**2 + 46*a**2 = 0. Calculate a.
-6, -1, 0
Let z(v) be the second derivative of v**4/12 + 5*v**3/2 + 27*v**2 + 7*v - 231. Factor z(x).
(x + 6)*(x + 9)
Let c be ((-132)/(-15)*5/(-3))/(246/(-369)). Let b(x) be the first derivative of -c*x**2 + 4/3*x**3 - 31 + 0*x. Factor b(a).
4*a*(a - 11)
Suppose d = -5*j - 7 + 4, -2*j = d. Factor -4*p**3 + p**2 + 0*p**d + 15*p**4 - 26*p**4 - p**5 + 5*p**3 + 10*p**4.
-p**2*(p - 1)*(p + 1)**2
Let a(r) be the first derivative of -r**6/4 - 21*r**5/5 - 33*r**4/8 + 13*r**3 + 2023. Determine w, given that a(w) = 0.
-13, -2, 0, 1
Let b = 163851 - 491551/3. Find c such that 0*c - 1/6*c**3 + 7/6*c**2 - b - 1/2*c**4 + 1/6*c**5 = 0.
-1, 1, 2
Let m(j) be the third derivative of -j**6/30 + j**5/5 + 8*j**4/3 - 32*j**3 - 1089*j**2. Find x, given that m(x) = 0.
-4, 3, 4
Suppose -32*t + 36*t = 16, 5*w + 4*t - 491 = 0. Let m = 197/2 - w. Find h such that m + 4*h + 1/2*h**2 = 0.
-7, -1
Factor -4*p**2 + 687 + 965 - 296 - 440*p.
-4*(p - 3)*(p + 113)
Let s(p) = -225*p**2 + 21295*p - 10485. Let r(x) = 16*x**2 - 1521*x + 749. Let y(t) = 85*r(t) + 6*s(t). Let y(i) = 0. What is i?
1/2, 151
Let g(k) be the first derivative of k**4/44 - k**3/33 - 28*k**2/11 + 190. Factor g(i).
i*(i - 8)*(i + 7)/11
Suppose 6*z - 16 = -4*d, 7*d + 6 = 5*z + 3*d. Let g(l) be the second derivative of 1/16*l**4 - 1/80*l**5 + 1/8*l**z - 1/8*l**3 + 0 + 21*l. Factor g(n).