.
2*y*(y - 2)**2*(y + 2)
Suppose 10*r + 94*r - 312 = 0. Let d(y) be the second derivative of -10/21*y**r + 0 - 1/21*y**4 - 12/7*y**2 + 3*y. Find m, given that d(m) = 0.
-3, -2
Let f(s) = 18*s + 75. Suppose 5*o - 9*g + 17 = -6*g, 0 = 3*g + 3. Let a be f(o). Factor 0 + a*x**3 + 15/4*x**2 - 3/4*x**4 + 0*x.
-3*x**2*(x - 5)*(x + 1)/4
Let r(b) be the second derivative of 0*b**2 + 6/7*b**7 + 28*b**4 + 0 + 24*b**3 + 13/5*b**5 - 143*b - 28/5*b**6. Factor r(m).
4*m*(m - 3)**2*(3*m + 2)**2
Let r(l) = l**2 + 16*l + 39. Let c be r(-16). Solve 221*u + 90 - c*u**3 - 126*u**3 + 495*u**2 - 283*u - 25*u**4 - 333*u = 0 for u.
-9, 2/5, 1
Suppose 5*v - 503 - 1852 = -5*q, 4*q + v - 1884 = 0. Factor -648 + q*p**2 - 473*p**2 - 68*p - 4*p.
-2*(p + 18)**2
Let d(l) = -756599*l**2 + 11667*l - 57. Let v(y) = -756601*y**2 + 11668*y - 53. Let a(r) = -2*d(r) + 3*v(r). Factor a(u).
-5*(389*u - 3)**2
Suppose -8*d**5 + 252*d**4 + 2227*d**3 - 1872*d**4 + 13290*d**2 - 27*d**5 - 5640 - 762*d**3 - 16100*d = 0. What is d?
-47, -3, -2/7, 2
Let o(d) be the first derivative of d**6/72 + 2*d**5/9 + 25*d**4/72 - 125*d**3/9 + 5*d**2 - 39. Let i(p) be the second derivative of o(p). Factor i(k).
5*(k - 2)*(k + 5)**2/3
Let r(i) be the second derivative of -29*i**4/6 + 92*i**3/3 - 15*i**2 + 2666*i. Factor r(o).
-2*(o - 3)*(29*o - 5)
Let c = -22888 - -22890. Factor -67/3*r**c - 385*r - 363 - 1/3*r**3.
-(r + 1)*(r + 33)**2/3
Let f = 313/1770 + 289/590. Factor 0 + 8/3*u + f*u**2.
2*u*(u + 4)/3
Let k(t) be the third derivative of -t**7/840 + 43*t**6/480 + 97*t**5/240 - 319*t**4/96 + 15*t**3/2 + 4417*t**2. Let k(y) = 0. Calculate y.
-4, 1, 45
Let h(o) = -o**3 + 7*o - 6. Let l be h(-3). Let u(m) be the third derivative of 3/8*m**4 - 1/20*m**5 - m**3 + m**2 + 0*m + l. Factor u(b).
-3*(b - 2)*(b - 1)
Factor -2/3*n**2 - 352/9 - 16*n + 2/9*n**3.
2*(n - 11)*(n + 4)**2/9
What is k in 3*k**3 + 120 - 813*k - 114 - 414 - 402*k**2 = 0?
-1, 136
Let v(f) be the second derivative of -46*f - 1/18*f**5 - 7/135*f**6 + 0*f**2 + 0 + 0*f**3 - 1/54*f**4 - 1/63*f**7. Suppose v(k) = 0. Calculate k.
-1, -1/3, 0
Let v(h) be the third derivative of -7/300*h**5 + 11/15*h**3 + 75*h**2 + 0 + h - 1/1200*h**6 - 29/240*h**4. What is m in v(m) = 0?
-11, -4, 1
Let t(p) be the second derivative of 1/1620*p**6 + 29/6*p**3 - 47*p + 0 + 0*p**2 + 0*p**5 - 1/27*p**4. Let h(b) be the second derivative of t(b). Factor h(i).
2*(i - 2)*(i + 2)/9
Let d(w) be the first derivative of w**7/4200 - 7*w**6/900 + 13*w**5/600 + 33*w**3 + 171. Let t(u) be the third derivative of d(u). Factor t(a).
a*(a - 13)*(a - 1)/5
Let b(s) be the first derivative of -3*s**5/10 - 81*s**4/8 - 271. Solve b(o) = 0.
-27, 0
Suppose 2/3*s**4 - 410/3*s + 0 + 74/3*s**3 - 338/3*s**2 = 0. Calculate s.
-41, -1, 0, 5
Let a be ((-56)/189)/((-2)/9). Let k(c) be the first derivative of -5*c**2 - 6 - a*c**3 + 6*c. Determine v, given that k(v) = 0.
-3, 1/2
Let o = 926 - 919. Suppose 0*w + 11*w = o*w. Let -2/13*r**4 + 0 + w*r - 4/13*r**3 + 0*r**2 + 2/13*r**5 = 0. Calculate r.
-1, 0, 2
Let b(g) = -g**3 + 9*g**2 + 2*g + 10. Let j be b(9). Suppose 3*k + 5 = -5*w + j, 2*w + 10 = 2*k. Factor -6*q**2 + k*q**3 - 3*q**4 - 7*q**3 - 8*q**3.
-3*q**2*(q + 1)*(q + 2)
Factor -78/7*y + 38/7 + 4/7*y**2.
2*(y - 19)*(2*y - 1)/7
Let q = -3070 - -3077. Let o(s) be the third derivative of -1/12*s**5 - 1/42*s**q + 0*s**4 - 11*s**2 + 0*s**3 + 1/12*s**6 + 0*s + 0. Solve o(u) = 0 for u.
0, 1
What is n in 25/4*n**2 + 16495/4*n - 825 = 0?
-660, 1/5
Let p(i) be the first derivative of -32*i**2 + 48*i + 57 - 68 + 0*i**4 + 4*i**3 + 0*i**4 + i**4 - 140. Factor p(n).
4*(n - 2)*(n - 1)*(n + 6)
Let h(d) = 694*d + 1390. Let u be h(-2). Solve c**3 - 118/9*c**4 + 0 + 4/9*c + 28/9*c**u + 77/9*c**5 = 0.
-2/7, -2/11, 0, 1
Let y be (17/((-238)/6))/((-12)/2). Let z(t) be the first derivative of 15 - y*t**2 - 4/21*t**3 - 1/28*t**4 + 6/7*t. What is c in z(c) = 0?
-3, -2, 1
Let l(y) = -y**2 + 2*y + 2. Let r be l(0). Determine a, given that -2*a**r + 3*a**2 - 12*a + 2*a**2 - 10 - 5*a**2 = 0.
-5, -1
Factor 2*j**2 + 2/3*j**3 - 12*j - 80/3.
2*(j - 4)*(j + 2)*(j + 5)/3
Let k(q) be the first derivative of 3*q**4/4 - 114*q**3 + 9027*q**2/2 + 41772*q - 2499. Factor k(i).
3*(i - 59)**2*(i + 4)
Suppose -156 = 49*u - 10*u. Let i(t) = -16*t**2 - 12*t - 2. Let y(j) = j**3 - 33*j**2 - 24*j - 5. Let g(p) = u*y(p) + 10*i(p). Determine n so that g(n) = 0.
-6, -1, 0
Let q be (15/(765/(-96)))/(20/864). Let v = -406/5 - q. Factor 2/17*a**2 + 0 + v*a.
2*a*(a + 1)/17
Let b(q) be the first derivative of 13*q**5/30 - 31*q**4/8 - 119*q**3/3 + 457*q**2/3 - 44*q + 180. Suppose b(s) = 0. Calculate s.
-6, 2/13, 2, 11
Let c be (-128)/(-1696)*901/102. Factor 8/3*n - 14/3*n**2 + 8 + c*n**3.
2*(n - 6)*(n - 2)*(n + 1)/3
Let n(s) = -s**2 + 13*s + 10. Suppose -11*i = -13*i + 26. Let q be n(i). Determine t, given that 45/2*t + q + 5*t**2 = 0.
-4, -1/2
Let b be (4*52/(-240) - (0 + -1)) + 406/(-3045). Factor 5/6*j**3 - 1/6*j**4 - 7/6*j**2 + b + 1/2*j.
-j*(j - 3)*(j - 1)**2/6
Let o(y) be the first derivative of 3*y**5/35 - 51*y**4/28 - y**3/7 + 51*y**2/14 + 315. Let o(m) = 0. Calculate m.
-1, 0, 1, 17
Determine k so that -2731*k + k**5 - 7394*k + 2520*k**4 + 2*k**5 + 15180*k**2 + 2532 - 10110*k**3 = 0.
-844, 1
Suppose 0 = 24*h - 22*h + 4*x - 22, -3*x + 12 = 0. Suppose h*a - 20 = -4*p + 7*a, a = -5. Factor 4/5*l**2 + 0*l - 18/5*l**3 + p.
-2*l**2*(9*l - 2)/5
Suppose 0 = -633*g + 3006 - 474. Factor 1/2*v**2 + 1/2*v**g + 0 + v**3 + 0*v.
v**2*(v + 1)**2/2
Let t(x) = x**3 + 2*x**2 - 13*x + 3. Let n be t(-4). Factor b**5 - 4*b**5 + 26*b**3 - n*b**3.
-3*b**3*(b - 1)*(b + 1)
Let u = -43 + 29. Let d be 33/7 - 4/u. Let -3/2*j + 6*j**3 - 9*j**2 + 6*j**4 - 9/2*j**d + 3 = 0. Calculate j.
-1, -2/3, 1
Let -56/3*l**4 + 967/3*l**3 + 0 + 1344*l - 1648*l**2 + 1/3*l**5 = 0. Calculate l.
0, 1, 7, 24
Let r(y) = -3 + 5 - 3 + 3. Let q(w) = -6*w**2 - w - 1. Let d(x) = -q(x) - 3*r(x). Let d(h) = 0. What is h?
-1, 5/6
Let z(i) be the first derivative of -i**5 + 95*i**4/4 + 40*i**3 - 190*i**2 - 400*i + 11544. Find s, given that z(s) = 0.
-2, -1, 2, 20
Suppose 67*f - 6 = 88 + 40. Factor -2 - 9/5*u + 1/5*u**f.
(u - 10)*(u + 1)/5
Let z(y) = 586*y**2 + 9650*y + 39310. Let s(p) = 195*p**2 + 3215*p + 13102. Let w(l) = 14*s(l) - 5*z(l). Solve w(k) = 0 for k.
-81/10
Suppose 3*u = 100 - 94. Suppose -72 + 132*c - 16*c**2 + 44*c**2 - 20*c**2 - 28*c**u = 0. What is c?
3/5, 6
Let k(x) = 77*x**4 - 443*x**3 - 1276*x**2 - 844*x. Let n(c) = -67*c**4 + 442*c**3 + 1277*c**2 + 845*c. Let j(d) = 7*k(d) + 8*n(d). Factor j(b).
3*b*(b + 1)*(b + 2)*(b + 142)
Let r(t) be the second derivative of 1/18*t**4 - 24*t - 16*t**2 + 22/9*t**3 + 6. Factor r(a).
2*(a - 2)*(a + 24)/3
Let i(n) = n**2 + 7*n + 12. Let b be i(-9). Let h = b - 28. What is o in o**h + 13 + o - 7 - 4 - 2*o**2 = 0?
-1, 2
Let a = 456821/21 - 21753. What is r in -4/7*r**3 + 8/21*r**2 - 2/21*r + 0 - 2/21*r**5 + a*r**4 = 0?
0, 1
Let k(o) = -4*o**2 + 2*o + 2. Let t(h) = 14*h**2 + 510*h + 33276. Let p(g) = -3*k(g) - t(g). Factor p(x).
-2*(x + 129)**2
Let i(l) be the first derivative of l**3/21 - 31*l**2/7 - 502. Factor i(n).
n*(n - 62)/7
Suppose -2*r - 40 = 1706*i - 1702*i, 3*r = -4*i - 40. Find g such that -24/5*g**3 - 16/5*g + 4/5*g**4 + 36/5*g**2 + r = 0.
0, 1, 4
Let f = -136079/7 - -19441. Find w such that 12/7*w**4 - 12/7*w**2 - 4/7*w**3 + f*w**5 - 4/7*w + 0 = 0.
-1, -1/2, 0, 1
Let u = -4/153013 - -1530206/2907247. Determine a, given that -6/19*a - 4/19 + u*a**2 = 0.
-2/5, 1
Let f be (-5)/(-15) - (-33)/9. Suppose -5 = f*l - 5*l. Let -2*d**3 + 3*d**4 - 3*d**5 - l*d**5 + 7*d**5 = 0. Calculate d.
0, 1, 2
Let s(i) = i**5 + 49*i**4 + 355*i**3 + 825*i**2 - 18*i - 6. Let p(o) = -o**4 + 3*o + 1. Let f(n) = -30*p(n) - 5*s(n). Find c such that f(c) = 0.
-33, -5, 0
Let j = 210/383 - -3126/2681. Let -9/7*o + 0 - 3/7*o**3 + j*o**2 = 0. What is o?
0, 1, 3
Factor 2/9*y**3 + 0*y - 38/9*y**2 + 0.
2*y**2*(y - 19)/9
Let h = 2929/1895880 - 4/11285. Let y(f) be the third derivative of -5*f**2 + 1/420*f**5 - h*f**6 + 1/84*f**4 + 0 + 0*f + 0*f**3. Factor y(u).
-u*(u - 2)*(u + 1)/7
Let q(s) be the first derivative of 0*s**2 - 13*s - 1/15*s**4 + 1/50*s**5 - 26 + 1/15*s**3. Let o(t) be the first derivative of q(t). Factor o(d).
2*d*(d - 1)**2/5
Let y be 5*(8/(-6) - (-28)/12). 