 -2/81, 0
Factor 4/3*t**2 + 250/3 + 502/3*t.
2*(t + 125)*(2*t + 1)/3
Solve 110889/2*w**5 + 40959/2*w**4 + 0 + 684*w**3 + 0*w + 6*w**2 = 0.
-1/3, -2/111, 0
Let p(q) be the first derivative of 2*q**3/33 + 736*q**2/11 + 1470*q/11 - 321. Factor p(a).
2*(a + 1)*(a + 735)/11
Suppose 0 = -2*h + s - 13, 4*s + 35598 = 4*h + 35662. Factor 12 - 15/2*u**2 - h*u - 3/2*u**3.
-3*(u - 1)*(u + 2)*(u + 4)/2
Let x(a) be the third derivative of a**5/150 - 5*a**4/2 - 151*a**3/15 - 1404*a**2. Determine v, given that x(v) = 0.
-1, 151
Let d be -6*12/360*-10. Suppose 3*l - 2 - 3 = -5*t, -2*l + 4 = 4*t. Factor 0 - 6/17*m**3 + l*m + 0*m**d - 2/17*m**4.
-2*m**3*(m + 3)/17
Let g(k) be the first derivative of -k**4/26 + 38*k**3 - 14079*k**2 + 2318342*k - 1491. Factor g(s).
-2*(s - 247)**3/13
Let l = 457 + -456. Let o be -6 - (-3 + l)/((-56)/(-232)). Factor o*u**2 + 0*u + 0 - 4/7*u**3.
-4*u**2*(u - 4)/7
Suppose -1376*c + 10*c**2 - 18*c**2 - 1380 + 0*c**2 + 2*c**2 + 10*c**2 = 0. What is c?
-1, 345
Let y(a) be the second derivative of 0*a**5 + 0 + 7/36*a**4 - 42*a - 1/3*a**3 + 0*a**2 - 1/90*a**6. Factor y(r).
-r*(r - 2)*(r - 1)*(r + 3)/3
Let 73*d**3 - 1936*d**5 + 33*d**2 + 1943*d**5 - 110*d**4 - 3*d**2 = 0. What is d?
-2/7, 0, 1, 15
Let v = -154019/2 + 77010. Factor 0 + 1/5*i**2 + v*i.
i*(2*i + 5)/10
Let n(b) be the third derivative of b**8/12600 + 17*b**7/4200 - 13*b**6/1800 + 41*b**5/30 + 10*b**2. Let y(k) be the third derivative of n(k). Factor y(u).
2*(u + 13)*(4*u - 1)/5
Factor 1196/5*j - 2/5*j**2 - 178802/5.
-2*(j - 299)**2/5
Factor -2/11*t + 332/11*t**4 + 336/11*t**2 + 0 - 666/11*t**3.
2*t*(t - 1)**2*(166*t - 1)/11
Solve -2/3*q**4 - 20*q + 0 - 62/3*q**2 - 20/3*q**3 = 0 for q.
-5, -3, -2, 0
Let x(c) = 155*c + 788. Let f be x(-5). Let u(y) be the third derivative of 0 + f*y**2 + 0*y + 1/15*y**5 + 2/3*y**3 - 1/3*y**4. Factor u(v).
4*(v - 1)**2
Let s(w) = -w**3 - w**2 - w - 2. Let q(k) = 7*k**3 + 112*k**2 - 41*k - 4. Let i(v) = -q(v) + 2*s(v). Let i(f) = 0. What is f?
-13, 0, 1/3
What is q in -6950*q**2 + 2*q**3 + 6655*q**2 + 6503*q**2 + 334*q**3 - 336*q + 2*q**4 + 7902*q**2 - 14112 = 0?
-84, -1, 1
Let b(v) be the first derivative of -v**4/26 + 122*v**3/39 - 920*v**2/13 + 8200*v/13 + 4411. Suppose b(n) = 0. Calculate n.
10, 41
Let c(t) be the second derivative of -1/24*t**6 + 0 + 5/8*t**4 + 5/3*t**3 + 0*t**5 - 29*t + 29/2*t**2. Let j(x) be the first derivative of c(x). Factor j(h).
-5*(h - 2)*(h + 1)**2
Let l = -960/7 - -8780/63. Let u = -418630/3 - -139544. Factor 2/3*z**2 + l*z + u.
2*(z + 3)*(3*z + 1)/9
Suppose -463*v + 904 + 1588 = 160*v. Let 3*q**5 - 3/2*q**v - 9/2*q**3 + 3/2*q + 3/2*q**2 + 0 = 0. What is q?
-1, -1/2, 0, 1
Factor -25*i - 89 + 2*i**2 - 48 + 11*i + 89 - 32*i.
2*(i - 24)*(i + 1)
Let q = -287 + 289. Suppose -1 + 24*t - 3*t**q + 40 + 21 = 0. Calculate t.
-2, 10
Let f = 412703 - 2888919/7. Determine w so that 0 + f*w**5 - 440/7*w**2 - 44/7*w**4 + 200/7*w + 282/7*w**3 = 0.
0, 1, 10
Let n be (1694/252 - 4) + (-15)/(-18)*-3. Factor 4/9 + n*o**2 + 2/3*o.
2*(o + 1)*(o + 2)/9
Let x be ((-9)/((-45)/10))/(-17 + 296/16). Determine k so that -4/3*k**2 - x*k**5 + 0 - 8/3*k + 4/3*k**4 + 4*k**3 = 0.
-1, 0, 1, 2
Let p(a) be the first derivative of 168 - 3*a**2 + 9/2*a + 1/2*a**3. Determine q so that p(q) = 0.
1, 3
Let x(d) = -2*d**3 - 6*d - 1. Let l(w) = 13*w**3 + 39*w**2 - 93*w + 113. Let b(u) = l(u) + 8*x(u). Factor b(f).
-3*(f - 7)*(f - 5)*(f - 1)
Let d(g) be the third derivative of -g**5/300 + 61*g**4/120 - 29*g**3/5 + g**2 + 414. Determine n, given that d(n) = 0.
3, 58
Let w = -9/10625 + 25509/10625. Factor -w + 2/5*d**4 + 26/5*d - 2/5*d**3 - 14/5*d**2.
2*(d - 2)*(d - 1)**2*(d + 3)/5
Let c(o) be the second derivative of -5/6*o**3 + 7*o**2 - 1/12*o**4 - 3*o + 5. Solve c(p) = 0.
-7, 2
Let f(d) be the third derivative of 25*d**8/224 + 7*d**7/4 + 267*d**6/40 + 79*d**5/10 + 7*d**4/2 + 2778*d**2. Solve f(n) = 0.
-7, -2, -2/5, 0
Suppose 3*y - 5*l = 127, -3*l = -y - 4*l + 37. Let s(c) = -36 + y - 2*c + 5*c. Let z(t) = -t**3 + t**2 - 7*t - 7. Let q(j) = 7*s(j) + 3*z(j). Factor q(d).
-3*d**2*(d - 1)
Let j = 55 + -934. Let a = j + 881. Find l such that 24/5*l - 3/5*l**4 - 6/5*l**3 + 12/5 + 9/5*l**a = 0.
-2, -1, 2
Let y be (-23 + 0)/((-1452)/(-162) + -9). Let o = -5585/9 + y. Suppose 2/3*j**2 - 2/9*j**4 + 0 + o*j + 0*j**3 = 0. What is j?
-1, 0, 2
Factor 154/3*u**2 - 155*u + 3.
(u - 3)*(154*u - 3)/3
Let m(y) be the third derivative of -y**6/40 - 17*y**5/4 - 39*y**4/4 + 252*y**3 - 35*y**2 - 6*y - 11. Find f, given that m(f) = 0.
-84, -3, 2
Let b be (23/2)/(2/4). Suppose -32*f**2 - b*f**2 + 68*f - 5 + 15*f**2 + 4*f**3 - 27 = 0. What is f?
1, 8
Factor 0*d + 0 - 6*d**2 - 7/3*d**3 + 1/3*d**4.
d**2*(d - 9)*(d + 2)/3
Factor -3144/5*j + 617796/5 + 4/5*j**2.
4*(j - 393)**2/5
Suppose 3*n - 2*t = -438, -3*n - 146 - 292 = 2*t. Let f = -146 - n. Factor 9/5*o**3 + f + 3/5*o**4 + 0*o**2 + 0*o.
3*o**3*(o + 3)/5
Let f be -1 + (-7)/((-35)/20). Suppose f*w - 9 = -3. Suppose -7*u**2 - 187 - 6*u**5 - 28*u**3 - 22*u**4 + 189 - 5*u**2 + w*u = 0. What is u?
-1, 1/3
Let j(x) be the second derivative of 2*x**6/15 - 96*x**5/5 + 828*x**4 - 16928*x**3/3 + 663*x - 2. Factor j(i).
4*i*(i - 46)**2*(i - 4)
Let m(q) be the second derivative of q**4/4 + 1265*q**3/2 - 2463*q. Let m(j) = 0. What is j?
-1265, 0
Find x such that -46128/5 + 1/5*x**5 + 35464/5*x + 51/5*x**4 - 8139/5*x**2 + 319/5*x**3 = 0.
-31, 3, 4
Let c be (0 + -21)*((-44)/12)/(-11). Let k be (0 + (-24)/(-84))*c/(-12). Factor 2/3 - 5/6*r + k*r**2.
(r - 4)*(r - 1)/6
Let r(q) be the first derivative of q**4 - 32*q**3/3 + 34*q**2 - 40*q - 2292. Factor r(f).
4*(f - 5)*(f - 2)*(f - 1)
Let f(y) = -3*y**2 - 855*y - 1688. Let w(o) = 14*o**2 + 4275*o + 8439. Let p(u) = 11*f(u) + 2*w(u). Suppose p(m) = 0. Calculate m.
-169, -2
Let w(r) be the first derivative of r**6/40 - 3*r**5/20 + r**4/4 - 9*r**2 + 81. Let i(u) be the second derivative of w(u). Find b such that i(b) = 0.
0, 1, 2
Let -5/2*x + 0 - 1/4*x**2 = 0. What is x?
-10, 0
Let m(r) = 50*r**2 + 280*r + 995. Let d(h) = -13*h**2 - 70*h - 249. Let q(u) = -u**3 - 3*u**2 + u - 1. Let z be q(-3). Let k(v) = z*m(v) - 15*d(v). Factor k(f).
-5*(f + 7)**2
Suppose -67*p + 64*p = -114. Let 5*z**5 + 30 - p*z - 28*z + 10*z**4 - 5*z - 90*z**3 - 44*z + 160*z**2 = 0. Calculate z.
-6, 1
Let m = 4543738/7 - 649105. Suppose m*d**2 - 3/7*d - 18/7 = 0. What is d?
-2, 3
Let f = 472 - 470. Let -8*v + 9*v - f*v - 5*v**2 + v**3 - 5*v + 0*v**2 = 0. Calculate v.
-1, 0, 6
Let f(n) be the second derivative of 9*n**6/70 - 933*n**5/28 - 965*n**4/14 + 1390*n**3/7 + 1044*n**2/7 - 5749*n. Let f(a) = 0. What is a?
-2, -2/9, 1, 174
Let a(q) be the first derivative of 5*q**4/4 + 170*q**3/3 + 465*q**2/2 - 244. Suppose a(o) = 0. What is o?
-31, -3, 0
Let i(v) be the second derivative of -v**5/220 - 13*v**4/132 + 845*v**3/66 - 6591*v**2/22 + 398*v. Determine o, given that i(o) = 0.
-39, 13
What is f in -224/3*f - 64/3*f**3 - 256/9 + 728/9*f**2 + 14/9*f**4 = 0?
-2/7, 2, 4, 8
Let j(v) = -7*v**2 + 2*v**4 + 21*v**2 - 3*v**4 - 12*v**2 - v**3. Let w(y) = 4*y**5 + 17*y**4 - 23*y**3 - 146*y**2 - 108*y. Let p(m) = j(m) + w(m). Factor p(n).
4*n*(n - 3)*(n + 1)*(n + 3)**2
Find t, given that -2/3*t**5 + 0 - 224/3*t**2 + 26/3*t**4 - 4/3*t**3 - 64*t = 0.
-2, -1, 0, 4, 12
Let m = -79 - -119. Suppose -15*w + m = -5*w. Suppose 16/11*h**3 + 8/11*h**2 + 0*h - 10/11*h**w + 0 = 0. Calculate h.
-2/5, 0, 2
Let y be ((-23359)/517 - -45)/(3/(-11) + 0). Let n(i) be the first derivative of -35 + 3/4*i**6 + 0*i - 1/4*i**4 - 6/5*i**5 + y*i**3 + 1/4*i**2. Factor n(r).
r*(r - 1)**2*(3*r + 1)**2/2
Let d be ((-2)/(-5) + -4)/(18/(-60)). Suppose 16*f - 34*f = -d*f. Factor -2/5*t**4 + 0 - 2/5*t**3 + 0*t**2 + f*t.
-2*t**3*(t + 1)/5
Let a(o) be the second derivative of 5*o**4/12 - 35*o**3/2 + 275*o**2 + o + 433. Factor a(k).
5*(k - 11)*(k - 10)
Let -2/5*u**2 + 1348/5*u - 227138/5 = 0. What is u?
337
Let h = 6578 - 6578. Let a(y) be the third derivative of 0*y**3 + 0*y + 0*y**5 - 20*y**2 + h + 0*y**4 - 1/840*y**7 + 1/480*y**6 - 1/672*y**8. Factor a(f).
-f**3*(f + 1)*(2*f - 1)/4
Suppose -11 = -5*j + 2*u, 0 = -5*j + u + 2 + 11. Let a be 32/j - (-12)/63*-7. Factor a*k - 40/3 - 4/3*k**2.
-4*(k - 5)*(k - 2)/3
Let f(l) = 3*l**4 - 30*l**3 + 93*l**2 - 86*l - 28. Let g(s) = 6*s**4 - 60*