 t(p) be the third derivative of p**7/42 + 7*p**6/24 + 5*p**5/4 + 65*p**4/24 + 10*p**3/3 + 536*p**2. Solve t(m) = 0.
-4, -1
What is j in -39/2*j**2 + 1/4*j**4 + 0*j + 0 + 77/4*j**3 = 0?
-78, 0, 1
Let m(g) = -395*g + 16592. Let s be m(42). Solve -2/5*z**s - 38/5*z + 0 = 0 for z.
-19, 0
Let d be 117/1365*(-931)/(-228)*5/2. Determine n so that -3/8 - 5/4*n - d*n**2 = 0.
-1, -3/7
Let d(r) = 2*r**2 + 25*r - 96. Let o be d(-23). Let p = o - 1539/4. Factor -9/4 + 6*u**3 + p*u**2 - 6*u.
3*(u - 1)*(u + 1)*(8*u + 3)/4
Let q(i) be the first derivative of 3*i**2 + 2/9*i**3 + 40 - 20/3*i. Suppose q(n) = 0. Calculate n.
-10, 1
Let b be -9*((-18)/(2 - -4) - 0). Find n, given that -33*n**2 + 12*n - 15*n**2 + 5*n**5 - 3*n**3 + 16*n**2 + b*n**4 - 9*n**4 = 0.
-3, -2, 0, 2/5, 1
Factor 51/7*i**2 - 15/7*i + 0.
3*i*(17*i - 5)/7
Determine d, given that -2/9*d**3 + 1852/9*d - 358/9*d**2 + 736/3 = 0.
-184, -1, 6
Let c(n) = -2486*n + 94470. Let p be c(38). Determine s so that 0 + 5*s + 0*s**p - 5/4*s**3 = 0.
-2, 0, 2
Let z(d) be the third derivative of -d**5/60 - 29*d**4/12 - 517*d**3/6 - 42*d**2 + 32*d - 2. Factor z(k).
-(k + 11)*(k + 47)
Let m(w) be the second derivative of 0*w**2 + 3*w + 3 - 3/32*w**5 - 3/8*w**3 + 17/32*w**4. What is v in m(v) = 0?
0, 2/5, 3
Let l be 385090/(-257244) - (-3 - 1)/2. Let b = l - 2/663. Find w such that 1/4 + 1/4*w**2 + b*w = 0.
-1
Suppose -4*m - 4*g + 416 = 0, 5*m - g - 96 = 4*m. Factor -m - 4*a**2 - 44 - 128*a + 20.
-4*(a + 1)*(a + 31)
Let y(n) be the first derivative of 4*n**5/25 + 17*n**4/5 + 48*n**3/5 - 184*n**2/5 - 448*n/5 - 598. Suppose y(d) = 0. Calculate d.
-14, -4, -1, 2
Let i = -22450 + 22454. Let h(g) be the third derivative of -1/3*g**i - 1/10*g**5 + 0 - 1/3*g**3 + 0*g + 16*g**2. Factor h(v).
-2*(v + 1)*(3*v + 1)
Let y(m) = m - 38. Let c be y(-7). Let r = c + 55. Factor -h + 9*h - 2*h**2 - r*h + 4.
-2*(h - 1)*(h + 2)
Solve 46/3*b**2 - 34/3*b**4 - 4 - 98/3*b + 98/3*b**3 = 0 for b.
-1, -2/17, 1, 3
Let w(u) be the second derivative of 1/78*u**4 - 3*u - 2/13*u**3 + 0*u**2 + 2. Factor w(i).
2*i*(i - 6)/13
Suppose -6*v - 4 = -4*v. Let a be -20*(2 + 4*v). Factor n**2 - a + 95 - 20*n + 6*n**2 - 2*n**2.
5*(n - 5)*(n + 1)
Let t(u) be the first derivative of -5*u**4/4 + 65*u**3 - 435*u**2 + 680*u - 10618. Factor t(g).
-5*(g - 34)*(g - 4)*(g - 1)
Let p = 2625/8528 + -101/656. Factor -12/13 + p*l**2 - 2/13*l.
2*(l - 3)*(l + 2)/13
Let q be ((-9)/4)/(-2*(-4)/(-32)). Suppose -11*k + 6 = -q*k. What is o in 3*o**2 - 6*o**2 + 3*o - 3*o**2 - o**k - 8*o = 0?
-5, -1, 0
Let n(s) be the third derivative of 0*s**4 + 14*s**2 + 0*s + 8/3*s**3 - 5/96*s**5 - 1/288*s**6 + 0. Let y(a) be the first derivative of n(a). Factor y(o).
-5*o*(o + 5)/4
Let f(u) be the first derivative of 35*u**6/6 + 390*u**5 + 7630*u**4 + 93040*u**3/3 + 32760*u**2 - 27040*u + 566. Solve f(n) = 0.
-26, -2, 2/7
Suppose 3*d = -5*a + 7, d = 4*a - 2 + 10. Factor 74*g + d*g**3 + 138*g - 338 - 87*g + 102*g**2 + 499*g.
2*(g + 13)**2*(2*g - 1)
Let l = 4500 - 4479. Let g(c) be the first derivative of 0*c + l + 5/3*c**3 + 5/4*c**4 + 0*c**2. Factor g(d).
5*d**2*(d + 1)
Let h = 634/9 - 628/9. Let s(d) be the second derivative of -1/3*d**4 + 0 + 2*d**2 + 17*d + h*d**3 - 1/5*d**5. Factor s(o).
-4*(o - 1)*(o + 1)**2
Let d(w) = -6*w + 93. Let c be d(0). Let h = c - 26. Factor 4*f - h*f**2 - 67*f**2 + 129*f**2.
-f*(5*f - 4)
Let a(i) be the third derivative of -i**7/1365 + i**6/78 + 6*i**5/65 + 19*i**4/78 + i**3/3 + 824*i**2. Find c such that a(c) = 0.
-1, 13
Let b(q) be the second derivative of -1/6*q**4 + 3/50*q**5 - 19*q + 4/5*q**2 + 1/75*q**6 + 2 - 1/5*q**3. Factor b(h).
2*(h - 1)**2*(h + 1)*(h + 4)/5
Let y(h) = -9*h**2 - 582*h + 1206. Let k(s) = -26*s**2 - 1749*s + 3619. Let f(l) = 6*k(l) - 17*y(l). Factor f(w).
-3*(w - 2)*(w + 202)
Let t be -139 + 1 + 12/4. Let f be 4/(-3)*t/30 + -4. Find m such that 0 - 3/2*m**f + 3*m = 0.
0, 2
Factor 210*n**2 + 221*n**2 - 429*n**2 + 16928 + 368*n.
2*(n + 92)**2
Let i(x) be the first derivative of x**3/3 + 571*x**2/2 - 572*x + 363. Factor i(k).
(k - 1)*(k + 572)
Let i = -1/10589 + 211787/74123. Find c, given that i*c**2 - 2/7*c - 6/7*c**3 - 12/7 = 0.
-2/3, 1, 3
Let u be 51/12 - 5/20. Let f(b) = -5*b**2 + b - 4. Let c(n) = -n + 3 - 2 - 2*n**2 + 3*n**2. Let q(x) = u*c(x) + f(x). Solve q(s) = 0.
-3, 0
Let l(p) = 4874*p + 141350. Let i be l(-29). Let j = -29 - -59/2. Factor 8*f**3 + j*f + 0 - i*f**2.
f*(4*f - 1)**2/2
Let g(l) be the first derivative of 5*l**3/3 + 315*l**2 + 1240*l + 7620. What is f in g(f) = 0?
-124, -2
Factor 10999*n**2 + 3362 - 10997*n**2 - 166*n + 2*n.
2*(n - 41)**2
Solve -1/9*z**3 + 14/9 + z - 2/3*z**2 = 0.
-7, -1, 2
Let f(t) be the third derivative of t**8/1680 + t**7/175 - t**6/200 - 4*t**5/75 + t**4/10 + 19*t**2 - 63. Factor f(w).
w*(w - 1)**2*(w + 2)*(w + 6)/5
Let w(n) = 2*n**2 - 18*n + 35. Let r be w(8). Suppose 0*s**5 - 9*s**3 + s + 3*s**5 - 9*s**4 - 8*s**2 + r*s**2 + 22*s**2 - 19*s = 0. What is s?
-2, 0, 1, 3
Let z(p) be the first derivative of 4/15*p**3 - 1/2*p**4 + 0*p**2 + 1/3*p**6 - 4/25*p**5 + 115 + 0*p. Determine y so that z(y) = 0.
-1, 0, 2/5, 1
Let j(g) be the first derivative of -g**6/2 + 26*g**5/5 - 49*g**4/4 - 38*g**3/3 + 20*g**2 - 459. Suppose j(x) = 0. Calculate x.
-1, 0, 2/3, 4, 5
Let n be (12*21/(-315))/((-12)/5 + 2). Factor 18/7*c + 3/7*c**n + 15/7.
3*(c + 1)*(c + 5)/7
Suppose -3*w + 555 = -2*z - 742, 3*z = -5*w + 2149. Let x = 434 - w. Suppose 3/5*o**x + 33/5*o - 21/5*o**2 - 3 = 0. What is o?
1, 5
Let n(z) be the second derivative of 0 + 8/3*z**2 + 1/126*z**7 + 8/45*z**6 - 93*z - 1/30*z**5 - 8/9*z**4 + 1/18*z**3. Solve n(g) = 0 for g.
-16, -1, 1
Let u(r) be the first derivative of -r**4 + 4*r**3/3 - 4122. Let u(g) = 0. Calculate g.
0, 1
Let a = 145133 + -145128. Factor -3/7*j**4 + 1/7*j**a - 3/7*j**3 + 0 + 6/7*j + j**2.
j*(j - 3)*(j - 2)*(j + 1)**2/7
Suppose 4*d = -4*b - 7180, -2*b = d + 1221 + 570. Let x = 30589/17 + d. Factor -x - 2/17*j + 2/17*j**3 + 6/17*j**2.
2*(j - 1)*(j + 1)*(j + 3)/17
Suppose s = 5*r + 16, -4 + 0 = -s + r. Let h be ((-4)/4)/s*-2. Solve -4*o**3 - 15*o**2 - 24*o**2 + 39*o**h = 0.
0
Let g(b) be the third derivative of 34*b**2 + 0*b - 1/60*b**5 + 1/8*b**4 + 0*b**3 + 0. Factor g(o).
-o*(o - 3)
Let u be (-420)/(-175) - ((-456)/(-30))/(-1). Solve 64*i + 128/5 - 184/5*i**3 - u*i**2 - 2*i**5 + 86/5*i**4 = 0.
-1, -2/5, 2, 4
Let v(l) be the third derivative of -l**6/720 - l**5/80 - l**4/24 - 43*l**3/6 - 267*l**2. Let n(u) be the first derivative of v(u). Factor n(d).
-(d + 1)*(d + 2)/2
Let a = -4143 - -41511/10. Let n(b) be the second derivative of 0 - 3/5*b**3 + a*b**2 + 31*b + 1/60*b**4. Find t such that n(t) = 0.
9
Suppose -124 = -9*l - 88. Factor -139*o**4 + 279*o**3 - 30*o**2 + 9*o**l - 74*o**4.
-3*o**2*(4*o - 5)*(17*o - 2)
Let i(n) be the first derivative of -50*n**2 + 50 - 35*n**3 - 20*n + 7*n**5 + 5/2*n**4. Determine q, given that i(q) = 0.
-1, -2/7, 2
Let t(p) be the third derivative of -19*p**4 + 90*p**2 + 0*p - 6859/60*p**6 + 361/5*p**5 + 8/3*p**3 + 0. Factor t(a).
-2*(19*a - 2)**3
Let p(x) be the second derivative of -1/40*x**6 + 0*x**3 + 0*x**4 + 0*x**2 + 239*x + 0 - 3/80*x**5. Factor p(b).
-3*b**3*(b + 1)/4
Let l = -324 + 327. Suppose 34 - 6 - 111*c - 18*c**2 - 3*c**l - 82 - 42*c**2 = 0. Calculate c.
-18, -1
Let u be 391 + -428 + (-642)/(-14). Determine o, given that -16/7 - 40/7*o**2 - 6/7*o**3 + u*o = 0.
-8, 1/3, 1
Let y(c) be the second derivative of -c**5/110 + 215*c**4/66 - 142*c**3/11 + 199*c + 1. Solve y(s) = 0 for s.
0, 2, 213
Let x = 6752 - 6752. Let u(l) be the first derivative of -19 + 0*l**2 - 8/9*l**3 + l**4 + x*l - 4/15*l**5. Factor u(m).
-4*m**2*(m - 2)*(m - 1)/3
Let r = -11543/15 - -2311/3. Let o(s) be the first derivative of 0*s**4 + r*s**5 - 4/3*s**3 + s**2 - 18 - 1/3*s**6 + 0*s. Find i, given that o(i) = 0.
-1, 0, 1
Let h(r) be the first derivative of r**6/6 - 11*r**5/30 - 13*r**4/6 - 2*r**3/9 + 4*r**2/3 + 1333. Let h(x) = 0. Calculate x.
-2, -2/3, 0, 1/2, 4
Factor -496407447/8 + 3/8*d**3 - 4941/8*d**2 + 2712609/8*d.
3*(d - 549)**3/8
Let f(j) = -j**2 + 19*j + 24. Let g be f(14). Let n be g - (-2 + -1) - 0. Factor 30*p - n*p + 3*p**2 + 33*p + 31*p.
3*p*(p - 1)
Suppose -74 + 164 = -3*z. Let b be 6 + (7 - (-282)/z). Factor -36/5*w**2 + b*w**3 + 0 - 3/5*w**4 + 24/5*w.
-3