 + i*t**3 - 8*t**2 + 41*t**2 - 30*t.
3*(t - 1)*(t + 2)*(7*t + 4)
Let u = -4652/9 - -517. Let l(o) be the third derivative of 1/18*o**4 + 0 + u*o**3 + 1/90*o**5 + 0*o - o**2. What is j in l(j) = 0?
-1
Let k = -99 - -109. Factor -125*b + 65*b + 0*b**4 - 45 + 20*b**3 + k*b**2 - 5*b**4 + 0*b**3.
-5*(b - 3)**2*(b + 1)**2
Let k(p) be the first derivative of 5*p**6/24 + 31*p**5/4 + 1415*p**4/16 + 3365*p**3/12 + 385*p**2 + 245*p - 1341. Suppose k(c) = 0. What is c?
-14, -1
Factor -941 - 7135710*b**2 + 47524*b + 51052048*b**2 - 1692334*b**2 + 4460*b + 957.
4*(3249*b + 2)**2
Suppose 3/8*x**5 - 291/4*x**3 - 1251/4*x**2 + 3/8*x**4 + 6723/8*x - 3645/8 = 0. What is x?
-9, 1, 15
Let g(l) be the second derivative of l**5/300 + l**4/60 - l**3/10 + 307*l**2/2 + 3*l + 17. Let k(m) be the first derivative of g(m). Factor k(v).
(v - 1)*(v + 3)/5
Let s be ((-1)/2)/(23/(-18) - 12/(-27)). Factor 6/5 + 3/5*c**3 - 6/5*c**2 - s*c.
3*(c - 2)*(c - 1)*(c + 1)/5
Let t(b) be the first derivative of 146 + 0*b**2 - 64/3*b**3 - 48*b**5 + 0*b + 63*b**4 - 8/3*b**6. Solve t(n) = 0.
-16, 0, 1/2
Let f(k) = 1174*k + 49312. Let o be f(-42). Let -352*y + 128/5 + 1792*y**2 + 2744*y**o + 4802/5*y**5 - 3920*y**3 = 0. What is y?
-4, 2/7
Let d(f) be the second derivative of 13*f**4/42 - f**3/7 - 10*f**2/7 - 2341*f. Factor d(y).
2*(y - 1)*(13*y + 10)/7
Let h(p) = -28*p**4 + 43*p**3 + 42*p**2 - 91*p. Let s(g) = 2*g**2 + g**2 + 5*g**4 - 15*g**2 + 5*g**2 - 7*g**3 + 15*g. Let y(m) = -6*h(m) - 34*s(m). Factor y(r).
-2*r*(r - 1)*(r + 2)*(r + 9)
Let d(m) be the first derivative of m**6/2520 + m**5/168 - m**4/28 + 17*m**3/3 - m - 29. Let p(w) be the third derivative of d(w). What is h in p(h) = 0?
-6, 1
Factor -2/15*i**3 + 120 + 122/15*i**2 - 128*i.
-2*(i - 30)**2*(i - 1)/15
Let k = -804405 + 3217621/4. Find d, given that d**2 + 1/4*d**3 + k*d - 3/2 = 0.
-3, -2, 1
Let x(s) be the first derivative of -s**6/3 + 4*s**5 - 8*s**4 - 4*s**3/3 + 17*s**2 - 16*s + 900. Factor x(b).
-2*(b - 8)*(b - 1)**3*(b + 1)
Let p(v) be the third derivative of 3/8*v**4 + 23*v**2 + 0 + 27/2*v**3 + 1/240*v**5 + 0*v. Determine b, given that p(b) = 0.
-18
Suppose -936/5 + 2/5*s**2 - 54/5*s = 0. What is s?
-12, 39
Suppose -7*n + 6*n + 29 = 0. Find f such that -42 + 32*f + n - 19 - 48 + 4*f**2 = 0.
-10, 2
Let o(p) = -3*p**2 + 96*p - 202. Let h(m) = -24*m**2 + 672*m - 1413. Let q(d) = 2*h(d) - 15*o(d). Factor q(c).
-3*(c - 2)*(c + 34)
Factor 101*j + 5/8*j**3 - 67/2 - 347/8*j**2.
(j - 67)*(j - 2)*(5*j - 2)/8
Factor -1368/11*s + 6/11*s**4 + 0 - 366/11*s**3 + 1392/11*s**2.
6*s*(s - 57)*(s - 2)**2/11
Let w(t) be the first derivative of t**6/780 - t**5/78 + t**4/52 + 3*t**3/13 + 15*t**2 - t - 34. Let l(p) be the second derivative of w(p). Factor l(j).
2*(j - 3)**2*(j + 1)/13
Let i be 4/(-10)*(3 + 3421/88). Let m = i + 117/4. Find u such that 11/2*u**2 - 1/2*u**3 - 35/2*u + m = 0.
1, 5
Let x = 2/204767 + 204763/409534. Let b = -3 + 5. Solve x*u**4 - 1/2*u + 1/3*u**3 + 1/6*u**5 - 1/3*u**b - 1/6 = 0.
-1, 1
Let q(b) = 9*b - 54. Let a be q(7). Suppose 0*y**3 - 3*y**4 - 2*y**5 + a*y**4 - 6*y**2 + 2*y**3 = 0. What is y?
-1, 0, 1, 3
Let g(r) be the second derivative of -27*r**5/40 - 11*r**4/2 - 2*r - 1828. Determine s so that g(s) = 0.
-44/9, 0
Let l(k) = -24*k - 70. Suppose -2*f + 16 = 2*a - 3*f, -40 = -4*a - 2*f. Let d = a - 27. Let y(t) = t**2 - 96*t - 279. Let q(v) = d*l(v) + 4*y(v). Factor q(i).
4*(i + 6)**2
Suppose -6*o = 4*o - 10. Let s = 2 - -10. Determine p, given that s*p + p**2 - o + 35 + 2 = 0.
-6
Let u be -1 + 0 + -893 + 20 + -21. Let j = u + 897. Factor 0*q**4 - 2/5*q + 0*q**j + 4/5*q**3 - 2/5*q**5 + 0.
-2*q*(q - 1)**2*(q + 1)**2/5
Suppose 45 + 9*n + 1/4*n**2 = 0. What is n?
-30, -6
Let u(w) be the second derivative of w**6/210 + w**5/140 - 43*w**4/84 - 85*w**3/42 - 3*w**2 + 4*w - 442. Factor u(x).
(x - 7)*(x + 1)**2*(x + 6)/7
Let u(a) be the first derivative of a**3 + 66*a**2 + 480*a - 10631. Let u(b) = 0. Calculate b.
-40, -4
Let m = 1467 + -1432. Suppose m*q = 22*q + 18*q. Determine s so that -5/2 + q*s + 5/2*s**2 = 0.
-1, 1
Let x = 1716713 + -5150131/3. Suppose 5*j - 3*p - 24 = 0, 3*j - 5*j = p - 3. Find l, given that -2/3*l**j - 8/3 + 2/3*l**2 + x*l = 0.
-2, 1, 2
Let u(z) be the first derivative of 2*z**5/45 + 5*z**4/9 + 34*z**3/27 - 28*z**2/9 + 3179. Factor u(t).
2*t*(t - 1)*(t + 4)*(t + 7)/9
Let l(t) be the first derivative of 0*t - 14*t**2 + 140 + 4/3*t**3. Find m, given that l(m) = 0.
0, 7
Let m be (-6)/(-2) - (-2420)/20. Suppose -18 = -m*t + 115*t. Factor -3/5 + 3/5*x**3 + 9/5*x - 9/5*x**t.
3*(x - 1)**3/5
Let j(c) = -22*c**3 + 6*c**2 + 64*c - 88. Let z = 0 + 16. Let a(o) = 7*o**3 - 2*o**2 - 21*o + 29. Let f(n) = z*a(n) + 5*j(n). Find p such that f(p) = 0.
-3, 2
Factor 174*y + 15*y**3 - 3600 - 382*y + 260*y**2 - 212*y - 5*y**4.
-5*(y - 6)**2*(y + 4)*(y + 5)
Let i(g) = -31*g**3 - 213*g**2 + 434*g - 220. Let t(x) = -6*x**3 + x**2 - x. Let y(m) = -i(m) + 5*t(m). Determine j so that y(j) = 0.
-220, 1
Let s = -3108/41 + 15581/205. Determine t, given that -s*t**5 - 6/5*t**4 - 4/5*t + 0 - 12/5*t**2 - 13/5*t**3 = 0.
-2, -1, 0
Let j(l) be the third derivative of -17*l**7/1365 + 7*l**6/65 + 11*l**5/195 - 7*l**4/13 - 5*l**3/39 + 252*l**2 - 1. Determine f, given that j(f) = 0.
-1, -1/17, 1, 5
Let w(m) be the first derivative of m**6/60 + 3*m**5/25 + 3*m**4/10 + m**3/3 + 3*m**2/20 + 98. Solve w(s) = 0 for s.
-3, -1, 0
Solve -56/5*y**2 + 12/5*y**4 - 12/5*y**3 + 18*y - 36/5 + 2/5*y**5 = 0 for y.
-6, -3, 1
Let s(b) be the third derivative of -b**6/780 + 19*b**5/130 + 155*b**4/78 + 51*b**2 - 4*b - 10. Factor s(x).
-2*x*(x - 62)*(x + 5)/13
Let h(i) be the third derivative of 19*i**5/15 - 20*i**4/3 + 8*i**3/3 - 110*i**2 - i + 1. Factor h(f).
4*(f - 2)*(19*f - 2)
Let z = 140 + -135. Let 20*f**2 - 6*f - 2*f**z + 13*f**4 - f**4 - 2*f**3 - 22*f**3 = 0. What is f?
0, 1, 3
Let c(j) be the third derivative of 2/9*j**5 - 2/63*j**7 - 1/36*j**4 + 0*j - 1/504*j**8 + 1/90*j**6 + 9*j**2 + 0 - 10/9*j**3. Let c(y) = 0. What is y?
-10, -1, 1
Let v(f) be the first derivative of -f**6/2340 + f**5/780 - 4*f**3/3 - 4*f**2 + 24. Let b(k) be the third derivative of v(k). Factor b(j).
-2*j*(j - 1)/13
Let h be -1*4/20*-35. Let v(j) be the third derivative of 1/840*j**8 + 0*j**3 + 0 + 1/75*j**5 - 2/525*j**h + 0*j**6 + 0*j - 1/60*j**4 + 6*j**2. Solve v(i) = 0.
-1, 0, 1
Suppose 42 = -2*y + 52. Suppose -28 = -5*v + 2*n, -v + 7 = y*n - 4. Solve -3*g**4 + g - 5*g - v*g**2 + 4*g + 9*g**3 = 0.
0, 1, 2
Let k(j) be the second derivative of j**4/48 - 1487*j**3/12 + 2211169*j**2/8 + 3321*j. Factor k(f).
(f - 1487)**2/4
Let a(y) be the first derivative of -y**5/15 + 26*y**4/3 - 1352*y**3/3 + y**2/2 + 20*y + 42. Let i(g) be the second derivative of a(g). Solve i(x) = 0 for x.
26
Let w be (-311696)/(-736890) - (-4)/(-174). Factor w*o**2 - 12/5 + 2/5*o.
2*(o - 2)*(o + 3)/5
Let h be -25 - (-25)/(1200/1224). Factor -3/2*c - h*c**2 + 5.
-(c - 2)*(c + 5)/2
Let a be 22*(9 + -10) + 16 + (-63)/(-8). Factor -3/8*l**4 - 9/8*l - 1/4 - 11/8*l**3 - a*l**2.
-(l + 1)**3*(3*l + 2)/8
Let j(f) be the first derivative of -f**6/12 + 3*f**5 - 111*f**4/4 - 46*f**3/3 + 735*f**2/4 - 225*f - 9763. Let j(t) = 0. Calculate t.
-2, 1, 15
Let x(p) = -37*p**4 - 411*p**3 + 12*p**2 + 396*p. Let h(q) = 44*q**4 + 412*q**3 - 14*q**2 - 394*q. Let d(w) = 5*h(w) + 6*x(w). Find a such that d(a) = 0.
-203, -1, 0, 1
Let r(i) be the first derivative of i**4/8 + 46*i**3/3 + 439*i**2/4 + 174*i + 8785. Determine l so that r(l) = 0.
-87, -4, -1
Suppose -688 + 4/7*p**2 + 4812/7*p = 0. Calculate p.
-1204, 1
Let l be (-48)/80*8/(-18). Let s(h) be the third derivative of 26*h**2 - 13/150*h**5 - 1/525*h**7 + 0*h + 0 + 1/50*h**6 + 1/5*h**4 - l*h**3. Factor s(k).
-2*(k - 2)**2*(k - 1)**2/5
Let w(j) be the third derivative of j**5/30 + 33*j**4/4 + 96*j**3 - 235*j**2. Factor w(m).
2*(m + 3)*(m + 96)
Let s(z) be the second derivative of -7*z**6/180 + 33*z**5/20 - 427*z**4/72 + 8*z**3 - 13*z**2/3 - 4*z + 460. Let s(f) = 0. What is f?
2/7, 1, 26
Let d = 277373 - 3051101/11. Factor d*n**2 - 24/11 + 8/11*n.
2*(n - 2)*(n + 6)/11
Let n(y) be the first derivative of 4*y**5/5 + 122*y**4 - 5180*y**3/3 + 6600*y**2 - 3981. Let n(r) = 0. Calculate r.
-132, 0, 5
Let i be 7/(126/66)*14/77. Let c(k) be the second derivative of -30*k - 1/5*k**