3*w**2 - 2/3*w + 2/3*w**3 + t.
2*(w - 1)**2*(w + 1)/3
Let r(c) be the second derivative of -22/5*c**5 + 0 - 400/3*c**3 + 14*c + 0*c**2 - 2/15*c**6 - 140/3*c**4. Factor r(j).
-4*j*(j + 2)*(j + 10)**2
Let x(p) be the third derivative of -1/72*p**6 + 5/72*p**4 + 2/9*p**3 - 1/630*p**7 + 0 - 1/60*p**5 + 62*p**2 - 2*p. Determine c, given that x(c) = 0.
-4, -1, 1
Let g be 16*1 + ((-2)/8)/(-16 - (-1143)/72). Find c, given that 6 + 2/5*c - 4/5*c**4 - g*c**2 - 66/5*c**3 = 0.
-15, -1, 1/2
Let p(u) be the first derivative of 2*u**6/15 - 14*u**5/75 - 59*u**4/30 - 76*u**3/45 + 8*u**2/15 + 5690. Determine f so that p(f) = 0.
-2, -1, 0, 1/6, 4
Let b be 2 + (-11)/6 + (-525)/4410. Let t(v) be the second derivative of 0*v**2 - 1/10*v**5 + 2*v + 8 - 1/147*v**7 - b*v**6 - 1/14*v**4 + 0*v**3. Factor t(o).
-2*o**2*(o + 1)**2*(o + 3)/7
Suppose -5*t - 4*w + 118 = 0, 273*w - 268*w - 120 = -5*t. Determine d so that t + 4*d + 2/11*d**2 = 0.
-11
Let u be (9 - 297/36)/(6/16). Suppose 21*q**3 - 40*q**3 + 24*q**3 + 62*q - 90*q**u + 23*q = 0. What is q?
0, 1, 17
Let i(p) be the first derivative of 80/3*p**3 + p**4 - 4 + 648*p + 234*p**2. Solve i(o) = 0 for o.
-9, -2
Let x(u) be the third derivative of -u**6/24 - 427*u**5/12 - 4255*u**4/24 - 2125*u**3/6 - 2192*u**2. Factor x(b).
-5*(b + 1)**2*(b + 425)
Suppose 3*a + 3*f = 9, 0 = -2*a + 3*a - 5*f + 3. Let x be (-33)/(-4) + -6 + (-3)/a. Let -x*v**2 + 3/4*v + 0 = 0. Calculate v.
0, 1
Let n(q) = 6*q**3 - 24*q**2 + 24*q - 15. Let d(c) = c**3 - 3*c**2 + 1. Let b(t) = 5*d(t) - n(t). Factor b(s).
-(s - 5)*(s - 2)**2
Let z(l) be the first derivative of 2*l**3/3 + 31*l**2/2 - 16*l - 597. Suppose z(w) = 0. What is w?
-16, 1/2
Let m(a) be the third derivative of 0*a + 0 + 1/75*a**5 - 1/30*a**4 - 1/450*a**6 - 4*a**2 + 5/3*a**3. Let c(y) be the first derivative of m(y). Factor c(d).
-4*(d - 1)**2/5
Let n be (-606)/60 + (-7000)/(-560). Factor -26/3*f - 14/15*f**2 - n.
-2*(f + 9)*(7*f + 2)/15
Let q(x) be the third derivative of x**10/211680 - 3*x**8/15680 - 85*x**4/24 + 170*x**2. Let h(g) be the second derivative of q(g). What is c in h(c) = 0?
-3, 0, 3
Let s = -6002 - -6007. Let t(z) be the first derivative of -3/5*z**s - 1 + 0*z**2 + 4/3*z**3 + z**4 + 0*z. Factor t(r).
-r**2*(r - 2)*(3*r + 2)
Suppose -5*i - 16 + 141 = 0. Factor 95*d**2 - 147*d**2 + 105*d**2 - d**4 + i*d**3 + 27*d.
-d*(d - 27)*(d + 1)**2
Let f = -43/93 + 289/558. Let r(v) be the third derivative of 7/144*v**4 - 17*v**2 + 0*v + 0 + f*v**3 - 1/90*v**5. Factor r(c).
-(c - 2)*(4*c + 1)/6
Let a(w) be the first derivative of -472/35*w**5 + 0*w**2 + 10/21*w**6 + 0*w + 184/21*w**3 + 215 + 67/7*w**4. Find m such that a(m) = 0.
-2/5, 0, 1, 23
Suppose -64*q**2 - 62*q**4 - 3*q**5 - 58*q**2 + 29*q**2 + 666*q - 447*q**3 - 61*q**4 = 0. Calculate q.
-37, -3, -2, 0, 1
Let p(l) be the first derivative of -11/4*l**4 + 5/6*l**6 - 85 + 0*l + 0*l**2 - 2*l**3 + 12/5*l**5. Factor p(w).
w**2*(w - 1)*(w + 3)*(5*w + 2)
Let o(h) be the third derivative of h**6/30 + 14*h**5/15 - 17*h**4/6 - 20*h**3 - h**2 - 7135*h. Factor o(v).
4*(v - 2)*(v + 1)*(v + 15)
Let x = 420231 + -8824841/21. Suppose -x*f**3 + 4/7*f**4 - 2/3*f**2 + 2/21 + 10/21*f = 0. What is f?
-1, -1/6, 1
Suppose -37/2*k**3 - 927/2*k - 81/2 + 537/2*k**2 - 6*k**4 = 0. Calculate k.
-9, -1/12, 3
Let k(o) = 15*o**2 - 61*o**2 + 1 - 36*o**2 + 0*o**2 - 16 - 6*o. Let r(q) = 82*q**2 + 5*q + 12. Let z(p) = -4*k(p) - 5*r(p). Solve z(i) = 0 for i.
-1/82, 0
Let o = -75053 - -975691/13. Factor -o*l**2 - 18/13*l + 20/13.
-2*(l - 1)*(l + 10)/13
Let c(l) = 3*l**2 - 9*l - 14. Let d be 1/(6 + (-57)/9). Let h(y) = -y**2 - y - 2. Let n(i) = d*c(i) - 12*h(i). Let n(u) = 0. Calculate u.
-11, -2
Let a(v) = -v + 3. Let f be a(11). Let u be 2/f - 8/(-32). Determine k so that 4*k**5 - k**2 - 7*k**5 + k**4 + u*k**3 + 2*k**5 + k**3 = 0.
-1, 0, 1
Let i(a) be the second derivative of 0 + 0*a**4 + 3*a - 2/5*a**2 - 1/5*a**3 + 1/50*a**5. Factor i(s).
2*(s - 2)*(s + 1)**2/5
Let w(k) be the second derivative of 2/15*k**4 - 1 + 3*k + 3/5*k**2 + 19/30*k**3 - 1/20*k**5. Solve w(n) = 0.
-1, -2/5, 3
Let f be -71 + 35 - (-1050)/28. Solve -2*b**4 - f*b**3 - 25/4*b + 10*b**2 + 0 - 1/4*b**5 = 0.
-5, 0, 1
Factor -31/2 - 2/3*j**3 - 139/3*j + 125/2*j**2.
-(j - 93)*(j - 1)*(4*j + 1)/6
Let x(t) = 4*t**4 + 360*t**3 - 368*t**2 - 328*t + 388. Let o(q) = q**4 + 120*q**3 - 122*q**2 - 108*q + 130. Let b(d) = 8*o(d) - 3*x(d). Factor b(c).
-4*(c - 1)**2*(c + 1)*(c + 31)
Let i(j) = -5*j**2 + 1591*j + 2. Let q be i(0). What is r in 0 + 38/7*r**q + 4/7*r + 114/7*r**3 + 32/7*r**5 + 16*r**4 = 0?
-2, -1, -1/4, 0
Let t(g) be the first derivative of 15*g**2/2 - 672*g + 288. Let j be t(45). Let 14/3*b**4 - 68/9*b**j + 16/9*b + 0 - 40/9*b**2 = 0. What is b?
-2/3, 0, 2/7, 2
Let h(y) be the third derivative of -2 + 95*y**2 + 7/75*y**5 + 0*y + 0*y**3 + 4/75*y**6 + 0*y**4 + 2/525*y**7. Factor h(u).
4*u**2*(u + 1)*(u + 7)/5
Let z be -9*((-96)/54)/8. Factor 0*t**z + 26*t**3 - 27 - 21*t**2 - 29*t**3 - 45*t.
-3*(t + 1)*(t + 3)**2
Let v(l) = l**2 + 467*l + 6. Let a(k) = 920*k + 10. Let m(p) = 3*a(p) - 5*v(p). Factor m(s).
-5*s*(s - 85)
Let c(t) be the third derivative of 0*t - 26/3*t**3 - 1/60*t**6 - 8/15*t**5 - 22 - 41/12*t**4 - t**2. Factor c(u).
-2*(u + 1)*(u + 2)*(u + 13)
Let c(l) be the third derivative of l**7/168 - 13*l**6/240 - 3*l**5/20 - 5*l**4/12 - 5*l**3/6 + 59*l**2. Let j(t) be the second derivative of c(t). Factor j(q).
3*(q - 3)*(5*q + 2)
Suppose -376*g + 954*g = 480*g + 294. Factor -7 - 23/3*q**2 + 43/3*q + 1/3*q**g.
(q - 21)*(q - 1)**2/3
Suppose 8*b + 2*v + 6 = 10*b, -4*b - 3*v = -12. Find r such that -68*r**2 + 1776*r + 2*r**b - 588 - 1412*r + 2*r**3 = 0.
3, 7
Suppose -1 + 7 = 2*k. Suppose 18 + 14 = 5*y - k*z, 20 = 3*y - 2*z. Factor 1 - y*i**2 + 9 - 18*i + 9*i**2 + 3*i.
5*(i - 2)*(i - 1)
Let c(n) be the first derivative of -5*n**6/2 + 578*n**5 + 1700*n**4 + 4870*n**3/3 + 975*n**2/2 - 2579. Suppose c(r) = 0. What is r?
-1, -1/3, 0, 195
Suppose -2958 = -11*g + 6579. Let l be (-35)/(-153) + (-102)/g. Factor -l*y**2 - 1/3 + 4/9*y.
-(y - 3)*(y - 1)/9
Determine h so that 4/19*h**3 + 94/19*h**2 - 148/19*h + 50/19 = 0.
-25, 1/2, 1
Let u(k) = -107*k**2 - 9135*k + 9089. Let g(w) = -38*w**2 - 3046*w + 3030. Let v(o) = -17*g(o) + 6*u(o). Factor v(a).
4*(a - 756)*(a - 1)
Find h, given that 476 + 331 - 207 + 5*h**3 - 167*h - 15*h**2 - 3*h = 0.
-6, 4, 5
Suppose y + 0*y = 4*c - 15, -4*c + 2*y + 14 = 0. Let d be 0 + c*(-42)/(-24). Factor 3*o + 10*o**2 - o**3 + 2*o**3 + 4 - 11*o**2 - d*o.
(o - 2)*(o - 1)*(o + 2)
Suppose -6 = -3*r - 2*t, 0 = 2*t - 22 + 16. Suppose r = 51*k - 30*k - 42. Find b, given that -9/4 + 3/2*b**k - 3/4*b = 0.
-1, 3/2
Factor -163*d**2 + 84*d**2 + 95 + 2*d - 103*d**2 + 0*d**3 - 2*d**3 + 87.
-2*(d - 1)*(d + 1)*(d + 91)
Let m(s) be the third derivative of -s**6/40 - 119*s**5/20 - 435*s**4 + 1800*s**3 - 2*s**2 + 20*s + 8. Solve m(b) = 0 for b.
-60, 1
Let l = -2400 - -1595. Let p = 805 + l. Find a such that 2/11*a + p + 6/11*a**2 + 6/11*a**3 + 2/11*a**4 = 0.
-1, 0
Let a(w) be the second derivative of w**6/150 - 7*w**5/200 + w**4/120 + 7*w**3/60 - 3*w**2/20 + 4*w - 16. Find v, given that a(v) = 0.
-1, 1/2, 1, 3
Let o be 7*(-1)/(-2254)*(-816)/(-5). Let w = o + -9/115. Factor w*k + 12/7*k**2 - 9/7*k**3 - 6/7.
-3*(k - 1)**2*(3*k + 2)/7
Factor 1/6*h**3 + 19/6*h**2 + 20 + 47/3*h.
(h + 2)*(h + 5)*(h + 12)/6
Let h(d) = d**2 - 27*d + 29. Let y be h(26). Suppose -14*a**y + 3*a**4 + 212*a**2 - 22*a**3 + a**4 - 168*a**2 + 4*a**5 - 16*a = 0. What is a?
-4, 0, 1
Let o = 470995/6 - 78499. Factor o*t**5 + 1/6*t**4 - 1/6*t**3 + 0*t - 1/6*t**2 + 0.
t**2*(t - 1)*(t + 1)**2/6
Suppose 17*h - 14*h = k + 5, -2*h - 2*k = 10. Let s be (-2)/(-7)*7 + h - -106. Determine w so that -16/3 - 176/3*w - 264*w**3 - 628/3*w**2 - s*w**4 = 0.
-1, -2/9
Let c(z) be the second derivative of -z**4/6 + 10*z**3/3 + 171*z**2 - 11*z + 40. Determine m, given that c(m) = 0.
-9, 19
Let a(k) be the second derivative of k**6/105 + 3*k**5/70 + k**4/21 - 148*k. Factor a(d).
2*d**2*(d + 1)*(d + 2)/7
Determine k, given that 2336/5 - 128/5*k**3 - 2/5*k**4 - 3472/5*k + 1266/5*k**2 = 0.
-73, 1, 4
Let i(x) = 6*x**2 - 2*x + 4. Let a(l) = 41*l**2 - 828*l - 165621. Let k(u) = 2*a(u) - 14*i(u). Let k(d) = 0. What is d?
-407
What is z in -444*z + 8000 - 2*z**