 first derivative of -33*q**2 - 56 - 5/3*q**3 + 56*q. Factor b(t).
-(t + 14)*(5*t - 4)
Let m(k) = -6*k**4 - 63*k**3 + 1009*k**2 - 954*k + 7. Let j(c) = 5*c**4 + 63*c**3 - 1011*c**2 + 955*c - 6. Let d(i) = 7*j(i) + 6*m(i). Factor d(o).
-o*(o - 31)**2*(o - 1)
Suppose 12*c - 2 = 130. Factor 2*k**2 - 12 + 16 - 3*k**2 + 3*k**2 - 5*k + c*k.
2*(k + 1)*(k + 2)
Let n(k) be the third derivative of k**5/80 - 17*k**4/96 - 7*k**3/6 - 2*k**2 - 1572*k. Solve n(c) = 0.
-4/3, 7
Let j(u) = u**3 + 10*u**2 + 10*u + 7. Let v be j(-9). Let y be (-3)/(v*(-12)/(-16)). Factor 0*t**2 + 2409 + t + 0*t**y - t**2 - 2407.
-(t - 2)*(t + 1)
Determine s so that -45*s**2 + 85/2*s + 0 + 5/2*s**3 = 0.
0, 1, 17
Let g(k) be the third derivative of k**10/100800 - k**9/40320 + 11*k**5/20 + k**3/2 + 18*k**2. Let s(h) be the third derivative of g(h). What is u in s(u) = 0?
0, 1
Let d(p) be the third derivative of -p**6/240 + 23*p**5/72 + 11*p**4/8 + 20*p**3/9 - 212*p**2 - 2. Factor d(c).
-(c - 40)*(c + 1)*(3*c + 2)/6
Find h such that -13345*h - 41209 - 227*h**2 - 27458*h + 2*h**3 + 632*h**2 - 3*h**3 = 0.
-1, 203
Suppose -109*y - 328 + 433 + 658 = 0. Let p(t) be the second derivative of 5/12*t**4 + 0*t**2 + 0 - 5/42*t**y - 6*t + 1/4*t**5 - 1/6*t**6 + 0*t**3. Factor p(i).
-5*i**2*(i - 1)*(i + 1)**2
Suppose -1517*s + 1524*s + 2198 = 0. Let j = s + 318. What is l in 0 + 2/9*l - 2/9*l**3 - 2/9*l**j + 2/9*l**2 = 0?
-1, 0, 1
Let z(t) be the second derivative of 5/3*t**3 + 9*t - 1/12*t**5 - 15/2*t**2 - 5/24*t**4 + 0. Let w(v) be the first derivative of z(v). Factor w(s).
-5*(s - 1)*(s + 2)
What is m in 12*m**2 + 428*m + 1977*m - 17*m**2 = 0?
0, 481
Suppose 9*l - 1 = 1 - 2. Suppose l + 2*a**5 + 26/5*a**4 + 0*a**2 - 12/5*a**3 + 0*a = 0. Calculate a.
-3, 0, 2/5
Let m(z) be the first derivative of -z**5/140 + z**4/7 - 6*z**3/7 - 29*z**2 - 36. Let f(o) be the second derivative of m(o). Find a such that f(a) = 0.
2, 6
Let p(q) be the second derivative of -q**5/10 + 19*q**4/18 - 10*q**3/3 + 8*q**2/3 + 8*q + 21. Find b such that p(b) = 0.
1/3, 2, 4
Let l(m) be the third derivative of 9/100*m**5 + 1/200*m**6 + m**2 + 16 + 0*m + 3/8*m**4 + 7/10*m**3. Factor l(h).
3*(h + 1)**2*(h + 7)/5
Factor 2/7*y**4 + 0 - 288/7*y**2 + 36/7*y**3 + 0*y.
2*y**2*(y - 6)*(y + 24)/7
Let k be 16 + -24 - 288/(-27). Solve 0 - 4*v**2 - 2/3*v**3 - 2/3*v**5 + 0*v + k*v**4 = 0 for v.
-1, 0, 2, 3
Factor -2/15*q**2 - 1082/15*q - 2156/15.
-2*(q + 2)*(q + 539)/15
Determine c so that -79/12*c**2 + 23/2*c - 31/12*c**3 - 14/3 + 9/4*c**4 + 1/12*c**5 = 0.
-28, -2, 1
Suppose -30*w + 28*w - 140 = t, -3*t + 5*w = 365. Let b be (-1 + (-11)/(-14))*(t - -128). Factor -12/7 + 9/7*v**2 - b*v**3 + 0*v.
-3*(v - 2)**2*(v + 1)/7
Let g = 486883/2 - 243440. Factor 0*x + 0 + 3*x**2 + g*x**3.
3*x**2*(x + 2)/2
Let p(t) be the first derivative of -t**6/6 + 9*t**5/4 - 35*t**4/12 - 15*t**3/2 + 20*t**2 - 307*t + 210. Let s(y) be the first derivative of p(y). Factor s(x).
-5*(x - 8)*(x - 1)**2*(x + 1)
Suppose -5*r - 190*x + 98*x = -89*x - 45, -x + 10 = 0. Solve 27/8 - 3/2*q**4 + 45/8*q**r - 15/8*q**2 - 45/8*q = 0 for q.
-1, 3/4, 1, 3
Let u = 2989/16530 - 39/2755. Factor -u*t**2 - 56/3*t - 1568/3.
-(t + 56)**2/6
Let l(y) be the first derivative of -97 + 26*y**3 - 21/4*y**4 - 84/5*y**5 + 10*y**6 - 39/2*y**2 + 6*y. Determine p so that l(p) = 0.
-1, 2/5, 1/2, 1
Suppose -17*b = -12*b + p - 8, -2*p - 4 = 0. Find l, given that -740*l - 6845 - 10*l**2 - 5*l**2 - 5*l**b = 0.
-37/2
Let x be -4*99/22*6/(-36). Let o(v) be the second derivative of 0 + 1/4*v**4 - 15*v + 0*v**x - 1/20*v**5 - 2*v**2. Determine z so that o(z) = 0.
-1, 2
Let z(r) be the third derivative of -r**5/390 - 43*r**4/156 - 460*r**3/39 - r**2 - 7*r + 460. Let z(s) = 0. What is s?
-23, -20
Let b(h) be the first derivative of 2*h**5/25 + 6*h**4/5 + 18*h**3/5 - 2031. Determine i so that b(i) = 0.
-9, -3, 0
Let r(s) = s**3 + 20*s**2 - 124*s + 28. Let j be r(-25). Factor 5*f + 90*f**2 + j*f**4 - 53*f - 126*f**2.
3*f*(f - 4)*(f + 2)**2
Let f(u) be the second derivative of -u**5/20 + 11*u**4/12 - 4*u**3 - 18*u**2 + 115*u - 16. Let f(n) = 0. Calculate n.
-1, 6
Let m(u) = -u**3 - 4*u**2 - 2*u + 17. Let o be m(-10). Let n be 7*13/(o/14). Factor -t + 1/2*t**4 + 5/2*t**2 + 0 - n*t**3.
t*(t - 2)*(t - 1)**2/2
Let s be (-2095)/419 - (-2 - -4)*1 - (-42)/1. What is w in -10/3*w - 95/3*w**4 + 0 + 25/3*w**5 - 25/3*w**2 + s*w**3 = 0?
-1/5, 0, 1, 2
Let w = 6470 - 6470. Let h(d) be the third derivative of 1/15*d**5 + 0*d**3 + 1/20*d**6 + 0*d + w + 0*d**4 - 16*d**2. Factor h(x).
2*x**2*(3*x + 2)
Factor -356/11*d**3 + 2/11*d**5 + 544/11*d**2 - 366/11*d + 92/11 + 84/11*d**4.
2*(d - 1)**4*(d + 46)/11
Let f = 5444/99 + -600/11. Let w(k) be the first derivative of 0*k**2 - 4/3*k + f*k**3 + 13. What is j in w(j) = 0?
-1, 1
Let g(p) = -4*p + 16 + 5*p - 5*p + 6*p. Let z be g(-7). Factor -14*f**3 + 7*f**3 + 4*f**2 + 5*f**3 + 2*f**z.
-2*f**2*(f - 3)
Let l(j) be the third derivative of j**7/1260 + j**6/18 + 5*j**5/3 - j**4/8 + 11*j**3/6 - 30*j**2. Let n(a) be the second derivative of l(a). Factor n(i).
2*(i + 10)**2
Let x(u) be the first derivative of 2*u**5/65 + 3*u**4/13 - 2*u**3/13 - 20*u**2/13 - 24*u/13 - 1701. Determine d, given that x(d) = 0.
-6, -1, 2
Suppose -3496*i + 14364 = 1250*i + 4872. Determine t so that -282/7*t + 6627/7 + 3/7*t**i = 0.
47
Factor 12*b**3 - 5184 + 1728*b - 1/4*b**4 - 216*b**2.
-(b - 12)**4/4
Let n = 557 + -1135. Let h = 583 + n. Find y, given that 6/11*y**h - 8/11*y**3 - 8/11*y**2 + 0 + 0*y + 10/11*y**4 = 0.
-2, -2/3, 0, 1
Let f(q) = -156*q**3 - 4*q**2 - 3*q + 19. Let c be f(2). Let h = 1251 + c. Factor 2*l**4 + h - 1/2*l**5 + 7/2*l + 9*l**3 + 10*l**2.
-l*(l - 7)*(l + 1)**3/2
Let j(o) be the second derivative of 5/21*o**7 - 12*o**2 + 13/3*o**4 - 14/15*o**6 + 0 - 6/5*o**5 + 7/3*o**3 - 130*o. Solve j(r) = 0 for r.
-1, 4/5, 1, 3
Determine k so that -25*k**5 - 13*k**3 + 414*k**4 - 7*k**3 - 459*k**4 = 0.
-1, -4/5, 0
Suppose 0 = -193*i - 100158 + 100544. Factor -16/5 - 76/15*w - 2*w**i - 2/15*w**3.
-2*(w + 1)*(w + 2)*(w + 12)/15
Let w(q) be the second derivative of -1/56*q**6 + 0 + 0*q**3 + 5/2*q**2 + 1/28*q**4 - 4*q - 3/140*q**5. Let y(i) be the first derivative of w(i). Factor y(v).
-3*v*(v + 1)*(5*v - 2)/7
Let p(b) be the second derivative of b**5/60 + 5*b**4/18 - 37*b**3/18 + 13*b**2/3 - 523*b + 1. Factor p(w).
(w - 2)*(w - 1)*(w + 13)/3
Let c(f) be the first derivative of f**6/45 - 4*f**4/3 + 64*f**3/9 - 16*f**2 + 5*f + 42. Let q(v) be the first derivative of c(v). Factor q(r).
2*(r - 2)**3*(r + 6)/3
Suppose 4*o = -3*w + 28, -4*w = -2*o - 2*w. Solve 184*a**3 - 4*a**5 + 296*a**2 - 358*a**4 + 23 + 29 + 105*a + 99*a + 394*a**o = 0 for a.
-1, 13
Factor 0 + f**5 - 2/5*f**4 + 0*f + 8/5*f**2 - 11/5*f**3.
f**2*(f - 1)**2*(5*f + 8)/5
Suppose 200*d**2 + 112*d + 105*d**3 + 1/2*d**5 + 35/2*d**4 + 0 = 0. What is d?
-28, -4, -2, -1, 0
Let r(y) be the second derivative of -y**4/6 - 7*y**3 + 22*y**2 - 29*y - 19. Suppose r(w) = 0. What is w?
-22, 1
Let m be (1/2 + 0)*(-329 + 329). Let d(v) be the second derivative of m + 7/90*v**4 + 2/5*v**2 - 23/45*v**3 + 20*v. Factor d(l).
2*(l - 3)*(7*l - 2)/15
Let v = -14 - -18. Suppose 0 = v*q - 32 - 4. Find r, given that q*r**4 + 7*r**5 - 4*r**2 + 2*r**3 - 5*r**2 - 7*r**3 - 2*r = 0.
-1, -2/7, 0, 1
Let g be -3*(-9 + (-60)/(-18)). Suppose z + g = -2*i + 11, i = -5*z + 6. Solve 0 - 4/7*c - 8/7*c**4 + 10/7*c**3 + z*c**2 = 0 for c.
-1, 0, 1/4, 2
Let k = -463288/5 + 92662. Suppose -18/5*h**2 - 42/5*h - k + 2/5*h**3 = 0. What is h?
-1, 11
Let w(u) = -6*u**2 - 2*u. Let m be w(2). Let d = m - -30. Find c such that -5*c**3 - 10 + 10 + 15*c + 0*c**2 + 10*c**d = 0.
-1, 0, 3
Let p(w) be the first derivative of -5*w**3/3 - 7885*w**2 - 12434645*w + 5330. Suppose p(t) = 0. Calculate t.
-1577
Let x(i) = -10*i - 1 + 5*i**2 + 3 - 8*i**2. Let n(t) = t**2 + t - 1. Let h = 49 + -48. Let g(y) = h*x(y) - n(y). Find o, given that g(o) = 0.
-3, 1/4
Factor -136/7 - 194/7*v**2 + 416/7*v + 10/7*v**3.
2*(v - 17)*(v - 2)*(5*v - 2)/7
Factor -258*p**2 - 45043 + 87*p + 252*p**3 - 78*p**4 + 45043 - 3*p**5.
-3*p*(p - 1)**3*(p + 29)
Let b be (-94)/(-5) + (-6)/(-5). Let 4 + 1577*d**2 + 4352*d**2 + 90*d + b*d + 198*d = 0. Calculate d.
-2/77
Let h = 3765235/65747 + 25/5977. Factor -h*r**2 + 300/11*r + 0 - 288/11*r**3 -