**2 + 409. Factor h(k).
4*k*(k - 3)*(k + 1)**2
Suppose 32 = 2*v + 4. Factor -12*p + v*p + p**3 - p**3 - 4*p**2 + 2*p**3.
2*p*(p - 1)**2
Determine m so that -16/5*m - 2/5*m**3 + 0 + 18/5*m**2 = 0.
0, 1, 8
Let c be -4*(-21)/(-90)*7/(-49). Let f(w) be the first derivative of c*w**3 + 0*w**4 - 2/25*w**5 - 1/30*w**6 - 6 + 1/10*w**2 + 0*w. Factor f(s).
-s*(s - 1)*(s + 1)**3/5
Let s = 6594 + -32964/5. Let -4/5*y**2 + 0*y - 16/5*y**4 - 14/5*y**3 - s*y**5 + 0 = 0. Calculate y.
-1, -2/3, 0
Let w = -885/17 - -10883/51. Let n = w - 161. Solve 2/3*g + 1/3*g**2 + n = 0.
-1
Let c(p) = -182*p - 180. Let b be c(-1). Suppose -l**b + 0 - 1/3*l = 0. What is l?
-1/3, 0
Factor -4/3*v - 14/3*v**2 + 10/3.
-2*(v + 1)*(7*v - 5)/3
Suppose 5*k + 103 = s - 163, 2*s - 524 = 2*k. Let z be (-667)/s - ((-1 - -1) + -3). Factor -10/9*u + 2/9*u**5 + z + 8/9*u**3 + 4/9*u**2 - 8/9*u**4.
2*(u - 2)*(u - 1)**3*(u + 1)/9
Let r(u) be the second derivative of u**4/6 - 157*u**3/3 - 158*u**2 + 2*u + 73. What is z in r(z) = 0?
-1, 158
Let u(c) be the third derivative of -c**5/210 - 2*c**4/7 - 23*c**3/21 - 313*c**2 + 2*c. Factor u(h).
-2*(h + 1)*(h + 23)/7
Let t(f) be the first derivative of -f**3/3 + 75*f**2 - 149*f - 56. Solve t(l) = 0.
1, 149
Let q(t) = 5*t**2 - 25*t + 20. Let u(z) = -5*z**2 + 25*z - 20. Let l(f) = -f**3 + 21*f**2 - 2*f + 36. Let p be l(21). Let j(a) = p*u(a) - 5*q(a). Factor j(y).
5*(y - 4)*(y - 1)
Factor -3*d**2 + 144*d + 2*d**3 - 12*d**3 - 21*d**2 + 11*d**3.
d*(d - 12)**2
Let b = 14165/1738 + 5/158. Let m be (-29)/11 + 3/1. Solve -24/11*l**4 + 104/11*l**3 - m - b*l**5 - 14/11*l + 28/11*l**2 = 0 for l.
-1, -1/3, 2/5, 1
Let u(l) = l**2 + 9*l - 1. Let w(x) = -10*x**2 - 96*x + 12. Let v(y) = 12*u(y) + w(y). Let v(r) = 0. Calculate r.
-6, 0
Let j(c) be the second derivative of -2*c**6/15 + 7*c**5/5 + 19*c**4/3 - 14*c**3/3 - 36*c**2 + 190*c + 2. Suppose j(u) = 0. What is u?
-2, -1, 1, 9
Let x(c) be the second derivative of c**4/72 - 5*c**3/36 + c**2/3 - 134*c. Factor x(m).
(m - 4)*(m - 1)/6
Let n(t) be the third derivative of 5*t**8/336 + 25*t**7/42 + 187*t**6/24 + 121*t**5/4 - 75*t**2. Factor n(f).
5*f**2*(f + 3)*(f + 11)**2
Suppose 10 - 493 = 3*i. Let u = i + 1773/11. What is v in 0*v + u*v**3 + 0*v**2 - 2/11*v**5 + 0 + 0*v**4 = 0?
-1, 0, 1
Factor 0*a - 5/4*a**3 + 0 - a**2 - 1/4*a**4.
-a**2*(a + 1)*(a + 4)/4
Let o(p) be the first derivative of p**8/12600 - p**7/6300 - 3*p**3 - 2. Let x(c) be the third derivative of o(c). Factor x(d).
2*d**3*(d - 1)/15
Let x be (26/40 + ((-42)/(-24))/(-7))/2. Determine r, given that 8/5*r**2 + x*r**4 + 0 - 4/5*r - r**3 = 0.
0, 1, 2
Let k(o) be the third derivative of -2*o**5/45 + o**4/18 + 10*o**3/3 - 103*o**2. Solve k(y) = 0 for y.
-5/2, 3
Let b be (480/(-150))/((-364)/65). Solve 0 - b*u**2 - 12/7*u = 0.
-3, 0
Let d(y) be the first derivative of -27*y**5/5 - 69*y**4/4 - 62*y**3/3 - 34*y**2/3 - 8*y/3 + 29. Solve d(f) = 0 for f.
-1, -2/3, -2/9
Suppose -2/5*a**5 + 0*a**2 + 0*a + 0 + 0*a**3 + 8/5*a**4 = 0. What is a?
0, 4
Let d(a) be the first derivative of -a**7/280 + a**6/24 + 17*a**3/3 - 2. Let l(w) be the third derivative of d(w). Factor l(b).
-3*b**2*(b - 5)
Let m be (-55)/22*(-84)/10. Suppose -m - 6 = -3*b. Determine o so that 6*o**2 - 2*o + 2*o**4 - 5*o + b*o + 6*o**3 + 0*o**2 = 0.
-1, 0
Let h(x) = x**3 + 7*x**2 - x - 6. Let l be h(-7). Let j be (l/3)/(8/120). Factor -2*i**3 + 4*i**4 + 0*i**5 - 4*i**3 - 3*i**j + 5*i**4.
-3*i**3*(i - 2)*(i - 1)
Let f be ((-5)/6)/((-190)/114). Let q(b) be the first derivative of -3 + f*b + 1/2*b**3 + 1/8*b**4 + 3/4*b**2. Factor q(t).
(t + 1)**3/2
Suppose 7*u**3 - 7*u + 9 + 3*u**2 - 8*u - 3*u**3 - u**3 = 0. Calculate u.
-3, 1
Let m(l) be the second derivative of 0*l**4 + 0*l**3 - 1/150*l**6 + 0 + 6*l - 1/210*l**7 + 0*l**2 + 0*l**5. Find n, given that m(n) = 0.
-1, 0
Let f = -16 - -21. Factor 5*b**f - b**4 + 2*b**4 + 10*b**2 - 5*b**3 - 11*b**4.
5*b**2*(b - 2)*(b - 1)*(b + 1)
Let a(b) be the second derivative of -12*b - 1/6*b**3 + 1 + b**2 - 1/12*b**4. Factor a(i).
-(i - 1)*(i + 2)
Let l(h) be the second derivative of 1/42*h**4 + 1/70*h**5 - 4*h - 4/7*h**2 + 0 - 4/21*h**3. Factor l(y).
2*(y - 2)*(y + 1)*(y + 2)/7
Determine w, given that 17/3*w**3 - 272/3*w + 64/3 - 4/3*w**4 + 20*w**2 = 0.
-4, 1/4, 4
Let f(m) be the first derivative of 25*m**7/42 + 25*m**6/27 + 2*m**5/9 - 4*m**4/9 + 40*m**3/3 - 10. Let t(c) be the third derivative of f(c). Factor t(x).
4*(5*x + 2)**2*(15*x - 2)/3
Let w(d) = -d - 8. Let o be w(-8). Let a be (-3 - -7)/(o - -2). Suppose -3*y**3 - 18*y + y**3 + 22*y - 2*y**a = 0. Calculate y.
-2, 0, 1
Let d be 8/44 - ((-141)/11 + 3). Suppose d*x - 15*x = -20. Find w such that -4/7*w**3 + 0*w + 0*w**2 + 0 - 2/7*w**x = 0.
-2, 0
Let s = 2 - -2. Factor -18*c - s*c**2 - 5 + 8*c**2 + 14*c - 3.
4*(c - 2)*(c + 1)
Let h(l) be the third derivative of l**7/70 + l**6/24 - l**5/30 + 10*l**2 - 5. Factor h(j).
j**2*(j + 2)*(3*j - 1)
Let 0 - 1/4*j**5 - 11/4*j**4 - 2*j - 27/4*j**3 - 25/4*j**2 = 0. What is j?
-8, -1, 0
Let g(w) = w**2 - 89*w + 1114. Let j be g(15). Factor 0*a - 1/7*a**j + 0 + 0*a**3 + 1/7*a**2.
-a**2*(a - 1)*(a + 1)/7
Let z(t) be the second derivative of -t**5/210 + t**4/7 - 12*t**3/7 - 15*t**2/2 - 24*t. Let f(a) be the first derivative of z(a). Determine n so that f(n) = 0.
6
Let g(x) = -x**3 - 10*x**2 + 28*x + 191. Let w be g(-11). Factor 0*y**w + 4/5*y**3 - 2/5*y + 0 + 0*y**2 - 2/5*y**5.
-2*y*(y - 1)**2*(y + 1)**2/5
Let t(a) be the second derivative of -1/20*a**6 + 1/20*a**5 + 0 + 1/84*a**7 + 1/12*a**4 + 1/4*a**2 - 1/4*a**3 - 13*a. Factor t(d).
(d - 1)**4*(d + 1)/2
Suppose 0 - 2/5*q**4 - 56/15*q**2 + 16/5*q**3 + 0*q - 2/15*q**5 = 0. Calculate q.
-7, 0, 2
Let v(c) be the third derivative of c**8/33600 - c**7/6300 + c**4 - 37*c**2. Let d(j) be the second derivative of v(j). Determine b, given that d(b) = 0.
0, 2
Let s(i) be the third derivative of -i**9/241920 + i**7/6720 - i**6/1440 - 7*i**5/60 - 17*i**2. Let b(w) be the third derivative of s(w). What is l in b(l) = 0?
-2, 1
Let y(k) be the first derivative of 2/7*k + 1/21*k**3 - 13 - 3/14*k**2. Factor y(h).
(h - 2)*(h - 1)/7
Let p(l) = -20*l**5 + 120*l**4 - 75*l**3 + 25*l**2 + 25. Let t(y) = 5*y**5 - 30*y**4 + 19*y**3 - 6*y**2 - 6. Let c(r) = 6*p(r) + 25*t(r). Factor c(k).
5*k**3*(k - 5)*(k - 1)
Factor 4*r**2 - 278*r - 71*r + 59*r - 146*r - 2*r**2 + 23762.
2*(r - 109)**2
Suppose 701*s = 680*s. Determine v so that 0*v - 49/6*v**2 - 1/6*v**5 - 21/2*v**3 + s - 5/2*v**4 = 0.
-7, -1, 0
Let s be (-656)/(-22) + (-20)/(-110). Let t be (-2)/12 - (-365)/s. Factor t*b**3 + 5*b**4 - 3*b**3 + b**5 + 2*b**5 + 4*b**4 + 3*b**2.
3*b**2*(b + 1)**3
Let n be 1932/336 + (-14)/8. Factor -8/7*d**2 - 9/7*d**5 - 4*d**3 - 30/7*d**n + 0*d + 0.
-d**2*(d + 2)*(3*d + 2)**2/7
Let l = -361 + 361. Let d(k) be the first derivative of 3 - 1/6*k**2 + 1/9*k**3 + l*k. Determine m so that d(m) = 0.
0, 1
Let k be (-18)/(-52) + -10 + 7 + 41/13. Determine q so that 1/2*q - 1/2*q**2 - 1/2*q**3 + k = 0.
-1, 1
Let j = 24 + -4. Suppose -3 = 5*k + 3*w - 13, 2*k - 2*w - j = 0. Determine d, given that -d + k*d - 8*d + 4*d**2 = 0.
0, 1
Factor 0 + 2/13*f**5 + 0*f**2 + 10/13*f**4 + 0*f - 12/13*f**3.
2*f**3*(f - 1)*(f + 6)/13
Let c(q) be the first derivative of 11/48*q**4 + 3/80*q**5 - 4 + 1/3*q**3 - 5*q - 1/2*q**2. Let a(x) be the first derivative of c(x). Factor a(t).
(t + 2)**2*(3*t - 1)/4
Let l(g) be the third derivative of 0*g**4 - 1/480*g**6 + 0 + 19*g**2 + 0*g - 1/840*g**7 + 0*g**5 + 0*g**3. Factor l(b).
-b**3*(b + 1)/4
Let q = 54 + -52. Let m be (q/14)/((-10)/(-10)). Let m*r**3 + 0 + 0*r + 0*r**2 - 2/7*r**4 + 1/7*r**5 = 0. What is r?
0, 1
Let x = -899683/8020 - -2243/20. Let y = 8906/2807 + x. Determine d so that -60/7*d**3 - 50/7*d**4 + y*d**2 + 24/7*d - 8/7 = 0.
-1, 2/5
Let j(a) be the second derivative of a**5/5 - 4*a**4 + 24*a**3 - 16*a. Suppose j(y) = 0. What is y?
0, 6
Let s(u) be the third derivative of u**4/12 - 25*u**3/6 + 13*u**2. Let r be s(14). Factor -2/13 + 6/13*y - 6/13*y**2 + 2/13*y**r.
2*(y - 1)**3/13
Suppose 2*j = -2*j + 52. Suppose -j*u + 25 = -8*u. Factor 4*c**3 - 2*c + 0 - 2*c**u + 0 + 0.
-2*c*(c - 1)**2*(c + 1)**2
Let q = 627/2 - 313. Let o be (-15)/(-12)*5*(-2)/(-25). Find b, given that o*b - q*b**3 + 1/2 - 1/2*b**2 = 0.
-1, 1
Let h(v) be the second derivative