k(l) = 8*l**3 - 12*l**2 - 18*l - 8. Let d(j) = -j**3 + j**2 + j + 4. Let b(r) = 6*d(r) + k(r). Factor b(f).
2*(f - 4)*(f - 1)*(f + 2)
Let b(c) be the first derivative of -225*c**7/112 + 15*c**6/8 - 3*c**5/4 + c**4/6 + 2*c**3 + 8. Let d(s) be the third derivative of b(s). Factor d(l).
-(15*l - 2)**3/2
Let p be ((-3)/2)/(6/(-16)). Suppose -p*s + 2*s + 6 = 0. Factor 4*k + k**2 - 9*k**3 + 3*k**4 - k**4 + 5*k**s - 3*k**2.
2*k*(k - 2)*(k - 1)*(k + 1)
Let k = -1073403/55 + 19517. Let q = k + -2/11. Determine h, given that -2/5 - 6/5*h**3 + 6/5*h - q*h**2 + 4/5*h**4 = 0.
-1, 1/2, 1
Let c(j) be the second derivative of j**6/225 + 2*j**5/75 + j**4/15 + 4*j**3/45 + j**2/15 + 64*j - 2. Factor c(d).
2*(d + 1)**4/15
Let x(f) be the first derivative of -5*f**3/3 + 250*f**2 - 310. Find w such that x(w) = 0.
0, 100
Let q(a) be the second derivative of -8/3*a**3 - 5/3*a**4 - 2/5*a**5 + 0 - 9*a - 2*a**2. Factor q(p).
-4*(p + 1)**2*(2*p + 1)
Let l = -59/20 - -3. Let b(x) be the third derivative of 5/24*x**4 + 1/3*x**3 - 1/120*x**6 + 5*x**2 + l*x**5 + 0 - 1/210*x**7 + 0*x. Factor b(s).
-(s - 2)*(s + 1)**3
Suppose 3*a + 3*z + 0*z = -3, -2*a - 4*z = 0. Let r be (4 - 2)/((-1)/a). Factor -15*l**r + 19*l**4 + 4 - 8*l**2 + 0.
4*(l - 1)**2*(l + 1)**2
Let p(o) be the third derivative of -o**5/360 - o**4/36 + 5*o**3/4 + 209*o**2. Determine v so that p(v) = 0.
-9, 5
Let g(b) be the third derivative of -5/24*b**4 + 0 + 0*b + 0*b**3 - 1/42*b**7 - 12*b**2 - 1/4*b**5 - 1/8*b**6. Suppose g(r) = 0. What is r?
-1, 0
Let l = 1681/6 - 555/2. Let m be (-14)/(-8)*8/6. Factor 4/3 - l*p - m*p**2 + 5/3*p**3.
(p - 2)*(p + 1)*(5*p - 2)/3
Let h(z) be the third derivative of -8*z**7/105 - 3*z**6/10 - 2*z**5/15 - 189*z**2. Factor h(b).
-4*b**2*(b + 2)*(4*b + 1)
Let w(i) = -3*i + 93. Let y be w(28). Suppose -y*c - 6 = -12*c. Factor -1/6 - 5/6*q - 4/3*q**c - 2/3*q**3.
-(q + 1)*(2*q + 1)**2/6
Let m(l) be the second derivative of -1/14*l**7 - 1089/20*l**5 + 0 + 1331/4*l**4 + 0*l**2 + 33/10*l**6 + 0*l**3 + 12*l. Suppose m(f) = 0. What is f?
0, 11
Let k(v) be the first derivative of v**6/30 + 3*v**5/10 + v**4 + 4*v**3/3 - 12*v + 1. Let i(h) be the first derivative of k(h). What is w in i(w) = 0?
-2, 0
Let k be -15*(717/(-105) - -4). Let n = k + -41. Let 2/7*h**2 - n*h + 8/7 = 0. Calculate h.
1, 4
Let k(o) = o**5 + o**4 - o**3 - o**2 + o. Let s(z) = -54*z**5 + 86*z**4 - 44*z**3 + 12*z**2 - 4*z. Let c = 25 + -24. Let i(y) = c*s(y) + 4*k(y). Factor i(u).
-2*u**2*(u - 1)*(5*u - 2)**2
Let c(j) = j**3 - 35*j**2 + j - 26. Let i be c(35). Let t(d) be the first derivative of 10*d - i - 15/2*d**2 + 5/3*d**3. Suppose t(p) = 0. What is p?
1, 2
Let a(t) = -14*t**5 - 239*t**4 + 187*t**3 + 72*t**2 - 3*t. Let x(l) = -l**4 - l**3 + l. Let z(o) = a(o) + 3*x(o). Find q such that z(q) = 0.
-18, -2/7, 0, 1
Let y be (-161)/1225*-5 + 2/14. Let j be -1 + -1 - (-13)/5. Factor 4/5 + 4/5*k**3 - j*k**2 - 1/5*k**4 - y*k.
-(k - 2)**2*(k - 1)*(k + 1)/5
Let q(h) = -13*h**4 + 31*h**3 + 245*h**2 + 202*h - 479. Let p(j) = -6*j**4 + 15*j**3 + 123*j**2 + 102*j - 240. Let g(o) = 7*p(o) - 3*q(o). Factor g(v).
-3*(v - 9)*(v - 1)*(v + 3)**2
Let j(q) = q**2 - 27*q + 59. Let l be j(20). Let k be 3/(l/(-6)) + 4/63. Factor 2/7*n**4 + 2/7*n**3 + 0 - k*n**2 - 2/7*n.
2*n*(n - 1)*(n + 1)**2/7
Factor -10/3*h**2 - 11/6*h**3 - 7/6*h + 1/3.
-(h + 1)**2*(11*h - 2)/6
Let f(x) be the second derivative of x**5/10 - x**4/4 + x**3/6 + 41*x. Factor f(z).
z*(z - 1)*(2*z - 1)
Suppose 4*h + 5*g = h + 33, -2*g + 42 = 3*h. Suppose 3*j - 7*j + h = 0. Factor -4*d**4 + 6*d**2 + d**3 - 6*d**3 - j*d - 14*d**2 + 3*d**4.
-d*(d + 1)*(d + 2)**2
Let h = -232 + 233. Let z be h*(6 - (-3 + 5)). Determine m so that -1/5*m**5 + 3/5*m - 2/5*m**3 - 2/5*m**2 - 1/5 + 3/5*m**z = 0.
-1, 1
Suppose 4*t = 4*v + 4, 0 = 4*t - 2*v + 7*v - 13. Let o be ((-7)/t)/((-12)/24). Solve 18*j + 2*j**2 - o*j - 9*j = 0.
-1, 0
What is y in -71*y**2 - 25*y**2 - 2726*y - 3*y**3 - 23659 + 2*y**3 - 346*y - 9109 = 0?
-32
Let c(i) = i**2 - 7*i + 6. Let w(m) = -m**2 + 8*m - 9. Let y(s) = 3*c(s) + 2*w(s). Factor y(a).
a*(a - 5)
Let g(u) be the third derivative of 0 + 1/300*u**5 - u**2 + 0*u + 1/30*u**3 + 1/60*u**4. Suppose g(m) = 0. What is m?
-1
Let m = -227/23940 - -2/133. Let g(n) be the third derivative of n**2 + m*n**5 + 0*n + 0 + 1/18*n**3 - 1/36*n**4. Factor g(l).
(l - 1)**2/3
Let h(a) = 2*a**4 - 10*a**3 + 24*a**2 - 10*a + 2. Let j(g) = -10*g**4 + 49*g**3 - 121*g**2 + 49*g - 11. Let f(k) = 22*h(k) + 4*j(k). Factor f(i).
4*i*(i - 3)*(i - 2)*(i - 1)
Let j(a) be the second derivative of -a**4/60 - 7*a**3/30 - 6*a**2/5 - 8*a - 2. Factor j(v).
-(v + 3)*(v + 4)/5
Suppose -4*l = 2*n + 26, 34 = -27*n + 23*n - 2*l. Let p be (400/10)/10 - 20/n. Factor 36/7*c**2 + 16/7 + p*c.
4*(3*c + 2)**2/7
Let n = -569/2 - -1139/4. Suppose -n*v**2 + 1/6 + 1/12*v**4 + 1/12*v**3 - 1/12*v = 0. What is v?
-2, -1, 1
Let v(q) be the second derivative of -5*q**4/66 + 9*q**3/11 - 10*q**2/11 - q - 259. Factor v(b).
-2*(b - 5)*(5*b - 2)/11
Let x be (376/120 - 3)/((-2)/(-3)). Suppose -6/5*w**2 + 0*w + 0 - w**3 + x*w**4 = 0. Calculate w.
-1, 0, 6
Let r(p) = -7*p**3 + 0*p - 18 - 5*p**2 - p + 15. Let z(y) = 76*y**3 + 56*y**2 + 12*y + 32. Let d(c) = -32*r(c) - 3*z(c). Determine t, given that d(t) = 0.
-1, 0
Let x(j) be the third derivative of -j**7/1785 + j**6/510 + 2*j**5/255 - 2*j**4/51 + j**2 + 13*j. Find t, given that x(t) = 0.
-2, 0, 2
Let m be 14/(-3 + 44/12). Let v be m*(1/12)/((-18)/(-16)). Find b, given that -14/9*b**3 - 4/9*b - 4/9*b**4 - v*b**2 + 0 = 0.
-2, -1, -1/2, 0
Let q be -6*(27/6 + -3). Let g = 12 + q. Factor 2*k**g - 1 - 3*k**3 + 0*k + 3*k - 1.
-(k - 1)**2*(k + 2)
Let m(j) be the second derivative of 49*j**5/40 - 7*j**4/4 + j**3 - 31*j**2/2 + j. Let b(x) be the first derivative of m(x). Factor b(h).
3*(7*h - 2)**2/2
Find k such that 78*k**3 - 11*k**4 + 6*k - 21*k**2 + 8*k**4 + 15*k**5 - 123*k**3 = 0.
-1, 0, 1/5, 2
Suppose -11 = -5*c - 2*s, -14 = c - 3*c - 4*s. Suppose 3*b = -c + 7. Suppose -2*k**2 - k**2 - k**b - 8*k - 2 - 2 = 0. What is k?
-1
Let k(b) be the third derivative of -b**8/2240 - b**7/420 + b**6/60 + b**5/5 + 3*b**4/8 - 8*b**2. Let u(h) be the second derivative of k(h). Factor u(a).
-3*(a - 2)*(a + 2)**2
Let j(z) be the first derivative of 1/5*z**5 + z**3 - 3/4*z**4 + 4 - 1/2*z**2 + 0*z. Let j(b) = 0. Calculate b.
0, 1
Let p(d) be the third derivative of -d**8/560 - 3*d**7/280 + d**6/30 + 4*d**3 + 7*d**2. Let z(q) be the first derivative of p(q). Factor z(h).
-3*h**2*(h - 1)*(h + 4)
Suppose 5*o = -3*j - 0*o + 29, -5*j + 11 = -o. Find z such that -74*z - j*z**2 + 26*z - 87 - 105 = 0.
-8
Let o(l) = l**4 + 317*l**3 + 11027*l**2 + 128621*l - 2. Let m(u) = u**4 - u**3 - u**2 + 2*u + 1. Let w(j) = 2*m(j) + o(j). Factor w(s).
3*s*(s + 35)**3
Let d = 43/26 - 58/39. What is h in -14/3*h - 98/3 - d*h**2 = 0?
-14
Solve -2/13*f**2 + 96/13 - 4/13*f = 0 for f.
-8, 6
Let p be 2*-6 + 6/36*90. Let -4/3*c**4 + 0 + 0*c - 4*c**p + 0*c**2 = 0. Calculate c.
-3, 0
Let y(x) = -x**4 - 3*x**2 + 3*x. Let d(j) = 2*j**4 + 2*j**2 - 2*j. Let n(a) = -a**2 - 10*a - 27. Let m be n(-5). Let i(g) = m*y(g) - 3*d(g). Factor i(b).
-4*b**4
Find l such that 3/2*l**3 + 1/2*l**4 + 0*l + l**2 + 0 = 0.
-2, -1, 0
Let g = 10121 - 10119. Factor 4/7*r**3 + 2/7*r**g + 0 + 2/7*r**4 + 0*r.
2*r**2*(r + 1)**2/7
Let t be (8/6)/(-4) + (-20)/(-6). Suppose 21 + t = 8*j. Factor -2/7*l**j - 2/7*l - 4/7*l**2 + 0.
-2*l*(l + 1)**2/7
Let q(b) be the second derivative of -b**4/24 + 2*b**3/9 - b**2/3 + 45*b. Factor q(i).
-(i - 2)*(3*i - 2)/6
Let m(b) be the first derivative of -b**4/5 - 76*b**3/15 - 14*b**2 - 68*b/5 + 224. Factor m(r).
-4*(r + 1)**2*(r + 17)/5
Let k(y) be the second derivative of y**5/20 + 13*y**4/12 + 2*y**3 - 25*y - 1. Factor k(l).
l*(l + 1)*(l + 12)
Factor -3/4*s**4 + 2*s**3 + 3/4*s**2 + 0*s + 0.
-s**2*(s - 3)*(3*s + 1)/4
Suppose 4*m - 8*m = -8. Factor -6*n + 20 - m*n**3 - 34 + 14 - 8*n**2.
-2*n*(n + 1)*(n + 3)
Let c(h) be the third derivative of -h**8/1120 - h**7/1260 + 3*h**6/40 + 3*h**5/20 + h**4/2 - 38*h**2. Let p(w) be the second derivative of c(w). Factor p(u).
-2*(u - 3)*(u + 3)*(3*u + 1)
Let c be 1/5 - (6 + (-59)/5). Let p(h) be the third derivative of -1/14*h**7 + 0 + 1/4*h**5 + 0*h + 1/4*h**4 - 1/20*h**c + 0*h**3 - 5*h**2. Factor p(n).
-3*n*