 - 36*a**2 + 200*a**3 - 2*a.
-3*a*(a + 1)*(a + 11)
Let s(f) = -3*f**2 + 15*f + 12. Let c(a) = -7*a**2 + 47*a + 38. Let o(b) = -3*c(b) + 8*s(b). Factor o(w).
-3*(w + 1)*(w + 6)
Let d(v) be the third derivative of -10*v**7/63 + 4*v**6/3 - 53*v**5/15 + 38*v**4/9 - 8*v**3/3 + 5*v**2 + 6. Determine i so that d(i) = 0.
2/5, 1, 3
Let t be (-1)/6 - 2/(-6). Let l(j) be the third derivative of 2/3*j**3 + 0 + 0*j + t*j**4 - 2*j**2 - 1/210*j**7 - 1/30*j**6 - 1/20*j**5. Factor l(o).
-(o - 1)*(o + 1)*(o + 2)**2
Let l = -90 + 27. Let n be (-47)/l + ((-10)/(-35))/2. Factor -4/3*k**3 - 2/9*k**5 - 2/9*k + 0 + n*k**2 + 8/9*k**4.
-2*k*(k - 1)**4/9
Let k = -23 + 29. Let u be 1 + 0 - (-6 + k). Factor 2 + 4 - 9*w**2 - u + 1 - 3*w.
-3*(w + 1)*(3*w - 2)
What is h in -192*h - 2*h**4 - 4*h**5 + 4*h**4 - h**4 + 3*h**4 - 144 + 52*h**3 - 4*h**2 = 0?
-2, -1, 3
Determine h, given that -30 + 3/2*h**3 + 3*h**2 - 57/2*h = 0.
-5, -1, 4
What is l in -4*l**2 - 1/2*l**3 + 1/2*l**4 + 6*l + 0 = 0?
-3, 0, 2
Let f = 7 + -4. Let r(i) = -i + 1. Let y(w) = w**2 - 2*w + 2. Let b(t) = f*y(t) - 6*r(t). Factor b(l).
3*l**2
Let q(n) = n**3 - n**2 + 1. Let k(s) = 114*s**3 + 9*s**2 - 117*s - 9. Let u(d) = k(d) + 3*q(d). Solve u(l) = 0.
-1, -2/39, 1
Suppose 0 = -j - 2*m + 11, 2*m + 3 - 4 = j. Suppose 3 + 3 = -3*k - 5*h, 4*k - j*h - 27 = 0. Factor 2*g**3 + 2*g**3 - 7*g**3 - k*g**4.
-3*g**3*(g + 1)
Let a(d) be the first derivative of 16*d**6/7 - 4688*d**5/35 + 27219*d**4/14 + 68104*d**3/21 + 11775*d**2/7 + 2500*d/7 - 49. Let a(m) = 0. What is m?
-2/3, -1/4, 25
Let l be (-4)/10*(-10)/1. Factor -h**4 + 14*h**3 + 6*h**2 + 7*h**l - 34*h**3.
2*h**2*(h - 3)*(3*h - 1)
Let r be (-4)/5 + 506/220. Let w = 40 + -38. Let -3/4*q**w + 0 + r*q = 0. What is q?
0, 2
Let c(j) be the third derivative of -1/510*j**5 - 7/204*j**4 - 7*j**2 + 8/51*j**3 + 0 + 0*j. Suppose c(z) = 0. Calculate z.
-8, 1
Solve 4/3*r - 16/9 - 2/9*r**2 = 0 for r.
2, 4
Factor 57 - 20*d**2 + 10*d**2 + 110*d + 23 + 45*d.
-5*(d - 16)*(2*d + 1)
Let n be 54/20 + 118/(-590). Factor -5 - n*l**2 + 15/2*l.
-5*(l - 2)*(l - 1)/2
Let m(n) be the first derivative of n**5/5 + n**4/3 - 17*n + 17. Let a(i) be the first derivative of m(i). Let a(x) = 0. What is x?
-1, 0
Let j = -116 - -205. Let b = 95 - j. What is i in 4 + 3*i**2 + 1/2*i**3 + b*i = 0?
-2
Let f(q) be the third derivative of 0 + 12*q**2 + 0*q**3 + 0*q + 1/60*q**5 + 1/420*q**7 - 1/80*q**6 + 0*q**4. Factor f(d).
d**2*(d - 2)*(d - 1)/2
Let a(x) be the first derivative of -25*x**6/6 - 11*x**5 - 35*x**4/4 - 5*x**3/3 - 95. Suppose a(k) = 0. What is k?
-1, -1/5, 0
Suppose -200 = 3*x - 203. Let s(l) be the first derivative of 1/3*l**3 - l**2 + 0*l + x + 1/4*l**4. Factor s(h).
h*(h - 1)*(h + 2)
Let k(m) be the first derivative of 25/9*m**2 + 20/27*m**3 + 0*m + 1/18*m**4 + 10. Suppose k(w) = 0. Calculate w.
-5, 0
Let y(b) be the third derivative of -49/18*b**4 - 1/270*b**6 - 7/45*b**5 - 2 - 686/27*b**3 + 0*b + 7*b**2. Determine o so that y(o) = 0.
-7
Find j such that 24/7*j**4 - 24*j**2 - 2/7*j**5 - 14*j + 0 - 44/7*j**3 = 0.
-1, 0, 7
Let a(d) be the second derivative of 0 - 1/2*d**2 + 4/9*d**3 + 1/90*d**6 - 2/45*d**5 - 1/18*d**4 + 6*d. Let o(h) be the first derivative of a(h). Factor o(q).
4*(q - 2)*(q - 1)*(q + 1)/3
Let w(b) be the third derivative of b**8/112 + b**7/42 + b**6/60 + 67*b**2 - 2*b. Determine d so that w(d) = 0.
-1, -2/3, 0
Let o = -48/959 - -1151/3836. Solve o*x + 3/2 - 1/4*x**2 = 0.
-2, 3
Let z(h) be the first derivative of 2*h**6/3 + 72*h**5/5 + 81*h**4 - 99. Find j, given that z(j) = 0.
-9, 0
Solve -21/2*m + 9 + 3/2*m**2 = 0.
1, 6
Suppose -6*b = -9*b + 5*j - 8, b + 3*j = 16. Let v be b/18 - ((-252)/(-81))/(-14). Factor 38/9*f**3 + 2/9*f - 10/3*f**2 + v - 14/9*f**4.
-2*(f - 1)**3*(7*f + 2)/9
What is i in -32/5*i - 88/5*i**2 + 0 + 18/5*i**4 - 48/5*i**3 = 0?
-2/3, 0, 4
Factor 436/9*r - 146/9 - 48*r**2 + 140/9*r**3 + 2/9*r**4.
2*(r - 1)**3*(r + 73)/9
Let i(b) be the third derivative of -b**8/168 - 2*b**7/105 - 117*b**2. Factor i(p).
-2*p**4*(p + 2)
Suppose 2*n - 5 = -y, -34 + 36 = 2*y. Factor -1/4*t**3 + 0*t**n + 0 + 0*t - 1/4*t**4.
-t**3*(t + 1)/4
Let h(c) be the second derivative of -2/21*c**4 + 1/35*c**5 + 2/21*c**3 + 0*c**2 + 0 - 2*c. Find k, given that h(k) = 0.
0, 1
Let q(v) be the first derivative of -v**4/22 - 26*v**3/33 - 23*v**2/11 - 2*v + 272. What is j in q(j) = 0?
-11, -1
Determine m so that -19/5*m**2 - 17/5 - 7*m - 1/5*m**3 = 0.
-17, -1
Let j(g) be the third derivative of 25*g**8/336 + 17*g**7/21 + 73*g**6/24 + 11*g**5/3 - 5*g**4/2 - 20*g**2. Find w, given that j(w) = 0.
-3, -2, 0, 1/5
Let q(y) be the second derivative of y**5/10 + 3*y**4 + 17*y**3/3 + 391*y. Factor q(c).
2*c*(c + 1)*(c + 17)
Let q = 19 - 14. Suppose -4*c + q*c - 2 = 0. Factor 0*x**4 + 3*x + 2*x**4 - 6*x**c - x + 2*x.
2*x*(x - 1)**2*(x + 2)
Let v(r) = 3*r**4 + 3*r**3 - r**2 - 3*r + 4. Let n(p) = -p**4 - p**3 - p**2 + p - 1. Let t(m) = -2*n(m) - v(m). Factor t(h).
-(h - 1)**2*(h + 1)*(h + 2)
Let h(b) = 2*b**2 - 3*b - 1. Let x be h(2). Let t(p) = p**2 + p + 1. Let m(d) = -13*d**2 + 12*d. Let z(s) = x*m(s) + 4*t(s). Factor z(r).
-(r - 2)*(9*r + 2)
Let f(z) = -22*z**3 - 24*z**2 - 17*z - 15. Let d(y) = y**3 - y**2 - y + 1. Let q(r) = 22*d(r) + 2*f(r). Factor q(m).
-2*(m + 1)*(m + 2)*(11*m + 2)
Let c = -32 + 32. Suppose c = -15*b + 7*b. Factor 0 + 0*o**2 + b*o**3 - 2/5*o**5 + 0*o**4 + 0*o.
-2*o**5/5
Let g(o) = 13*o**3 - 30*o**2 - 43*o + 60. Let i(q) = -3*q**3 + 7*q**2 + 11*q - 15. Let m(w) = -4*g(w) - 18*i(w). Factor m(j).
2*(j - 5)*(j - 1)*(j + 3)
Let r(n) = 19*n**2 - 659*n + 27546. Let g(l) = 60*l**2 - 1976*l + 82636. Let m(s) = -5*g(s) + 16*r(s). Factor m(y).
4*(y - 83)**2
Solve 0 + 5/8*m**4 + 1/2*m - 1/8*m**5 - 3/8*m**3 - 5/8*m**2 = 0 for m.
-1, 0, 1, 4
Let r(j) = 2*j**2 + 277*j - 6612. Let p(a) = -a**2 - 278*a + 6615. Let c(l) = -5*p(l) - 4*r(l). Determine f, given that c(f) = 0.
47
Let q(j) be the third derivative of -3*j**2 + 0*j + 1/10*j**6 + 0 + 0*j**3 + 0*j**4 - 1/2*j**5 - 1/175*j**7. Suppose q(i) = 0. What is i?
0, 5
Let p be 2/(-13) - 10947/(-3471). Determine t so that -2/5*t - 4/5*t**2 + 4/5 + 2/5*t**p = 0.
-1, 1, 2
Suppose 3*g + 0*j - 4*j - 22 = 0, -14 = 3*g + 5*j. Let -52*h - h**g + 52*h = 0. What is h?
0
Let u be (-33)/15 - (2 + (-1 - 4)). Let t(f) be the first derivative of -u*f + 8/5*f**2 - f**3 + 3. Determine n so that t(n) = 0.
2/5, 2/3
Let y(p) be the first derivative of 0*p**2 + 0*p + 9/20*p**5 - 14 + 3/8*p**4 - 1/4*p**3. Factor y(q).
3*q**2*(q + 1)*(3*q - 1)/4
Let i = 544 + -542. Factor 5/6*k**i - 1/6*k**3 + 0 - 2/3*k.
-k*(k - 4)*(k - 1)/6
Let j(q) be the third derivative of 1/270*q**6 + 1/135*q**5 + 1/1890*q**7 + 0*q + 22*q**2 + 0*q**4 + 0*q**3 + 0. Determine l so that j(l) = 0.
-2, 0
Let n(t) = -37*t**3 + 17*t**2 - 38*t + 16. Let v(p) = -23*p**3 + 11*p**2 - 25*p + 10. Let m(c) = -5*n(c) + 8*v(c). Solve m(b) = 0.
-5, 0, 2
Let a(f) be the second derivative of -55*f**4/8 + 18*f**3 - 15*f**2 - 2*f - 5. Factor a(m).
-3*(5*m - 2)*(11*m - 10)/2
Let p(d) = -2*d**5 + d**4 + 28*d**3 + 51*d**2 + 39*d + 10. Let t(m) = 234*m - 235*m + m**2 + 1 + m**4 - 1. Let o(f) = 2*p(f) + 2*t(f). Factor o(b).
-4*(b - 5)*(b + 1)**4
Let l be -2*4/(-16)*2. Let v(t) = -t**2. Let m(r) = 3*r**2 - 15*r + 6. Suppose 0 = 4*d - 7*d - 18. Let s(z) = d*v(z) + l*m(z). Factor s(w).
3*(w - 1)*(3*w - 2)
Let u(r) be the second derivative of -r**7/441 + r**6/21 - 43*r**5/105 + 116*r**4/63 - 32*r**3/7 + 128*r**2/21 - 62*r. Solve u(v) = 0 for v.
1, 2, 4
Let p(t) = t**2 - 9*t + 4. Let f be p(10). Factor 4 + 2*d**3 + 10*d**2 - 2 + 4 + 0*d**3 + f*d.
2*(d + 1)**2*(d + 3)
Let r(x) be the second derivative of -2/45*x**3 + 1/5*x**2 + 0 + 8*x - 1/90*x**4. Let r(u) = 0. What is u?
-3, 1
Let q = -1324 + 1324. Let v = 0 + 3. Solve 18/5*u**4 + q - 8/5*u**5 + 0*u + 2/5*u**2 - 12/5*u**v = 0 for u.
0, 1/4, 1
Suppose 6*u**3 + 3*u**5 + 367*u**4 - 735*u**4 + 377*u**4 = 0. What is u?
-2, -1, 0
Suppose -3*b = -5*b. Let j = 5/28 + 1/14. Factor b*t + 0 + 0*t**3 + j*t**2 - 1/4*t**4.
-t**2*(t - 1)*(t + 1)/4
Suppose -3*h - 726 = -4*m, m - 2*h - 186 = h. Let k be (m/54)/(4/6). Solve -v**2 - 10 + 10 + k*v**2 = 0 for v.
0
Let q be ((-6)/2)/(3/(-5)). Let w(a) be the third derivative of -1/28*a**4 + 0 + a**2 + 1/14*a**3 + 0*a + 1/140*a**q. Find v such that w(v) =