. Factor a - 2/7*i**2 + 2/7*i.
-2*i*(i - 1)/7
Let z(c) be the third derivative of c**5/450 - 74*c**4/45 + 21904*c**3/45 + 453*c**2. Let z(r) = 0. Calculate r.
148
Let g(m) be the second derivative of m**5/16 - 5*m**4/6 + 65*m**3/24 - 15*m**2/4 - 123*m. Find c, given that g(c) = 0.
1, 6
Let d(a) be the third derivative of a**5/420 - a**4/28 - a**3/6 + 16*a**2. Let d(z) = 0. What is z?
-1, 7
Let n(q) = -q**2 - 18*q - 43. Let r be n(-15). Suppose -5*p + r*y + 8 = 6*y, -2 = 4*p - y. Factor -1/3*i**4 + 5/6*i**2 - 1/6*i**3 - 1/3*i + p.
-i*(i - 1)*(i + 2)*(2*i - 1)/6
Factor 867 + 29*t**2 + 25*t**2 - 73*t**2 + 22*t**2 + 102*t.
3*(t + 17)**2
Let r(h) be the third derivative of h**6/960 - h**5/96 + 7*h**4/192 - h**3/16 - 28*h**2 - 1. Determine f so that r(f) = 0.
1, 3
Let m(c) = -c. Let h be m(0). Let a be (-2)/(-23) + (-990)/(-253). Solve -6/19*p + 8/19*p**3 + h*p**a - 4/19 - 2/19*p**5 + 4/19*p**2 = 0 for p.
-1, 1, 2
Let h(t) = -t**2 + t - 1. Let v(y) = y**4 - 2*y**3 - 4*y**2 + 5*y + 3. Suppose 5*s - o + 4 = -5, -s - 9 = -2*o. Let a(l) = s*v(l) + h(l). Factor a(m).
-(m - 2)**2*(m + 1)**2
Let b be (13 - 261/18)*(-12)/11. Find y, given that b*y + 14/11*y**2 + 4/11 = 0.
-1, -2/7
Let l(c) be the first derivative of 0*c + 1/8*c**4 + 0*c**2 + 0*c**3 - 26. Factor l(a).
a**3/2
Let v be ((-472)/(-6195))/((-4)/(-14)). Find x, given that 2/15*x**5 + 0 - v*x**3 + 8/5*x**2 - 16/15*x - 2/5*x**4 = 0.
-2, 0, 1, 2
Let r(v) = -2*v**3 + v**2 + v + 1. Let p(x) = 3*x**4 + 11*x**3 - 13*x**2 - 7*x + 2. Let f(c) = p(c) + 4*r(c). Factor f(g).
3*(g - 1)**2*(g + 1)*(g + 2)
Factor 36/5*w + 3/5*w**2 + 12.
3*(w + 2)*(w + 10)/5
Let m(u) = 7*u**3 + 27*u**2 + 97*u + 82. Let w(r) = -3*r**3 - 14*r**2 - 49*r - 40. Let q(v) = 2*m(v) + 5*w(v). Suppose q(n) = 0. Calculate n.
-12, -3, -1
Find c such that 3/8*c**2 - 21/2 + 9/8*c = 0.
-7, 4
Let m(d) = -d**3 - 21*d**2 - 3*d + 2. Let a be m(0). Solve -72/7 + 24/7*n - 2/7*n**a = 0.
6
Let c(f) = -f**2 - 8*f + 11. Let o be c(-9). Factor -3*n**3 + 4*n**2 - 6*n - n**o - 12*n**2.
-3*n*(n + 1)*(n + 2)
Suppose 1 = -n + 3*l + 8, -45 = 5*n + l. Let v be n*((-12)/8)/3. Factor -3/5*g**2 + 0*g + 0 - 3/5*g**v + 6/5*g**3.
-3*g**2*(g - 1)**2/5
Let k be 1/2*12/3. Suppose -4*p - 15 - 2*p + 0*p + 5*p**k - 4*p = 0. What is p?
-1, 3
Let w = 130 + -386/3. Let n(i) be the second derivative of 0 + 7*i - w*i**3 - 2*i**2 - 1/3*i**4. What is x in n(x) = 0?
-1
Suppose 0 = 29*r - 30*r + 4*c + 18, 0 = -2*r + 4*c + 20. Suppose 30*o**4 + 126/5*o**r - 100*o**3 + 16*o - 24/5 = 0. Calculate o.
-2/5, 1/3, 2/5, 3
Let f(b) be the second derivative of b**4/30 - 2*b**3/3 + 9*b**2/5 + 53*b. Let f(a) = 0. What is a?
1, 9
Factor 152 - 160*u - 297*u**3 + 299*u**3 + 16 + 34*u**2.
2*(u - 2)**2*(u + 21)
Let a be -2 + 2/(20/50). Factor -1/6*s**a + 1/2 + 1/6*s**2 + 5/6*s.
-(s - 3)*(s + 1)**2/6
Let v(i) be the first derivative of 3*i**4/5 + i**3/5 - 24*i**2/5 - 12*i/5 + 30. Factor v(u).
3*(u - 2)*(u + 2)*(4*u + 1)/5
Let f = 1370 - 1370. Let r(x) be the third derivative of f + 1/12*x**3 + 0*x - 1/48*x**5 - 3/32*x**4 + 2*x**2. Solve r(j) = 0.
-2, 1/5
Let z(a) be the third derivative of -a**6/30 - 47*a**5/5 - 2209*a**4/2 - 207646*a**3/3 + 5*a**2 + 12*a. Let z(u) = 0. Calculate u.
-47
Let y(q) be the second derivative of q**7/84 - 13*q**6/30 + 213*q**5/40 - 143*q**4/6 + 121*q**3/3 + 782*q. What is i in y(i) = 0?
0, 2, 11
Let a(r) = 30*r**5 + 51*r**4 - 21*r**2 - 21*r - 21. Let p(o) = 3*o**5 + 5*o**4 - 2*o**2 - 2*o - 2. Let m(f) = -2*a(f) + 21*p(f). Determine h so that m(h) = 0.
-1, 0
Let b be (-8)/((-5)/3 + 1). Let l be 2 + 4/b*0. Factor 1 - 3 - 2*o**4 - 2*o**5 + 4*o**3 + o**2 + 3*o**l - 2*o.
-2*(o - 1)**2*(o + 1)**3
Let l be 8/(-12)*(-5 - 1) + -4. Let c(h) be the third derivative of -10*h**2 - 1/4*h**4 + l + 0*h + 1/60*h**5 + 3/2*h**3. Let c(v) = 0. Calculate v.
3
Let g(v) = -v**3 + 2*v**2 - 5*v - 5. Let z(i) = -i**3 + i**2 - 6*i - 6. Suppose -94 + 79 = 3*m. Let x(r) = m*z(r) + 6*g(r). Let x(q) = 0. Calculate q.
0, 7
Let j(v) be the second derivative of -2*v**5/15 + 13*v**4/36 - v**3/9 - v**2/2 + 2*v - 3. Suppose j(p) = 0. What is p?
-3/8, 1
Let a(m) = m**2 - 19*m + 78. Let n be a(16). Factor 11*y**2 - 4*y**2 - n - 10*y**2 - 21*y.
-3*(y + 2)*(y + 5)
Let g(k) = -7*k**3 - 16*k**2 - 3*k - 3. Let l(f) = -4 + 15*f**3 + 4 + 8 - 1 + 7*f + 32*f**2. Let v(p) = -7*g(p) - 3*l(p). Let v(q) = 0. Calculate q.
-4, 0
Let d(q) = -4*q**3 - 1. Let t be d(-1). Let u be (-3)/(-9) + 0 + (-16)/(-6). Determine j so that -u*j - 132*j**2 - t*j**3 + 126*j**2 + 12*j**3 = 0.
-1/3, 0, 1
Let n(h) be the third derivative of -h**8/20160 + h**7/1260 + 3*h**5/20 + 17*h**2. Let b(l) be the third derivative of n(l). Solve b(z) = 0 for z.
0, 4
Suppose 83*o + 43*o = 252. Let d(h) be the first derivative of -12/35*h**5 + 4/7*h + 8/21*h**3 - 2/7*h**4 + 1 + 6/7*h**o - 2/21*h**6. Factor d(g).
-4*(g - 1)*(g + 1)**4/7
Suppose 3/4*b**3 - 4*b**2 + 23/4*b - 3/2 = 0. Calculate b.
1/3, 2, 3
Find l such that -1455*l + 99*l**2 - 5*l**3 + 106*l**2 - 1594*l + 849*l + 2000 = 0.
1, 20
Let t(d) be the third derivative of d**7/2520 + d**6/270 + d**5/90 + 3*d**3/2 + 8*d**2. Let y(c) be the first derivative of t(c). Factor y(b).
b*(b + 2)**2/3
Let n = 96 - 93. Let c = -28 - -30. Find f such that 0*f**c + 7/3*f**n - f**4 - 4/3*f + 0 = 0.
-2/3, 0, 1, 2
Let q(m) = 2*m + 23. Let p be q(11). Let v = 47 - p. What is z in 75/2*z**v + 2 + 15*z + 125/4*z**3 = 0?
-2/5
Let q(f) be the third derivative of 1/16*f**4 + 0*f - 1/120*f**5 + 33*f**2 + 5/6*f**3 + 0. Factor q(k).
-(k - 5)*(k + 2)/2
Let r(i) = 6*i**5 + 15*i**4 + 12*i**3 + 9*i**2 + 6*i + 3. Let q(x) = 13*x**5 + 31*x**4 + 23*x**3 + 19*x**2 + 14*x + 7. Let h(b) = 3*q(b) - 7*r(b). Factor h(u).
-3*u**2*(u + 1)**2*(u + 2)
Let -6/13*o**2 + 32/13*o - 24/13 - 2/13*o**3 = 0. Calculate o.
-6, 1, 2
Let q be 18/4 + 1/2. Suppose q*p = 2*p. Find r such that p*r - r + 0*r + 3*r**2 - 2*r**2 = 0.
0, 1
Let r = -18619/2 + 9310. Factor 1/2 + 0*b**3 + 0*b - b**2 + r*b**4.
(b - 1)**2*(b + 1)**2/2
Let m(h) be the third derivative of -24*h**2 + 1/132*h**6 + 1/1155*h**7 + 7/132*h**4 + 0*h + 3/110*h**5 + 2/33*h**3 + 0. Determine g, given that m(g) = 0.
-2, -1
Suppose -2 = -k - 3. Let i be (-1 - k)*(-2)/6. Factor -2*y + 2*y**2 + i*y + 4*y - y**2 + 1.
(y + 1)**2
Let l(f) = -121*f**3 - 80*f**2 + 43*f - 4. Let h be (-2 + 4 - 0) + -5. Let t be 0 + h*1/3. Let d(p) = p**2 - p. Let g(a) = t*l(a) - 3*d(a). Factor g(c).
(c + 1)*(11*c - 2)**2
Let i(o) be the first derivative of -8/5*o**2 + 8 - 32/5*o - 2/15*o**3. Solve i(t) = 0 for t.
-4
Let l be 756/(-38) - (24/(-57))/(-4). Let w be 4 - (-10)/75*l. Determine y so that -w*y + 2/3 + 0*y**2 + 4/3*y**3 - 2/3*y**4 = 0.
-1, 1
Let f = 3618/5 + -723. What is u in 3/5*u**2 + 0 + 6/5*u - f*u**3 = 0?
-1, 0, 2
Let k be 2 + (-33)/18 + ((-1705)/30)/(-31). Factor -2*i + 2/7*i**3 + 8/7 + 4/7*i**k.
2*(i - 1)**2*(i + 4)/7
Let w(a) be the second derivative of a**8/84 - a**6/15 + a**4/6 - a**2 + 11*a. Let c(x) be the first derivative of w(x). Determine s so that c(s) = 0.
-1, 0, 1
Find v, given that 3/2*v**2 - 1/2*v**3 + 5*v + 0 = 0.
-2, 0, 5
Let x(w) be the second derivative of w**7/525 + w**6/180 + w**5/300 + 3*w**3/2 - w. Let m(r) be the second derivative of x(r). Find d, given that m(d) = 0.
-1, -1/4, 0
Let m(l) be the first derivative of 2*l**3/15 + 2*l**2 + 18*l/5 - 535. Determine o so that m(o) = 0.
-9, -1
Let m = 4107/2 + -2033. Solve -m*o**2 + 105/2*o**4 - 14*o - 2 + 18*o**5 + 26*o**3 = 0.
-2, -1, -1/3, -1/4, 2/3
Let u(c) be the second derivative of c**6/10 + 3*c**5/10 - 19*c**4/4 + 14*c**3 - 18*c**2 - 46*c + 3. Find g, given that u(g) = 0.
-6, 1, 2
Let f(x) = -13*x**2 + 24*x + 37. Suppose 2*l = -2*s + 1 - 5, 3*s = -l + 2. Let a(v) = 6*v**2 - 12*v - 18. Let q(i) = l*f(i) - 9*a(i). Let q(c) = 0. What is c?
-1, 7
Suppose -3*u - 3*o = 2*o + 2105, -2104 = 3*u + 4*o. Let x be (-1320)/u - (-2)/(-7). What is s in -8/5*s + x + 2/5*s**2 = 0?
2
Let u = -109 + -31. Let d be (-108)/u + (0 - (-1)/(-5)). Factor 0 - 2/7*z + d*z**3 - 2/7*z**5 + 0*z**2 + 0*z**4.
-2*z*(z - 1)**2*(z + 1)**2/7
Let h(w) be the third derivative of w**6/30 + 9*w**5/40 + w**4/4 - w**3/2 - 3*w**2. Let l(d) be the first derivative of h(d). Determine f, given that l(f) = 0.
-2, -1/4
Let p(t) be the first derivative of -t**3/2 - 207*t**2/2 - 14283