
Let r be 104/50 - (-22)/(-275). Suppose 15/2*l - 5/2*l**3 + 5 + 0*l**r = 0. Calculate l.
-1, 2
Let j(k) be the second derivative of 1/4*k**5 - k - 5*k**2 - 2 + 0*k**4 - 5/2*k**3. Factor j(g).
5*(g - 2)*(g + 1)**2
Let k(g) be the first derivative of 2 + 1/15*g**3 - 1/5*g**2 + 1/5*g. Factor k(m).
(m - 1)**2/5
Let f be ((-66)/12)/(-11)*0. Let k(t) be the first derivative of -4 + 3/20*t**5 + 0*t**3 + 3/16*t**4 + f*t**2 + 0*t. Determine a so that k(a) = 0.
-1, 0
Let x(c) = 3*c + 8. Let q be x(-1). Suppose 4*t - 5*y - 1 = 0, -3*t + q*y - y = 0. Let 2/3 + 6*u**2 - t*u = 0. Calculate u.
1/3
Let f(r) = r**4 - r**3 - r**2 + 1. Let b(t) = 8*t**4 + 6*t**3 - 29*t**2 - 24*t + 3. Let c(m) = b(m) - 3*f(m). Suppose c(d) = 0. What is d?
-3, -4/5, 0, 2
Let v(p) = p**2 + p. Let a(n) = -n**3 + n. Let k(i) = -a(i) - 2*v(i). Factor k(l).
l*(l - 3)*(l + 1)
Let q(l) be the first derivative of 0*l**3 - 2/45*l**5 - 1/6*l**4 + 0*l - 26 + 4/9*l**2. Suppose q(s) = 0. What is s?
-2, 0, 1
Let k = -9 + 8. Let y = k - -3. Suppose 2*q**4 + 4 - 8*q**2 + 2*q**4 + 0*q**y = 0. Calculate q.
-1, 1
Let b be (2/3)/(6/63). Let y(t) = t**2 - 8*t + 10. Let m be y(b). Factor -8*h**4 - h**5 + 4*h**m + 8*h**5 - 10*h**4 + 7*h**5.
2*h**3*(h - 1)*(7*h - 2)
Let z(b) be the third derivative of b**5/60 + b**4/24 + 2*b**2. Let u(i) = 3*i**2 - 6*i + 16. Suppose -11 = 5*f - 6. Let h(x) = f*u(x) + 2*z(x). Factor h(n).
-(n - 4)**2
Let i = -191 - -195. Suppose 3*k - i = -2*v, -k + 5 = -4*v - 1. Solve 1/2*z**4 - 5/2*z**3 - k + 1/2*z**5 - 1/2*z**2 + 4*z = 0.
-2, 1
Let v = 11806 + -11804. Factor -1/4*g**v - 3/4 + g.
-(g - 3)*(g - 1)/4
Suppose 0 = 13*j + j. Let b(z) be the third derivative of 1/60*z**6 + 0*z + 6*z**2 + 2/27*z**5 + 1/27*z**4 + j*z**3 + 0. Factor b(w).
2*w*(w + 2)*(9*w + 2)/9
Let f(r) be the second derivative of -3*r**5/5 + 20*r**4/3 - 74*r**3/9 + 4*r**2 - 101*r - 1. Factor f(q).
-4*(q - 6)*(3*q - 1)**2/3
Let c(o) be the second derivative of o**6/540 - o**4/36 - o**3/2 + 5*o. Let r(f) be the second derivative of c(f). Factor r(p).
2*(p - 1)*(p + 1)/3
Let d(p) be the third derivative of p**7/840 + p**6/20 + 3*p**5/5 - 36*p**2. Solve d(y) = 0 for y.
-12, 0
Suppose -51 = -2*x + 27. Solve x*l**4 - 10*l**2 + 15*l**3 - 12*l**4 - 16*l**4 - 16*l**4 = 0.
0, 1, 2
Let z = 531/724 + -3/4. Let s = z - -757/1991. What is y in s + 2/11*y**2 + 6/11*y = 0?
-2, -1
Let c(p) be the first derivative of p**6/5 - 38*p**5/25 + 3*p**4/10 + 38*p**3/15 - 6*p**2/5 - 303. Find x, given that c(x) = 0.
-1, 0, 1/3, 1, 6
Let x(q) be the first derivative of 0*q + 2/27*q**3 + 2/15*q**5 - 11 + 1/6*q**4 + 0*q**2 + 1/27*q**6. Factor x(p).
2*p**2*(p + 1)**3/9
Let t(k) be the third derivative of -k**6/240 + k**5/20 - 5*k**2 - 6. Factor t(r).
-r**2*(r - 6)/2
Let r(v) be the third derivative of -v**7/75 - 19*v**6/300 + 23*v**5/50 - 53*v**4/60 + 2*v**3/3 - 83*v**2. Let r(d) = 0. Calculate d.
-5, 2/7, 1
Factor -90*i - 24*i**2 - 160 + 11*i**2 + 8*i**2 + 0*i**2.
-5*(i + 2)*(i + 16)
Factor 85*q + 22*q**2 + 28 - 75*q - 24*q**2.
-2*(q - 7)*(q + 2)
Let s(n) be the second derivative of n**4/24 - 2*n**3 + 23*n**2/4 - 161*n. Solve s(l) = 0.
1, 23
Let j(v) be the second derivative of 0*v**3 + 0 - v**4 + 15*v + 0*v**2 + 1/5*v**5. Factor j(t).
4*t**2*(t - 3)
Let g(y) = y**2 - 103*y + 1322. Let r be g(15). Find l, given that 0 + 4/5*l**r + 4/5*l = 0.
-1, 0
Let y(h) be the first derivative of -49*h**6/9 - 56*h**5/15 - 2*h**4/3 - 2. Suppose y(c) = 0. What is c?
-2/7, 0
Let k(v) be the first derivative of v**7/189 + 2*v**6/135 - v**4/27 - v**3/27 - 10*v + 2. Let z(w) be the first derivative of k(w). Factor z(f).
2*f*(f - 1)*(f + 1)**3/9
Let t(j) = -j**2 - 10*j + 5. Let b be t(-11). Let i(q) = -2*q - 9. Let l be i(b). Find u, given that -3*u**l + 5*u**3 + 3*u**2 - 8 + 3*u**2 = 0.
-2, 1
Suppose -3*g = 6*y - 4*g, 0 = -y + g. Let f be 15/7*18/15. Determine o so that -12/7*o**2 + f*o + y + 2/7*o**3 = 0.
0, 3
Determine f, given that 18*f**2 - 18 - 3/5*f**3 + 3/5*f = 0.
-1, 1, 30
Let g(q) be the second derivative of q**4/3 - 4*q**3 + 16*q**2 - 104*q. Factor g(d).
4*(d - 4)*(d - 2)
Let t(f) = 2*f**3 + f**2. Let c be t(1). Let l = 19 + 5. Factor x**4 - 8*x**4 + 36 + 3*x**4 - 32*x**2 - 24*x**c + l*x.
-4*(x - 1)*(x + 1)*(x + 3)**2
Let r be -5 - 10/(-10)*5/1. Factor -1/2*s + 1/2*s**2 + r.
s*(s - 1)/2
Let d(t) be the first derivative of -t**4/6 - 22*t**3 - 1089*t**2 - 23958*t - 527. Factor d(g).
-2*(g + 33)**3/3
Let v(f) be the first derivative of 5 - 1/40*f**5 + 3*f + 0*f**2 - 1/12*f**4 + 0*f**3. Let r(m) be the first derivative of v(m). Suppose r(q) = 0. Calculate q.
-2, 0
Let w(p) be the second derivative of p**4/20 + 3*p**3/5 + 12*p**2/5 - 39*p - 4. What is v in w(v) = 0?
-4, -2
Suppose -19*u + 20*u = 1. Let l be -2*5/(-5)*u*1. Factor 0 + 4/5*a**l + 8/5*a.
4*a*(a + 2)/5
Factor p**2 + 4*p**4 - 2*p**4 + 13*p**3 - 2*p**2 + 0*p**2 - p**5 + 11*p**2.
-p**2*(p - 5)*(p + 1)*(p + 2)
Let i(z) = -2*z**4 + 28*z**3 - 46*z**2 + 20*z - 3. Let c(v) = -v**4 + 29*v**3 - 48*v**2 + 20*v - 4. Let o(w) = -3*c(w) + 4*i(w). Suppose o(q) = 0. What is q?
0, 1, 2
Let o be 4975/161 - 15/345. Factor -16/7*f**4 - o*f**2 - 32/7 - 100/7*f**3 - 176/7*f.
-4*(f + 2)**3*(4*f + 1)/7
Let g(z) be the third derivative of -z**5/15 + z**4/3 + 16*z**3/3 - 2*z**2 - 36*z. Factor g(s).
-4*(s - 4)*(s + 2)
Let w(j) be the second derivative of j**4/24 - j**2/4 - 57*j. Factor w(o).
(o - 1)*(o + 1)/2
Let y(l) = l**3 - 18*l**2 + 76*l + 10. Let w(q) = -q**3 + 18*q**2 - 77*q - 8. Let j(p) = 5*w(p) + 4*y(p). What is v in j(v) = 0?
0, 9
Let n(o) be the second derivative of o**4/7 - 2*o**3/21 - 83*o. Factor n(c).
4*c*(3*c - 1)/7
Factor -37*f - 22 + 24*f + 5*f**2 - 2*f - 23 - 25*f.
5*(f - 9)*(f + 1)
Let h be (8/10)/(7/(245/14)). Let t(f) be the second derivative of -3/5*f**2 + h*f + 0 + 1/20*f**4 + 1/10*f**3. Solve t(z) = 0 for z.
-2, 1
Let -3*y**3 + 0*y - 3/2*y**4 + 9/2*y**2 + 0 = 0. Calculate y.
-3, 0, 1
What is h in 94 - 273*h + 228*h + 6 + 5*h**2 = 0?
4, 5
Let b = -80 + 82. Suppose -b*s + 321*s**2 - 320*s**2 - s**3 + 4*s = 0. Calculate s.
-1, 0, 2
Let p be 2543/6*(-3 - (-117)/27). Let n = p + -564. Suppose 8/9*h**2 + 4/9 - 2/9*h**3 - n*h = 0. Calculate h.
1, 2
Let b(y) = y**3 + 2*y**2 - y + 2. Let n(l) = 4*l**3 - 8*l - 3*l + 7*l**2 + 7 + 6*l + l. Let q(t) = 21*b(t) - 6*n(t). Suppose q(c) = 0. Calculate c.
-1, 0, 1
Let 0*k - 2/9*k**4 - 86/9*k**2 + 0 + 88/9*k**3 = 0. Calculate k.
0, 1, 43
Let v be (-82)/(-30) - 32/(288/21). Factor -2/5*o + v*o**2 + 0.
2*o*(o - 1)/5
Let g = 25/762 - -669/254. Let 0 + 2/3*i**4 - g*i**3 - 8/3*i**2 + 2/3*i**5 + 0*i = 0. What is i?
-2, -1, 0, 2
Let w(m) = 2*m**2 + 9*m - 9. Let f(q) = q**2 - 1. Let b(u) = -3*f(u) + w(u). Let v be b(8). Solve -3 + o**v - 2*o + 0 + 4 = 0.
1
Suppose 32 = -3*t + 4*i + 1, t + 1 = -i. Let f be (0 + 20/25)/((-2)/t). Factor 0 - f*a**3 - 1/2*a**2 + 0*a.
-a**2*(4*a + 1)/2
Suppose -213*a + 18 = -207*a. Factor -1/6 + 1/6*q**a + 1/2*q - 1/2*q**2.
(q - 1)**3/6
Let d be (-2 + 2)/(-3 + 1). Suppose d = 2*f - 85 + 13. Factor 36 - 15*n**3 - 8*n**2 + 8*n**4 - f - n + 16*n**5.
n*(n - 1)*(n + 1)*(4*n + 1)**2
Let j(i) be the first derivative of 0*i - 12 + 3/40*i**5 + 1/2*i**3 + 0*i**2 + 3/8*i**4. Let j(q) = 0. What is q?
-2, 0
Suppose -46*x - 3 = -45*x. Let q be ((-3)/(-1) + (-11)/3)*x. Find j, given that 0 - 6/7*j - 2/7*j**q = 0.
-3, 0
Let p(y) be the third derivative of y**6/240 - y**5/120 - y**4/12 + y**3/3 + 14*y**2 - 1. What is f in p(f) = 0?
-2, 1, 2
Let o(j) be the first derivative of 0*j**3 + 2 + 0*j - 1/20*j**5 + 3/2*j**2 + 1/4*j**4. Let v(f) be the second derivative of o(f). Factor v(c).
-3*c*(c - 2)
Let z = 1591/930 + -52/31. Let m(v) be the third derivative of 2/3*v**3 + 0*v + 6*v**2 + 0 - z*v**5 - 7/24*v**4. Factor m(d).
-(d + 4)*(2*d - 1)
Let m(n) be the first derivative of -3*n**2 - 38*n - 6. Let v be m(-7). Find b, given that -4/13*b**3 + 0*b**2 - 2/13 + 2/13*b**v + 4/13*b = 0.
-1, 1
Let t = -66 + 57. Let k be (6/(-35))/(3*t/135). Factor k*g**4 + 3/7*g**3 + 0*g - 3/7*g**2 + 0.
3*g**2*(g + 1)*(2*g - 1)/7
Let d(w) be the third derivative of w**6/360 - w**5/15 + 2*w**4/3 - 2*w**3 + 2*w**2. Let h(p) be the first derivative of d(p). Factor h(t).
(t - 4)**2
Let k(a) be the third derivative of -a**7/42 + 5*a**6/4 + 8*a**5 + 245*a**4/12 + 55*a**3/2 + 90*a**2 + 1.