1)
Let d(l) = -6*l**2 + 21*l + 15. Let c(j) = j**2 - 3*j - 2. Let o(i) = -15*c(i) - 2*d(i). Suppose o(b) = 0. Calculate b.
0, 1
Let u(p) = 2*p - p + 5*p - 3*p**2. Let q(l) = -5*l + 4*l - 3*l + l**2 + 3*l. Let n(a) = -4*q(a) - u(a). Find s, given that n(s) = 0.
-2, 0
Determine b so that 2/5*b**3 + 0 - 2/5*b**2 + 0*b = 0.
0, 1
Let n(o) be the second derivative of 3*o + 1/15*o**3 + 3/10*o**4 + 1/15*o**6 - 2/5*o**2 - 13/50*o**5 + 0. Solve n(z) = 0 for z.
-2/5, 1
Let r(y) = -y**2 + 7*y + 7. Let f be r(8). Let t be f - (-3)/3*14. Factor 2*d**3 + 11*d - 16 - d**2 - 9*d**2 - 2*d**2 + t*d.
2*(d - 2)**3
Let d(a) be the first derivative of -4 + 1/4*a**3 - 9/16*a**4 + 0*a + 0*a**2 + 9/20*a**5 - 1/8*a**6. Factor d(w).
-3*w**2*(w - 1)**3/4
Factor 4*w**2 - 8*w**3 + 4*w**3 - 3*w**4 - 5*w**4.
-4*w**2*(w + 1)*(2*w - 1)
Let g(k) be the second derivative of 2*k - 1/60*k**6 - 13/108*k**4 + 0 + 2/27*k**5 - 2*k**2 + 2/27*k**3. Let m(n) be the first derivative of g(n). Factor m(z).
-2*(z - 1)**2*(9*z - 2)/9
Suppose -3*c - 4*j = -14, c + 0*j + 2*j - 6 = 0. Factor 0*o - 1/2*o**c + 1/2*o**3 + 0.
o**2*(o - 1)/2
Let b(v) be the second derivative of -v**5/140 - v**4/84 + v**3/42 + v**2/14 + 6*v. Factor b(k).
-(k - 1)*(k + 1)**2/7
Let q(y) = -62*y - 1. Let c be q(1). Let m be (c/15 + 4)*-6. Solve 4/5*n - 2/5*n**3 + 0 - m*n**4 - 2/5*n**5 + 6/5*n**2 = 0 for n.
-2, -1, 0, 1
Suppose 10 = -5*r, -6*s + 3*s = -4*r - 8. Factor -1/2*j + s - 1/2*j**2.
-j*(j + 1)/2
Let b(d) be the second derivative of -d**6/10 - d**5/20 + 5*d**4/12 + d**3/6 - d**2 + 20*d. Factor b(j).
-(j - 1)*(j + 1)**2*(3*j - 2)
Suppose 5*b - 25 = 6*r - 4*r, -5*r - b = -5. Find l such that -2/7*l**5 + 0 + 0*l + 0*l**4 + 0*l**2 + r*l**3 = 0.
0
Suppose 5*n - 4*p = -p + 95, -4*n - 3*p = -49. Let d be n/(-12)*(-18)/12. Suppose 2/7*u**d + 0 + 4/7*u = 0. Calculate u.
-2, 0
Let x = 6 - 4. Let t(k) = -x*k - 3*k**2 - 2*k**2 - 3*k. Let u(w) = w**2 + w. Let v(h) = -2*t(h) - 9*u(h). Factor v(q).
q*(q + 1)
Let m(f) = f**3 - 10*f**2 + 2. Let k be m(10). Suppose 4*q - 4*q - 9*q**k + 8*q**2 = 0. What is q?
0
Let c(a) = -a**2 - 8*a + 33. Let x be c(-11). Determine z so that 2/3*z + x - 2/3*z**2 = 0.
0, 1
Let f(c) = 8*c**2 - 6*c - 10. Let o(h) = -1 + h**2 - 2 - h + 1 + 1. Let z(x) = -f(x) + 10*o(x). Determine j, given that z(j) = 0.
0, 2
Determine k so that 2/3*k**2 + 0 + 4/3*k = 0.
-2, 0
Let o(q) be the third derivative of q**10/120960 - q**8/26880 - q**4/24 - q**2. Let l(s) be the second derivative of o(s). Factor l(t).
t**3*(t - 1)*(t + 1)/4
Suppose 0 = 3*s - 11 + 8. Let f(c) = -c**4 + c**2 + c - 1. Let n(j) = -5*j**4 + 4*j**2 + 4*j - 4. Let a(p) = s*n(p) - 4*f(p). Suppose a(m) = 0. Calculate m.
0
Let f = 6/11 - 97/198. Let a(j) be the third derivative of -f*j**3 + j**2 - 1/180*j**5 + 1/36*j**4 + 0*j + 0. Determine t so that a(t) = 0.
1
Let v(c) be the first derivative of c**6/6 - 4*c**5/5 - c**4/2 + 8*c**3/3 + c**2/2 - 4*c - 38. Factor v(y).
(y - 4)*(y - 1)**2*(y + 1)**2
Factor 3*i**2 - i**2 - i**2.
i**2
Factor 2*b**4 + 7/3*b - 7/3*b**3 - 5/3*b**2 - 1/3.
(b - 1)**2*(b + 1)*(6*b - 1)/3
Factor -4/7*c**2 + 4/7 + 2/7*c - 2/7*c**3.
-2*(c - 1)*(c + 1)*(c + 2)/7
Let q = 21 - 1. Suppose 0*m - m + 7 = -2*c, -4*m = -4*c - q. Solve -1/4*x + 1/2*x**4 + 0*x**m - 1/2*x**2 + 0 + 1/4*x**5 = 0.
-1, 0, 1
Let k(z) be the third derivative of z**7/315 - z**6/45 + z**5/18 - z**4/18 + z**2. Factor k(m).
2*m*(m - 2)*(m - 1)**2/3
Let g(x) be the first derivative of -3*x**2 - 4/3*x**3 - 2 + 1/3*x**6 - 2*x + x**4 + 6/5*x**5. Factor g(s).
2*(s - 1)*(s + 1)**4
Suppose 5*b + 2*a + 0*a = -8, 0 = b - 2*a - 8. Let z = b - -2. Suppose f**z + f + 0*f**2 - 4*f + 2 = 0. What is f?
1, 2
Let y = -369/2 + 188. Let -y*h**2 + 0 - 3/2*h**3 + 5/2*h**5 + 7/2*h**4 - h = 0. Calculate h.
-1, -2/5, 0, 1
Let q(a) = a**4 + a**3 + a**2. Let n(s) = 21*s**5 + 30*s**4 + 3*s**3 - 12*s**2. Let k(p) = -n(p) - 6*q(p). Factor k(g).
-3*g**2*(g + 1)**2*(7*g - 2)
Let l = 76 + -74. Factor -5/3*u**4 + 0 + 2/3*u**l + u**3 + 0*u.
-u**2*(u - 1)*(5*u + 2)/3
Let y(q) be the first derivative of 3*q**5/5 - 3*q**4/4 - 2*q**3 + 5. Factor y(b).
3*b**2*(b - 2)*(b + 1)
Suppose 39 = 5*o + 9. Suppose -2*k = k - o. Suppose h - h**2 - 2*h**2 + 4*h**k = 0. Calculate h.
-1, 0
Let a(g) = -g**5 + 2*g**3 + 3*g**2 - g - 3. Let b(h) = -2*h**5 + 4*h**3 + 7*h**2 - 2*h - 7. Let d(f) = -14*a(f) + 6*b(f). Factor d(w).
2*w*(w - 1)**2*(w + 1)**2
Let q(l) = -8*l**2 + 37*l + 38. Let o(t) = -3*t**2 + 12*t + 13. Let c(y) = -7*o(y) + 2*q(y). Find f such that c(f) = 0.
-1, 3
Let p(x) be the first derivative of -242*x**3/21 + 44*x**2/7 - 8*x/7 + 5. Factor p(l).
-2*(11*l - 2)**2/7
Let y = 634/7 - 90. Let b be -1*6/21*-1. Solve 0*l + b*l**2 + 2/7*l**4 + 0 - y*l**3 = 0 for l.
0, 1
Let y(m) be the second derivative of -1/30*m**4 + 1/210*m**7 - 4*m + 0 + 0*m**5 + 0*m**2 - 1/30*m**3 + 1/75*m**6. Factor y(s).
s*(s - 1)*(s + 1)**3/5
Let f = 171/77 + -15/11. Let f - 3/7*g**2 - 3/7*g = 0. Calculate g.
-2, 1
Let h be (12/9)/((-8)/(-16)). What is m in -h*m**4 - 4/3*m**2 - 14/3*m**3 + 2/3*m + 0 = 0?
-1, 0, 1/4
Let u(s) be the third derivative of -1/6*s**4 + 1/30*s**7 + 0*s**3 + 0*s - 3*s**2 + 0 - 1/24*s**6 - 4/15*s**5. Factor u(m).
m*(m - 2)*(m + 1)*(7*m + 2)
Let l(b) be the second derivative of -b**6/960 - b**5/480 + b**4/96 - 4*b**2 - 3*b. Let g(c) be the first derivative of l(c). Let g(o) = 0. Calculate o.
-2, 0, 1
Let o(i) be the third derivative of -9*i**7/70 + 3*i**6/10 + i**5/4 - 3*i**4/2 + 2*i**3 + 14*i**2. Find d, given that o(d) = 0.
-1, 2/3, 1
Suppose -2*j + 3 + 5 = 0. Let i(l) be the second derivative of -3*l - 1/80*l**5 + 1/16*l**j + 0 - 1/8*l**3 + 1/8*l**2. Suppose i(m) = 0. Calculate m.
1
Let s(o) be the first derivative of o**7/2940 + o**6/420 + o**5/140 + o**4/84 + 2*o**3/3 + 3. Let v(u) be the third derivative of s(u). Factor v(l).
2*(l + 1)**3/7
Let k = -7/11 + 25/22. Let a(o) be the second derivative of -1/3*o**3 - o + 0 + k*o**2 + 0*o**4 - 1/30*o**6 + 1/10*o**5. Suppose a(q) = 0. Calculate q.
-1, 1
Let k(h) = -1. Let c(o) = -o**2. Let t(y) = -4*y**2 + 2*y - 15. Let a(b) = 6*c(b) - t(b). Let g(n) = 2*a(n) + 22*k(n). Factor g(w).
-4*(w - 1)*(w + 2)
Let p(x) = -x**2 + 8*x. Let l be p(8). Let k(h) = h**2 + h + 3. Let q be k(l). Factor 0*w - 4*w + 2*w**q + 4*w.
2*w**3
Let j(m) = 2*m - 6. Let w be j(4). Let v(k) = k**2 - k + 1. Let u be v(w). Solve 0*c**2 + c**5 - 4*c**u - c**2 + c**4 + 3*c**5 = 0 for c.
-1, -1/4, 0, 1
Suppose -b + 16 = 4*h - 4*b, h - 4 = -4*b. Factor -3*x**2 - h*x**2 + 2*x + 2*x + x**2.
-2*x*(3*x - 2)
Let b(u) be the second derivative of -u**5/100 + u**4/20 - u**3/10 - u**2 + 3*u. Let f(j) be the first derivative of b(j). What is g in f(g) = 0?
1
Factor -8 + z**2 + 13*z - 7*z - 4*z.
(z - 2)*(z + 4)
Factor -2/3 + o - 1/3*o**2.
-(o - 2)*(o - 1)/3
Let i(f) = 16*f**3 - 10*f**2 - 9*f + 10. Let z(b) be the first derivative of -3*b + b**3 + 3 - 5/4*b**4 + 3/2*b**2. Let g(r) = 4*i(r) + 14*z(r). Factor g(j).
-2*(j - 1)*(j + 1)*(3*j - 1)
Let b = 16 - 12. Let 28*j + 3*j**2 + 36 + b*j - 8*j + j**2 = 0. What is j?
-3
Let 2*v**2 + 10/7*v + 6/7*v**3 + 2/7 = 0. Calculate v.
-1, -1/3
Let d = -226/9 + 25. Let z = d + 7/9. Factor z*x**2 + 0 + 2/3*x**3 + 0*x.
2*x**2*(x + 1)/3
Let r be 76/80 - 2/10. Let l = r - 5/12. Factor -3*p**2 + 4/3*p**3 - l + 2*p.
(p - 1)**2*(4*p - 1)/3
Let v(j) be the second derivative of 5*j**4/12 - 5*j**3/6 - 5*j**2 + 15*j. Let v(l) = 0. Calculate l.
-1, 2
Let p(q) = q**2 - q. Let u be p(2). Factor -4*z**2 + 2*z**2 - u*z**4 + 4*z**2.
-2*z**2*(z - 1)*(z + 1)
Let k(p) be the third derivative of -p**5/12 + 5*p**4/12 - 5*p**3/6 - 8*p**2. Solve k(s) = 0 for s.
1
Suppose -8/7*a - 2/7*a**2 + 0 = 0. Calculate a.
-4, 0
Let h(m) = -m**2 - m + 1. Let c(f) = 2*f + 4. Let a = 3 + -2. Let u be (3 - 0) + (0 - a). Let j(o) = u*h(o) - c(o). Factor j(z).
-2*(z + 1)**2
Let o(a) be the first derivative of -1/9*a**6 - 16/3*a**2 - 2 - 4/15*a**5 - 64/3*a + 32/9*a**3 + 4/3*a**4. Factor o(q).
-2*(q - 2)**2*(q + 2)**3/3
Let v = 1/89 + 443/178. Let x(f) be the first derivative of -1/3*f**3 - v*f**2 - 2*f + 3 + 5/4*f**4 + 3/5*f**5. Find u such that x(u) = 0.
-1, -2/3, 1
Let d(v) be the third derivative of -v**7/105 + v**6/60 + v**5/10 - 5*v**4/12 + 2*v**3/3 - v**2. Suppose d(x) = 0. What is x?
-2, 1
Let b(x) be the second deriv