 3. Let b(v) = 3*v**4 + 4*v**3 + 2*v**2 - 4*v + 5. Suppose -2*x - 15 = -5*x. Let u(t) = x*k(t) + 3*b(t). Factor u(p).
-p*(p - 2)*(p - 1)*(p + 1)
Let y = 1427/35 + -285/7. Let p = 41/105 - y. Factor -p*d**4 + 0*d - 1/3*d**2 + 0 + 2/3*d**3.
-d**2*(d - 1)**2/3
Let i(q) = -7*q**4 - 5*q**3 - 9*q**2 + q - 4. Let y(p) = 8*p**4 + 4*p**3 + 9*p**2 - 2*p + 5. Let t(x) = 5*i(x) + 4*y(x). Factor t(d).
-3*d*(d + 1)**3
Let s(z) be the second derivative of 5*z**7/6 + 8*z**6/3 - 6*z**5 - 55*z**4/6 + 85*z**3/6 + 15*z**2 - 20*z. Determine o, given that s(o) = 0.
-3, -1, -2/7, 1
Factor 0 - 12/5*r**2 + 2/5*r**3 - 14/5*r.
2*r*(r - 7)*(r + 1)/5
Let a(n) be the second derivative of n**4/10 - n**3/3 + 2*n**2/5 - 11*n. Find b such that a(b) = 0.
2/3, 1
Suppose -2 = 2*d - 6. Let k be (1/(-2))/(d/(-24)). Let l(z) = -z**2 + 8*z - 1. Let o(i) = -i**2 + 9*i - 1. Let h(p) = k*o(p) - 7*l(p). Factor h(x).
(x - 1)**2
Let h = 20 + -18. Let j(o) be the third derivative of 1/40*o**5 + 1/60*o**6 + 4*o**h + 0 + 0*o**3 - 1/48*o**4 + 0*o. Find a, given that j(a) = 0.
-1, 0, 1/4
Let n be 6/(-8)*((3 - 9) + 2). Factor 3*g**n + 3/4*g + 0 + 15/4*g**2.
3*g*(g + 1)*(4*g + 1)/4
Suppose 5 = -4*h + 13. Suppose h*o = 6*o. Determine i, given that -2/7*i + o + 2/7*i**2 = 0.
0, 1
Let v(k) = 21*k**3 + 16*k**2 + k - 5. Let n(o) = 4*o**3 + 3*o**2 - 1. Let j(w) = 11*n(w) - 2*v(w). Suppose j(b) = 0. Calculate b.
-1, -1/2, 1
Let p(y) be the second derivative of -2*y**5/5 - y**4 + 2*y**2 + 32*y. Find f such that p(f) = 0.
-1, 1/2
Let n = 50267 + -1407153/28. Let a = n + -45/4. Factor -4/7 - a*g**2 + 6/7*g.
-2*(g - 2)*(g - 1)/7
Let j = -1 + 9. Let y(b) be the first derivative of 1 - j*b - 6*b**2 - 1/4*b**4 - 2*b**3. Factor y(h).
-(h + 2)**3
Let g(l) be the third derivative of -1/9*l**3 + 0*l - 1/90*l**5 - l**2 - 1/18*l**4 + 0. What is b in g(b) = 0?
-1
Suppose -5*j = -64 + 24. Let o(u) = -u**3 + 9*u**2 - 7*u - 5. Let b be o(j). Factor 3*r**3 - 3*r**3 + r**b - r**4.
-r**3*(r - 1)
Suppose y = 2*d + 2*d - 9, 5*y - 5 = -5*d. Let t(v) be the third derivative of 1/240*v**5 - d*v**2 + 0*v**3 + 0 - 1/96*v**4 + 0*v. Factor t(k).
k*(k - 1)/4
Solve -80*u - 5/2*u**2 - 640 = 0 for u.
-16
Let y be 93/72 + 5 + -6. Let r(d) be the first derivative of 0*d - y*d**6 - 2 + 0*d**2 + 2/3*d**3 - 9/4*d**4 + 3/2*d**5. Factor r(o).
-o**2*(o - 2)**2*(7*o - 2)/4
Suppose -m + 10 + 11 = 0. Let k = -13 + m. Factor -2*a**5 - 4*a**3 + 2*a - 8*a**2 - 4*a - 8*a**4 - k*a**3.
-2*a*(a + 1)**4
Let a(w) be the second derivative of 0 + 2*w**2 + w + 10/3*w**3 - 5/6*w**6 + 7/4*w**4 - w**5. Find g such that a(g) = 0.
-1, -2/5, 1
Suppose -4*t + 3*t + 11 = 4*v, v + 5*t - 17 = 0. Find o, given that 4*o**2 - 7*o**3 + 2*o + 0*o**5 + 2*o**5 - v*o**4 - 2 + 3*o**3 = 0.
-1, 1
Let q(o) be the third derivative of 0*o**5 + 0 + 1/210*o**7 + 0*o + 6*o**2 - 1/60*o**6 + 0*o**4 + 0*o**3. Factor q(y).
y**3*(y - 2)
Let x(d) be the first derivative of d**4/2 + 4*d**3/3 + d**2 + 7. Suppose x(y) = 0. Calculate y.
-1, 0
Suppose -2*c = 2*p - 8, -c - 6 = -0*c - 4*p. Let m(y) be the first derivative of 2/5*y**c - 1 - 2/5*y - 2/15*y**3. What is s in m(s) = 0?
1
Let q(k) be the second derivative of 1/15*k**3 + 0 + 2*k + 0*k**2 + 0*k**4 - 1/50*k**5. Let q(u) = 0. What is u?
-1, 0, 1
Let d(i) = i**3 + 7*i**2 + 6*i - 3. Let y be d(-6). Let v be (-13)/(-20) + y/12. Let -v - 2/5*h**5 - 2/5*h + 4/5*h**3 + 4/5*h**2 - 2/5*h**4 = 0. Calculate h.
-1, 1
Let v = 5245/7 - 749. Factor 2/7*j - v*j**2 + 0.
-2*j*(j - 1)/7
Let z(q) be the third derivative of q**6/420 + q**5/210 + 4*q**2. Determine k, given that z(k) = 0.
-1, 0
Let b(p) be the first derivative of -p**6/10 + 9*p**4/20 + 2*p**3/5 - 8. Find g, given that b(g) = 0.
-1, 0, 2
Let u(m) = 4*m**3 - 3*m**2 - m + 3. Let x(s) = 12*s**3 - 10*s**2 - 4*s + 8. Let t(p) = -8*u(p) + 3*x(p). Find a, given that t(a) = 0.
-1/2, 0, 2
Let o = -3221995/9 - -357537. Let x = -462 - o. Factor 0*w + x*w**3 + 8/9*w**5 - 14/9*w**4 + 0 + 2/9*w**2.
2*w**2*(w - 1)**2*(4*w + 1)/9
Let h = -7 + 8. Factor 5 + 20*z - h - 7*z**3 + 28*z**2 + 19*z**3.
4*(z + 1)**2*(3*z + 1)
Factor -4/3 - 2/9*u**3 + 22/9*u - 8/9*u**2.
-2*(u - 1)**2*(u + 6)/9
Let r(z) be the first derivative of z**6/15 - 2*z**5/5 + 7*z**4/10 - 2*z**3/5 + 10. Factor r(x).
2*x**2*(x - 3)*(x - 1)**2/5
Suppose 10*m = 5*p + 5*m + 15, -4*p = -3*m + 9. Solve -2/11*g**2 + 0 + p*g = 0 for g.
0
Let f be (-1)/(-2 + 3) + 17. Suppose -2*i - 3*p = -39 + 8, -4*i + 71 = 3*p. Factor -30*t**4 + 9*t**5 + 24*t**3 + f*t**3 + t + 3*t - 3*t**3 - i*t**2.
t*(t - 1)**2*(3*t - 2)**2
Let g = -1489/3 + 497. Factor -10/3*k - g - 8/3*k**2.
-2*(k + 1)*(4*k + 1)/3
Let y(i) be the first derivative of 7*i**4 - 8/9*i - 1 - 98/45*i**5 + 4*i**2 - 218/27*i**3. What is l in y(l) = 0?
2/7, 1
Factor -6 + 5*k**5 - 24*k**2 - k**3 - 21*k + k**5 + 6*k**4 - 5*k**3 - 3*k**5.
3*(k - 2)*(k + 1)**4
Let p be ((-4)/16 - 1)*-12. Let g = -15 + p. Factor 0 + 0*k + 1/2*k**4 + g*k**3 + 0*k**2.
k**4/2
Let x(y) be the second derivative of y**6/720 + y**5/80 - 5*y**3/6 - y. Let j(p) be the second derivative of x(p). Let j(t) = 0. What is t?
-3, 0
Let x be (-112)/(-52) - (0 - -2). Suppose 2/13*d + 6/13*d**3 + x*d**4 + 0 + 6/13*d**2 = 0. What is d?
-1, 0
Let u(z) = z**3 - 13*z**2 + 23*z - 7. Let c be u(11). Let v(w) be the second derivative of 1/2*w**3 - 1/4*w**4 - c*w + 0 + 0*w**2. Factor v(b).
-3*b*(b - 1)
Factor 307 - 307 + z**2 + z**5 - z**4 + 2*z - 3*z**3.
z*(z - 2)*(z - 1)*(z + 1)**2
Let b be (-6)/(-5220)*2365/6. Let s = b - 1/116. Factor s*j**2 + 0 + 2/9*j**3 + 0*j.
2*j**2*(j + 2)/9
Let f(b) = b**3 + 3*b**2. Let l(n) = 6*n**3 + 21*n**2. Suppose 3*j - 2*x - 87 = 0, 0 = -3*x - 9 - 0. Let v(g) = j*f(g) - 4*l(g). Suppose v(i) = 0. What is i?
0, 1
Let -4/7*h + 3/7*h**2 + 1/7*h**4 + 4/7*h**3 - 4/7 = 0. What is h?
-2, -1, 1
Let p(x) be the second derivative of -x**7/1680 - x**6/360 - x**5/240 - x**4/12 - 3*x. Let r(w) be the third derivative of p(w). Factor r(u).
-(u + 1)*(3*u + 1)/2
Factor -2/15*f**2 + 2/5*f + 8/15.
-2*(f - 4)*(f + 1)/15
Let i(t) be the third derivative of -t**8/6720 + t**6/1440 - 2*t**3/3 - 3*t**2. Let q(n) be the first derivative of i(n). Factor q(j).
-j**2*(j - 1)*(j + 1)/4
Let l(x) be the first derivative of -1/15*x**3 - 2/5*x + 1/2*x**2 - 1/4*x**4 + 3/25*x**5 + 1. Let l(h) = 0. Calculate h.
-1, 2/3, 1
Let s(v) = 10*v**4 - 10*v**3 - 6*v**2. Let c(h) = h**4 + h**3 + h**2. Let q(t) = -2*c(t) + s(t). Factor q(g).
4*g**2*(g - 2)*(2*g + 1)
Let i(x) be the first derivative of 2*x**4 - 11*x**3 + 19*x**2/2 + 10*x + 4. Let n(p) = 7*p**3 - 33*p**2 + 20*p + 11. Let s(g) = -5*i(g) + 4*n(g). Factor s(r).
-3*(r - 2)*(r - 1)*(4*r + 1)
Suppose 0 = -4*p + 3*d, -5*p + 0*d - 2*d = -23. Let i = -3 + 9. Let -1 - 124*t**5 - 8*t + 1 + 140*t**4 + i*t**p - 40*t**2 + 26*t**5 = 0. Calculate t.
-2/7, 0, 1
Let z(j) = j**2 - 5*j + 6. Let o be z(4). Let g be 2*(-3)/12*(-3)/1. Factor a + 0 - g*a**o.
-a*(3*a - 2)/2
Let z(a) be the second derivative of a**4/36 - a**3/3 + 3*a**2/2 + 3*a. Find q such that z(q) = 0.
3
Let q be (-10)/(-8) + (-10)/(-40). Factor -3/4 + q*f**2 + 0*f - 3/4*f**4 + 0*f**3.
-3*(f - 1)**2*(f + 1)**2/4
Let c(f) be the second derivative of -f**5/20 + 2*f**4/3 - 7*f**3/6 - 4*f. Let h be c(7). Factor 0*v + h + 2/9*v**4 + 0*v**2 - 2/9*v**3.
2*v**3*(v - 1)/9
Let c = 1 + -1. Suppose 0*a + a = c. Determine t so that a*t + 0 - 44/5*t**4 + 2/5*t**3 - 42/5*t**5 + 4/5*t**2 = 0.
-1, -1/3, 0, 2/7
Suppose -4*b + 678 = -q, 4*b - 3*q - 58 - 616 = 0. Let c = -1188/7 + b. Determine v so that -2/7*v - c*v**2 + 0 = 0.
-1, 0
Let u(m) be the second derivative of m**7/42 + m**6/15 - 3*m**5/20 - m**4/3 + 2*m**3/3 - 2*m. Factor u(n).
n*(n - 1)**2*(n + 2)**2
Let z(q) be the second derivative of q**5/80 - q**4/16 + q**3/12 - 9*q. Solve z(h) = 0 for h.
0, 1, 2
Let d(f) be the first derivative of 7/2*f**4 + 8*f - 7 + 20*f**2 + 46/3*f**3. What is m in d(m) = 0?
-2, -1, -2/7
Factor 22*m**3 + 10*m**2 + 20 - 17*m**3 - 51*m + 16*m.
5*(m - 1)**2*(m + 4)
Let q(r) = -r**3 + 3*r**2 + 2*r - 2. Let w be q(4). Let z be w*(0 + 2/(-5)). Suppose -22*l + 2 - z*l**3 - 10*l**3 - 32*l**2 - 6 = 0. Calculate l.
-1, -2/7
Let i(w) be the second derivative of -w**7/63 + 4*w**6/45 - w**5/6 + w**4/9 - 19*w. Solve i(p) = 0.
0, 1, 2
Let t(g) = -2*g - 15. Let d(j) = j + 8. Let c(b) = 10*d(b) + 6*t(b). Let q b