- 3. Let y(u) = h*i(u) + k(u). Solve y(r) = 0.
-2, 0, 1
Let d = 7 + -1. Let f be d + (-5 - (0 - 2)). Let 0 - 6/7*b**4 + 6/7*b**2 + 2/7*b**f - 2/7*b = 0. What is b?
-1, 0, 1/3, 1
Suppose -t + 2*g - 5 = -1, g - 2 = 0. Let h(l) be the second derivative of 0 - 1/20*l**5 + 1/12*l**4 + 3*l + 0*l**2 + t*l**3. Factor h(j).
-j**2*(j - 1)
Suppose 2*f = -8, 0 = -g + f - 5*f - 16. Let u(q) be the first derivative of 2/3*q**3 + g*q - 6/5*q**5 + q**4 - 3 + 0*q**2. Factor u(l).
-2*l**2*(l - 1)*(3*l + 1)
Let s = 27 + -22. Let a(o) be the first derivative of -1/4*o**2 + o**3 - 12/5*o**s + 0*o - 1/8*o**4 - 4/3*o**6 + 2. Factor a(t).
-t*(t + 1)**2*(4*t - 1)**2/2
Let a be 11/(-55) - 32/(-10). Factor -16*p**3 + 12 + 21*p**4 + 75*p**2 + 3*p**3 - 44*p**a - 3*p**5 - 48*p.
-3*(p - 2)**2*(p - 1)**3
Let l(r) = -r - 2. Suppose 5*x = -4*z + z - 17, 2*z = -x - 9. Let w be l(z). Determine f so that 2/3*f**5 + 0 + 0*f - 4/3*f**w - 8/3*f**4 + 10/3*f**3 = 0.
0, 1, 2
Suppose -12 - 26 = -4*l + 3*a, 0 = -l + 2*a + 12. Suppose -14 = -2*b - 0*b - 5*x, 5*b - l = x. Factor -s**4 - 1/3*s**b + 0 + 0*s + 4/3*s**3.
-s**2*(s - 1)*(3*s - 1)/3
Let f = 20 - 20. Factor f + 14/3*y**2 + 10/3*y**3 + 4/3*y.
2*y*(y + 1)*(5*y + 2)/3
Let r be ((-6)/9)/(2/(-6)). Factor 0*w - 1/3*w**5 + 1/3*w**3 + 0 + 0*w**4 + 0*w**r.
-w**3*(w - 1)*(w + 1)/3
Let p(h) = 24*h**2 - 96*h + 33. Let l(w) = -3*w**2 + 12*w - 4. Let y(d) = -33*l(d) - 4*p(d). Factor y(q).
3*q*(q - 4)
Let m be 9/(-3) - 41 - -1. Let i = m + 173/4. Find g, given that 0 - i*g**2 + 1/4*g = 0.
0, 1
Let z(n) be the second derivative of n**6/210 + n**5/35 + n**4/28 - 43*n. Solve z(o) = 0.
-3, -1, 0
Factor 3/4*d**2 + 0*d + 1/4*d**3 - 1.
(d - 1)*(d + 2)**2/4
Suppose -8*m + 11*m = 15. Factor -2/5*g**3 + 4/5*g**m + 0 + 0*g + 2/5*g**4 + 0*g**2.
2*g**3*(g + 1)*(2*g - 1)/5
Let f(g) be the second derivative of -g**9/13608 + g**7/3780 + g**3/3 + 4*g. Let r(i) be the second derivative of f(i). Factor r(v).
-2*v**3*(v - 1)*(v + 1)/9
Let m be 7 + 4/2*-1. Suppose -v = -m*j + 13, j + 3*v = 2*j + 3. Factor b**4 + 2*b**3 - b**2 - j*b**3 + b + 0*b**2.
b*(b - 1)**2*(b + 1)
Suppose -1 = -6*x + 5. Let m(f) = f - 1. Let n be m(x). Factor n - 1/4*i**3 + 1/4*i**2 + 0*i.
-i**2*(i - 1)/4
Let j(o) be the first derivative of o**6/30 + o**5/25 - o**4/10 - 39. Factor j(a).
a**3*(a - 1)*(a + 2)/5
Let r(b) be the second derivative of 125*b**5/4 + 125*b**4/2 + 50*b**3 + 20*b**2 + 10*b. Determine j so that r(j) = 0.
-2/5
Let v(t) = t**2 - t - 1. Let g be v(3). Let n = g + 3. Suppose n*p + 3 - 1 + 6 + 2*p**2 = 0. Calculate p.
-2
Let w be (65/(-15) - -5)/(14/3). Find x such that 1/7*x**3 + 1/7 - w*x - 1/7*x**2 = 0.
-1, 1
Let v(k) = -3*k - 2. Let n be v(6). Let f be (-23)/n + (-4)/10. Solve -3/4*t**3 - f*t**2 + 0 - 1/4*t**4 - 1/4*t = 0 for t.
-1, 0
Suppose -2*c = w - 14, 28 = -0*c + 4*c + 4*w. Factor -8 - c*i - 11*i - 6*i + 14*i**2.
2*(i - 2)*(7*i + 2)
Let s(t) be the first derivative of -1/3*t**6 - 3 + 0*t**5 + 1/2*t**4 + 0*t + 0*t**2 + 0*t**3. Suppose s(k) = 0. Calculate k.
-1, 0, 1
Let j = 2902/9 - 322. Factor 2/9*h - j*h**2 + 0 + 2/9*h**3.
2*h*(h - 1)**2/9
Let u be 2 + 26 - (-1 + -2). Let m = -213/7 + u. Factor 2/7*z**5 + 2/7 - m*z**3 - 4/7*z**2 + 2/7*z**4 + 2/7*z.
2*(z - 1)**2*(z + 1)**3/7
Let h(q) be the third derivative of -q**6/200 + 9*q**5/100 - 27*q**4/40 + 27*q**3/10 + 2*q**2. Factor h(u).
-3*(u - 3)**3/5
Let p(m) = 3*m**2 - 3*m - 6. Let b(k) = 9*k**2 - 8*k - 17. Let f(y) = 3*b(y) - 8*p(y). Suppose f(g) = 0. What is g?
-1, 1
Let j(y) = 7*y**5 - 2*y**4 - 2*y**3 + 2*y**2 + 5. Let h(p) = 8*p**5 - 2*p**4 - 2*p**3 + 2*p**2 + 6. Let s(u) = 5*h(u) - 6*j(u). Factor s(z).
-2*z**2*(z - 1)**2*(z + 1)
Let q(w) = w**4 - 6*w**3 - 9*w**2 - 5*w + 3. Let v(a) = -12*a**4 + 66*a**3 + 100*a**2 + 56*a - 34. Let g(k) = -68*q(k) - 6*v(k). Factor g(n).
4*n*(n + 1)**3
Suppose -l - 7 = -9. Let f(s) be the second derivative of 0*s**4 + 1/10*s**5 - 1/6*s**3 - 1/42*s**7 + s + 0*s**6 + 0 + 0*s**l. Find g such that f(g) = 0.
-1, 0, 1
Let z be 413/154 + -1 - (-8)/(-44). Factor -l**2 + 1 - 3/2*l**3 + z*l.
-(l - 1)*(l + 1)*(3*l + 2)/2
Let x(y) be the third derivative of -y**5/40 + y**4/16 + 3*y**3/2 + 23*y**2. Find j such that x(j) = 0.
-2, 3
Let t(m) = 2*m**3 + 11*m**2 + 8*m. Let b(p) = p**2 + p**2 - p**2. Suppose 6 = 3*d - d. Let v(h) = d*b(h) - t(h). Let v(z) = 0. Calculate z.
-2, 0
Let p = 249/4 + -62. Factor 0 - 1/4*l + 0*l**2 + p*l**3.
l*(l - 1)*(l + 1)/4
Find a, given that 6*a + 21*a**4 + a**3 - 19*a**2 - 7*a**3 - 2*a**2 = 0.
-1, 0, 2/7, 1
Solve -2/3*n**2 + 2/3*n + 0 = 0 for n.
0, 1
Let f(u) be the second derivative of -u**5/50 - 3*u**4/5 - 36*u**3/5 - 216*u**2/5 - 42*u. Factor f(d).
-2*(d + 6)**3/5
Let w be (0 + (-2 - -3))*1. Solve w - 4 + 1 - 1 + 3*l**2 = 0.
-1, 1
Let g = 19/18 - 8/9. Let b(j) be the third derivative of 0*j + 0 + g*j**5 + 1/30*j**6 + 0*j**3 - 1/6*j**4 - j**2 - 1/21*j**7. Find y such that b(y) = 0.
-1, 0, 2/5, 1
Let x be (-12)/(5 - 1) - (-75)/21. Factor -8/7 + x*v**2 - 4/7*v.
4*(v - 2)*(v + 1)/7
Let 3*l + 16*l**2 - 30*l**2 + 11*l**2 = 0. What is l?
0, 1
Suppose 2*u + 0*u = 864. Let q be (2/6)/(30/u). Factor -22/5*z**3 + 10*z**5 + 8/5*z + q*z**2 + 0 - 12*z**4.
2*z*(z - 1)**2*(5*z + 2)**2/5
Let n(k) = k**5 + k**3 - k**2 + k. Let m(r) = -4*r**5 + 2*r**4 - 4*r**3 + 5*r**2 - 5*r. Let x(z) = -m(z) - 5*n(z). Determine s so that x(s) = 0.
-1, 0
Let v(g) = g**2 - 5*g - 7. Let k be v(5). Let h = k + 11. Factor 3*n**h - 3*n**2 - n**4 + 2 - n**2.
2*(n - 1)**2*(n + 1)**2
Suppose 2*l + 4*s = 16, -5*l + 4*l + 3*s = 2. Suppose 1 = -j + l. Factor q**j + 5/4*q**2 + 0 + 1/2*q + 1/4*q**4.
q*(q + 1)**2*(q + 2)/4
Factor 0 + 6/7*k - 2/7*k**2.
-2*k*(k - 3)/7
Let i = 261 + -3391/13. Suppose -4/13*a + 6/13 - i*a**2 = 0. Calculate a.
-3, 1
Let d(m) be the first derivative of -7*m**5 + 75*m**4/2 - 215*m**3/3 + 60*m**2 - 20*m - 16. Suppose d(t) = 0. What is t?
2/7, 1, 2
Find m, given that 6/5*m**2 - 3/5*m**5 + 12/5*m**4 + 0 + 0*m - 3*m**3 = 0.
0, 1, 2
Let d(x) = -x + 5. Let u be d(2). Factor 2/5*m**u + 0*m**2 - 2/5*m + 0.
2*m*(m - 1)*(m + 1)/5
Let j(m) = m**2 - 2. Let v be j(2). Suppose -v*s = 3*s. Factor 0*u - u**2 + u + s*u.
-u*(u - 1)
Let i be 2/(-12)*6/(-4). Suppose -4*o - 4*z = -0*o + 4, -o + 5*z + 5 = 0. Factor -1/4*m**3 + 0*m**2 + i*m + o.
-m*(m - 1)*(m + 1)/4
Let p(d) be the third derivative of -d**6/150 - 2*d**5/75 - d**4/30 + d**2. Suppose p(g) = 0. Calculate g.
-1, 0
Let t(m) be the first derivative of 1 - 1/3*m**3 + 1/2*m + 0*m**4 + 0*m**2 + 1/10*m**5. Let t(s) = 0. What is s?
-1, 1
Factor 4/13 + 6/13*u - 40/13*u**2.
-2*(4*u + 1)*(5*u - 2)/13
Let x(z) be the second derivative of z**9/52920 - z**8/23520 - 5*z**4/12 - 4*z. Let f(m) be the third derivative of x(m). Suppose f(c) = 0. What is c?
0, 1
Let i(n) be the third derivative of -2*n**2 + 0*n - 1/240*n**6 + 0*n**3 + 0 + 0*n**4 - 1/120*n**5. Determine u, given that i(u) = 0.
-1, 0
Let w = -1/195 - -2929/780. Let t = w - 41/12. Factor t*k**4 + 0*k + 1/3*k**3 + 0 + 0*k**2.
k**3*(k + 1)/3
Let l be (26/(-39))/((-2)/(-12)). Let u be (l/1)/((-4)/2). Let -2/7*j**u + 0 - 2/7*j = 0. Calculate j.
-1, 0
Let z(x) be the first derivative of -x**5/25 - x**4/20 + x**3/15 + x**2/10 + 15. Solve z(o) = 0 for o.
-1, 0, 1
Let m(d) = 3*d**2 + 6*d - 1 - d**2 - 4*d**2. Let j(t) = 3 + t - t + 10*t**2 - 30*t + 1. Let z(a) = -3*j(a) - 16*m(a). What is n in z(n) = 0?
1, 2
Let m(g) = 5*g**3 + g**2 + 4*g - 4. Let c(p) = 11*p**3 + 2*p**2 + 9*p - 9. Let b(d) = -4*c(d) + 9*m(d). Factor b(v).
v**2*(v + 1)
Factor -2*d**4 - 6*d**2 + 7*d**4 + 5*d**3 + 0*d**4 - 10 - 25*d - 9*d**2.
5*(d - 2)*(d + 1)**3
Let p(b) be the first derivative of -2*b**3/39 + 7*b**2/13 - 12*b/13 + 18. Factor p(w).
-2*(w - 6)*(w - 1)/13
Suppose -4*b - 6 = 2. Let j be (b - 1) + (3 - 0). Determine c so that j*c + 0 + 2/3*c**2 = 0.
0
Suppose -h = -6*h + 20. Suppose -5*c + c = h*u - 40, -c = 5*u - 30. What is j in -j - c*j - j**2 + 5*j = 0?
-1, 0
Find g, given that 2*g**4 - g**5 + 9*g - 10*g - 4*g**2 + 0*g**5 + 2 + 2*g**3 = 0.
-1, 1, 2
Suppose 2*x + 8 = 6*x. Suppose -5 + 9 = x*b. Let -16 + 16 + o**b = 0. What is o?
0
Let c(r) be the first derivative of 9*r**4/10 - 26*r**3/5 - 29*r**2/5 - 2*r - 2. Factor c(o).
2*(o - 5)*(3*o + 1)**2/5
Let s be (-69)/(-21) + 6/(-21). Let q be 1/9*s*6. Suppose 8/3*f - 8/3 - 2/3*f**4 