e of y(z). Factor c(u).
(u + 1)*(5*u - 2)
Let y(r) = r**2 - 1. Let u(a) = 8*a**2 - 2*a - 7. Let i(q) = -4*u(q) + 28*y(q). Suppose i(k) = 0. What is k?
0, 2
Let j(m) be the first derivative of 0*m**4 + 4/15*m**5 + 1 - 4/9*m**3 - 1/9*m**6 + 0*m + 1/3*m**2. Determine z, given that j(z) = 0.
-1, 0, 1
Let l be (-2 + 4)/2 - 1. Solve 2/3*x**3 + l + 2/9*x + 2/3*x**2 + 2/9*x**4 = 0.
-1, 0
Let x(u) be the first derivative of u**5/30 - u**3/3 - u**2/2 - 3. Let z(i) be the second derivative of x(i). Let z(y) = 0. What is y?
-1, 1
Suppose 0*j - 2 = j. Let m be (j - -3)*(-1)/(-5). Factor -m*h**2 - 1/5*h + 0.
-h*(h + 1)/5
Let g(o) = -2*o - 10. Let f be g(-5). Let u(w) be the third derivative of -1/300*w**6 + 0*w + f + 0*w**3 + 0*w**5 + 2*w**2 + 0*w**4. Factor u(b).
-2*b**3/5
Let q(t) be the second derivative of t**4/12 - 4*t**3/3 + 8*t**2 - 12*t. Factor q(m).
(m - 4)**2
Let c(m) be the third derivative of 0*m**6 + 1/168*m**8 + 0*m + 0*m**3 - 3*m**2 + 1/15*m**5 + 0 - 2/105*m**7 - 1/12*m**4. Solve c(w) = 0.
-1, 0, 1
Factor 1/6*z**3 + 0*z - z**2 + 0.
z**2*(z - 6)/6
Let l = -124 - -256. Let f be (-7)/(-22) - (-24)/l. Solve -1/4*j + 1/4*j**3 - 1/2 + f*j**2 = 0 for j.
-2, -1, 1
Let s(l) = l**3 - 1 - 4*l**3 + 2*l**3 - 4*l**2 - l. Let j be s(-4). Factor a**4 - a - 3*a**3 + j*a**2 + 0*a**2 + 0*a.
a*(a - 1)**3
Suppose 0 = -c - 4*c. Let l(k) = 3*k**2 + c*k + 4*k - 7*k**2. Let x(j) = j**3 - 5*j**2 + 5*j - 1. Let g(d) = -3*l(d) + 2*x(d). Determine w so that g(w) = 0.
-1, 1
Let w(x) be the second derivative of -x + 1/189*x**7 + 0*x**4 + 0*x**6 + 0*x**3 + 0 + 0*x**2 - 1/90*x**5. Let w(p) = 0. Calculate p.
-1, 0, 1
Let o(s) be the first derivative of s**6/5 - 16*s**5/25 - 4*s**4/15 + 64*s**3/45 + 16*s**2/15 + 27. Factor o(c).
2*c*(c - 2)**2*(3*c + 2)**2/15
Let t = -1622/7 - -232. Determine c so that -2/7*c**4 + 0*c**2 + t*c**3 + 0*c + 0 = 0.
0, 1
Determine u so that -2*u - 1/2*u**3 + 2*u**2 + 0 = 0.
0, 2
Let f(d) be the third derivative of 0*d + 0*d**4 + 0*d**5 + 1/210*d**7 + 0*d**3 - 1/240*d**6 - 1/672*d**8 + 0 + 5*d**2. Solve f(g) = 0 for g.
0, 1
Let r(w) = 2*w**3 - 24*w**2 + 24*w - 22. Let g be r(11). What is d in g*d**2 + d + 2/3 - 1/3*d**3 = 0?
-1, 2
Suppose 2*k = -2*a + 2, 5 = -4*k - k. Let n(x) be the third derivative of 3*x**a + 1/3*x**3 + 1/30*x**5 + 0*x - 1/6*x**4 + 0. Factor n(h).
2*(h - 1)**2
Let y(b) be the third derivative of -b**6/540 + b**5/135 + 6*b**2. Find t, given that y(t) = 0.
0, 2
Let l(k) be the first derivative of -1/20*k**4 + 1/10*k**3 - 1 + 3*k - 1/10*k**2 + 1/100*k**5. Let g(o) be the first derivative of l(o). Factor g(p).
(p - 1)**3/5
Let u(z) be the third derivative of -z**7/840 + z**6/480 + z**5/48 + z**4/32 + 5*z**2. Find d, given that u(d) = 0.
-1, 0, 3
Suppose -3*n + n = -2. Let y be (-2)/(-4)*10*n. Factor w**5 - 3*w**4 + y*w**5 - 3*w**5.
3*w**4*(w - 1)
Let f(w) be the second derivative of -w**5/25 - 11*w**4/90 - 4*w**3/45 + w**2/15 + 32*w. Factor f(g).
-2*(g + 1)**2*(6*g - 1)/15
Let m(j) be the second derivative of -1/60*j**5 + 0*j**3 - 3/2*j**2 + 3*j + 0 - 1/12*j**4. Let r(x) be the first derivative of m(x). Factor r(d).
-d*(d + 2)
Let a be (-27)/60*-2 - 2/4. What is p in 0*p + 0*p**3 - 1/5 - 1/5*p**4 + a*p**2 = 0?
-1, 1
Let s = 11/3 + -1. Find n such that -8/3*n + 2/3 + 4*n**2 + 2/3*n**4 - s*n**3 = 0.
1
Let q(n) = 4*n**2 - n + 19. Let p(c) = 3*c - 3*c + 8 + 2*c**2 + 2. Let b(s) = 11*p(s) - 6*q(s). Factor b(h).
-2*(h - 2)*(h - 1)
Let c(w) = -14*w**2 + 48*w - 88. Let m(d) = 9*d**2 - 32*d + 59. Let f(g) = 5*c(g) + 8*m(g). Solve f(y) = 0.
4
Let s(q) be the second derivative of q**7/231 + 2*q**6/165 - q**4/33 - q**3/33 + 5*q. Let s(i) = 0. What is i?
-1, 0, 1
Suppose 3*b = b + 32. Factor 4*d**3 + 13*d**2 - b*d**2 - d**3.
3*d**2*(d - 1)
Let k = -35 - -20. Let i be (k/(-4))/(-5)*-4. Determine f so that -i*f**3 + 5*f**3 - f**3 + f - 2*f = 0.
-1, 0, 1
Let y(h) be the first derivative of h**8/1680 + h**7/420 + h**6/360 + 2*h**3/3 - 2. Let o(r) be the third derivative of y(r). Solve o(s) = 0 for s.
-1, 0
Suppose 0*u - 4*u + 8 = 0. Factor u*l**2 - 5*l**3 - 3 + 4*l**4 + 1 + 2 - l**5.
-l**2*(l - 2)*(l - 1)**2
Let u(o) be the second derivative of o**4/3 - 2*o**2 + 3*o. Factor u(d).
4*(d - 1)*(d + 1)
Suppose -52*s + 45*s + 14 = 0. What is j in -2/3*j**s + 2/9 + 4/9*j = 0?
-1/3, 1
Let b(p) = 18*p**2 - 6. Let f be b(2). Let d be (f/(-55))/(9/(-10)). Factor 2/3*k**2 - 2*k + d.
2*(k - 2)*(k - 1)/3
Let t = -8 - -10. Find p, given that p**t + 0*p**2 - p**2 + p**4 - p**2 = 0.
-1, 0, 1
Let p(r) be the third derivative of -r**7/420 + r**6/240 - 2*r**2. Determine u, given that p(u) = 0.
0, 1
Suppose -4 = -9*a + 5*a. Let r(x) be the first derivative of 19/3*x**3 - 4*x + a - 9/5*x**5 + 2/3*x**6 - 5/2*x**4 + 6*x**2. Solve r(c) = 0.
-1, 1/4, 2
Suppose 75 = -i - 2*i. Let y be (-130)/6*5/i. Solve -2*x + 1/3 + y*x**2 - 4*x**3 + 4/3*x**4 = 0 for x.
1/2, 1
Let m(p) = p**2 + 6*p - 5. Let s(x) = 2*x**2 + 7*x - 6. Let u(y) = 3*m(y) - 2*s(y). Factor u(g).
-(g - 3)*(g - 1)
Let t(o) = -52*o**2 + 22*o + 10. Let d = 21 + -11. Let f(v) = -17*v**2 + 7*v + 3. Let y(p) = d*f(p) - 3*t(p). Factor y(j).
-2*j*(7*j - 2)
Let v = 14 + -9. Suppose -2*b = 3*w - 6, -5*w + 2*b = 1 + v. Factor 1/5*a**2 + w*a - 1/5.
(a - 1)*(a + 1)/5
Let u(q) be the first derivative of 1/6*q**3 + 1/12*q**4 + 1 + 1/60*q**5 - q**2 + 0*q. Let a(c) be the second derivative of u(c). Suppose a(r) = 0. What is r?
-1
Let q(m) be the third derivative of m**7/735 - m**6/420 - m**5/70 + m**4/84 + 2*m**3/21 - 8*m**2. Determine k so that q(k) = 0.
-1, 1, 2
Let w(p) = -2*p**4 + 2*p**3 - 2*p + 14. Let l(t) = 4*t**4 - 5*t**3 + t**2 + 5*t - 27. Let n(j) = -6*l(j) - 11*w(j). Solve n(y) = 0 for y.
-1, 1, 2
Let m(z) be the first derivative of -z**6/24 + z**5/5 - z**4/4 + 10. Factor m(u).
-u**3*(u - 2)**2/4
Determine d, given that -20*d**2 + 38 + 0*d + 6*d + 6*d - 2 + 4*d**3 = 0.
-1, 3
Let b = 6 + -1. Determine f, given that -f**b + 2*f**2 + 3*f**3 - f**4 - 4 + 3 - f**3 - f = 0.
-1, 1
Let o(f) = f**3 + 7*f**2 - 8*f + 3. Let l be o(-8). Suppose 15 = l*m - 3*y, 0 = -4*m + 3*y - y + 10. Solve 2/7*q**2 + 0*q - 4/7*q**3 + m + 2/7*q**4 = 0 for q.
0, 1
Factor 0 + 0*u**3 + 0*u + 3/4*u**4 + 3/4*u**5 + 0*u**2.
3*u**4*(u + 1)/4
Find z, given that 1129*z - 1129*z - 2*z**2 = 0.
0
Factor 2*w**4 - 10*w + 14*w + 10*w**2 + 8*w**3 + 0*w**4.
2*w*(w + 1)**2*(w + 2)
Let r(z) be the third derivative of -z**11/1829520 + z**9/332640 - z**5/20 - 2*z**2. Let y(t) be the third derivative of r(t). Factor y(b).
-2*b**3*(b - 1)*(b + 1)/11
Let t(n) be the first derivative of n**7/168 - n**6/60 + n**5/80 + 5*n + 8. Let u(j) be the first derivative of t(j). Solve u(o) = 0.
0, 1
Let b = -8 - -10. Let -19*l**3 - l**2 - 3*l**b + 7*l**3 = 0. Calculate l.
-1/3, 0
Let q be -9 + 5 - 422/(-106). Let y = q - -55/106. Find a such that 1/2*a**3 - y*a - 1/2*a**2 + 1/2 = 0.
-1, 1
Let q(v) be the first derivative of v**4/26 - 4*v**3/39 - 4*v**2/13 + 16*v/13 + 7. What is i in q(i) = 0?
-2, 2
Let s(i) be the third derivative of -i**7/1680 + i**6/360 - i**5/240 - 7*i**3/6 + 8*i**2. Let q(p) be the first derivative of s(p). Let q(o) = 0. What is o?
0, 1
Suppose -5*v = -4*b - 14, 3*v + 3*b + 4 = 7. Suppose -u + 2 = x, -5*u + v*x + 2 = 3*x. Factor 0*z**4 + 0*z - 2/3*z**3 + u + 2/3*z**5 + 0*z**2.
2*z**3*(z - 1)*(z + 1)/3
Suppose -18*v + 6 = -15*v. Let b(y) be the second derivative of 0 - y**4 + 4/3*y**3 - 1/15*y**6 - y**2 + 2/5*y**5 - v*y. Let b(f) = 0. Calculate f.
1
Factor 3/5*y**4 + 0*y + 3/5*y**5 + 0 + 0*y**2 + 0*y**3.
3*y**4*(y + 1)/5
Let i(l) be the third derivative of l**6/40 + l**5/30 - 5*l**4/24 - l**3/3 + l**2. Let o(y) = -y**3 - y**2 + y. Let b(h) = -i(h) - 2*o(h). Factor b(r).
-(r - 2)*(r + 1)**2
Let 0*v**3 - 5*v**2 + 0*v**2 + 3*v**3 - 8*v**3 = 0. Calculate v.
-1, 0
Let l(o) = 2*o**4 + 14*o**3 - 42*o**2 + 34*o - 14. Let z(w) = w**4 - w**3 - w**2 + w - 1. Let d(g) = l(g) - 6*z(g). Suppose d(b) = 0. Calculate b.
1, 2
Let p = -4/11 + 34/33. What is z in -p - 1/3*z + 1/3*z**3 + 2/3*z**2 = 0?
-2, -1, 1
Let l(i) = -2*i**2 - 2*i + 2. Let t be 1 - 2/(6/9). Let s(d) = -d**3 + d + 1. Let g(h) = t*s(h) + l(h). Factor g(j).
2*j*(j - 2)*(j + 1)
Let s(v) be the second derivative of -v**7/14 + v**6/10 + 3*v**5/20 - v**4/4 - 20*v. Solve s(n) = 0 for n.
-1, 0, 1
Let h(i) be the third de