7*a + 6 = -5*a. Suppose -c - a*c = -3*k - 13, 5*k = -2*c + 13. Factor 2 - m**3 + c*m - m**4 + 0*m + 3*m**2 + m.
-(m - 2)*(m + 1)**3
Let z(u) be the second derivative of -5*u**7/42 + 7*u**6/6 - 4*u**5 + 10*u**4/3 + 40*u**3/3 - 40*u**2 - 2*u. Factor z(v).
-5*(v - 2)**4*(v + 1)
Let a be (-7)/28 + 57/36. Factor 2*w - a - 2/3*w**2.
-2*(w - 2)*(w - 1)/3
Let w(i) be the third derivative of 0*i + 0 - 4*i**2 - 2/9*i**4 - 8/9*i**3 + 7/9*i**5. Suppose w(d) = 0. What is d?
-2/7, 2/5
Suppose -5*j + 30 = -2*k - 3*k, 2*j = 0. Let d be (4/20)/((-2)/k). What is h in d*h**2 - 9/5*h**5 + 0 + 0*h + 9/5*h**3 - 3/5*h**4 = 0?
-1, -1/3, 0, 1
Let o be -1 - (-3)/(-1) - -4. Suppose o*d + 3*d + 8 = -4*r, -2*d = -3*r - 6. Factor d*l - 2/3*l**3 + 0*l**2 + 0.
-2*l**3/3
Find p, given that 0*p + 8/3*p**3 + 2*p**2 + 2/3*p**4 + 0 = 0.
-3, -1, 0
What is u in 164*u - 164*u - 2 + 2*u**2 = 0?
-1, 1
Let z(x) = -x**3 + 4*x**2 - 4*x + 3. Suppose v - 2 - 1 = 0. Let d be z(v). Factor d + 4/7*u**3 + 0*u**2 - 2/7*u + 0*u**4 - 2/7*u**5.
-2*u*(u - 1)**2*(u + 1)**2/7
Let p(u) = 3*u**2 - 9*u - 5. Let d(w) = w**2 - 3*w - 2. Let m(k) = 11*d(k) - 4*p(k). Factor m(h).
-(h - 2)*(h - 1)
Let a(d) be the third derivative of d**5/270 + d**4/12 - 10*d**3/27 + 11*d**2. Let a(r) = 0. What is r?
-10, 1
Let r(h) be the second derivative of 2*h**6/75 - 13*h**5/100 + 11*h**4/60 - h**3/15 + 20*h. What is c in r(c) = 0?
0, 1/4, 1, 2
Factor 17*m**2 - 31*m**2 + 10*m**2 - 2*m - 2*m**3.
-2*m*(m + 1)**2
Let o = 83 + -327/4. Let y(w) = w**2 + 9*w + 10. Let m be y(-8). Factor 1/4 - o*i + i**m.
(i - 1)*(4*i - 1)/4
Let t(z) be the first derivative of 5 + 3*z**4 + 2*z**3 - 3/5*z**5 - 18*z**2 - 27*z. Solve t(d) = 0.
-1, 3
Let s(j) be the first derivative of j**3 + j**2/4 + 10. Factor s(w).
w*(6*w + 1)/2
Let n(l) = -10*l**4 - 22*l**3 - 18*l**2. Let u(t) = -t**5 + 49*t**4 + 109*t**3 + 91*t**2. Let g(q) = 11*n(q) + 2*u(q). Factor g(y).
-2*y**2*(y + 2)**3
Suppose 3*r = 4*r + 4*d - 25, 5*d = 25. Let -4 + 9*j**3 - 16*j - 2*j**2 - 2*j**r - 4 - 5*j**3 + 6*j**3 + 2*j**4 = 0. What is j?
-1, 2
Solve 4/3*v - 2/3*v**2 + 2 = 0.
-1, 3
Let f(k) be the third derivative of -k**6/360 + k**5/60 + k**4/8 + 5*k**3/18 + 4*k**2 - 8. Factor f(n).
-(n - 5)*(n + 1)**2/3
Let z(x) be the second derivative of 1/3*x**3 - x + 1/18*x**4 - 1/540*x**6 + 0 + 0*x**2 - 1/180*x**5. Let d(n) be the second derivative of z(n). Factor d(j).
-2*(j - 1)*(j + 2)/3
Let j = -3 - -9. Let h(g) be the second derivative of -1/15*g**4 - 1/30*g**j + 0*g**3 + 4/25*g**5 + g + 0 - 5/42*g**7 + 0*g**2. Factor h(l).
-l**2*(l + 1)*(5*l - 2)**2/5
Let q(o) be the second derivative of -o**6/420 + o**5/210 + o**4/42 - o**2/2 - 4*o. Let r(h) be the first derivative of q(h). Determine t so that r(t) = 0.
-1, 0, 2
Let t(x) be the second derivative of x**7/147 + 2*x**6/105 - x**5/70 - x**4/21 - 10*x. Suppose t(z) = 0. What is z?
-2, -1, 0, 1
Let g(j) be the first derivative of -1/120*j**6 - 1/30*j**5 - 1/24*j**4 + j**2 + 0*j**3 + 0*j - 3. Let p(c) be the second derivative of g(c). Factor p(o).
-o*(o + 1)**2
Let k be ((-3)/(2 + 1))/(-1). Let q = 3 - k. Factor 32/7*u**q - 16/7*u + 2/7.
2*(4*u - 1)**2/7
Suppose 8/11*k**2 + 2/11*k**3 + 10/11*k + 4/11 = 0. Calculate k.
-2, -1
Let x(k) be the second derivative of -k**6/90 + k**5/5 - 3*k**4/2 - k**3/3 + 4*k. Let c(s) be the second derivative of x(s). Suppose c(p) = 0. What is p?
3
Let g(o) be the first derivative of 2*o**3 - 3*o**3 - 7*o - 3 + 4*o + 3*o**2. Factor g(a).
-3*(a - 1)**2
Let n(l) = -l**2 - 4*l + 3. Let v be -1*(2 + -1) - -2. Let i be -1 + 0 + (-2 - v). Let s(m) = -m**2 - 5*m + 4. Let r(k) = i*n(k) + 3*s(k). Factor r(g).
g*(g + 1)
Let l(w) be the first derivative of 5*w**4/18 + 8*w**3/9 - w**2 + 17. Factor l(h).
2*h*(h + 3)*(5*h - 3)/9
Suppose 3*m = 2*o - 110, 0 = 2*o - 7*o - 3*m + 254. Let g = o + -154/3. Find f, given that 2/3*f**4 - 4/3*f - g + 4/3*f**3 + 0*f**2 = 0.
-1, 1
Let w = 10 - 10. Let m(d) be the third derivative of 1/120*d**6 + 1/6*d**3 + 2*d**2 + 0*d - 1/24*d**4 - 1/60*d**5 + w. Suppose m(a) = 0. Calculate a.
-1, 1
Let m(z) be the second derivative of -z**4/9 - 16*z**3/9 - 32*z**2/3 - 7*z. Factor m(f).
-4*(f + 4)**2/3
Let n(x) be the first derivative of x**3 - 4. Factor n(m).
3*m**2
Let t(s) = s - 11. Let j be t(8). Let l = j - -3. Let l + 0*c**2 + 6/5*c**4 + 4/5*c**3 + 0*c = 0. What is c?
-2/3, 0
Let r(m) = m**2 - 6*m. Let l be r(6). Let a(s) be the first derivative of l*s - 1/2*s**4 - 4 + 0*s**3 + s**2. Factor a(c).
-2*c*(c - 1)*(c + 1)
Find o, given that -1/4*o - 3/4*o**3 + 0 + 1/4*o**4 + 3/4*o**2 = 0.
0, 1
Let w(m) = -m**2 + 1 - 2 + 4 - 5*m. Let g be w(-5). Find j such that -4/7*j + 22/7*j**4 + 18/7*j**2 - 30/7*j**g + 0 - 6/7*j**5 = 0.
0, 2/3, 1
Let t(l) be the third derivative of -l**7/7560 + l**6/1080 - l**5/360 + l**4/24 - l**2. Let h(j) be the second derivative of t(j). Find s such that h(s) = 0.
1
Let c(n) be the third derivative of -n**10/264600 + n**9/211680 + n**5/60 - n**2. Let u(s) be the third derivative of c(s). Let u(g) = 0. Calculate g.
0, 1/2
Let i(m) be the third derivative of -m**7/630 - m**6/360 + m**5/60 + m**4/72 - m**3/9 + 7*m**2. Factor i(x).
-(x - 1)**2*(x + 1)*(x + 2)/3
Let z(a) be the third derivative of 0*a**3 - 1/60*a**5 - 4*a**2 + 1/840*a**8 + 0*a + 3/200*a**6 - 1/150*a**7 + 0 + 1/120*a**4. Find g, given that z(g) = 0.
0, 1/2, 1
Let p(f) be the first derivative of -5*f**3/3 - 5*f**2 + 15*f + 3. Find u such that p(u) = 0.
-3, 1
Let g(a) = 28*a - 107. Let l be g(4). Factor 0*c**2 + 0*c**3 + 2/9*c**4 + 0 + 0*c + 2/9*c**l.
2*c**4*(c + 1)/9
Let z(u) = 2 - u**2 + 13*u + 2 - 2*u**2. Let w(c) = -2*c**2 + 9*c + 3. Let d(j) = -7*w(j) + 5*z(j). Factor d(h).
-(h - 1)**2
Let o = 0 + 0. Let m = 122/3 + -40. Factor 2/3*r**3 + 4/3*r**2 + o + m*r.
2*r*(r + 1)**2/3
Factor -j**2 + 33*j**2 + 150*j - 134*j + 12*j**3.
4*j*(j + 2)*(3*j + 2)
Solve 2/7*n**2 - 2/7*n**3 + 0 + 0*n = 0.
0, 1
Let c = 5 + -7. Let d = 2 - c. Factor 0*o**3 - d*o**3 + o**2 + o**3 - 2*o**4 - o**5 + 5*o**4.
-o**2*(o - 1)**3
Suppose 3 = -3*w + 9. Suppose 3*f - w*f**2 + 8 + 5*f**2 - 8 = 0. What is f?
-1, 0
Suppose 0 = 5*d - 12 - 8. Factor 2*i**3 + 3*i**4 + 2*i**4 - 4*i**d.
i**3*(i + 2)
Suppose 6/13 + 4/13*v - 2/13*v**2 = 0. What is v?
-1, 3
Let y(v) be the first derivative of -1/50*v**5 + 0*v**2 + 0*v**3 - 1/60*v**4 - 3 - 3*v. Let h(r) be the first derivative of y(r). Solve h(j) = 0 for j.
-1/2, 0
Let u(i) = 2*i**2 - i - 1. Let o be u(-1). Let s be 3 - (-10)/(-14) - o. Solve 4/7 - s*b**2 + 2/7*b = 0 for b.
-1, 2
Let h(j) = -j**2 - 2*j + 5. Let y be h(3). Let u = -10 - y. Determine q so that u - 6/5*q - 3*q**2 = 0.
-2/5, 0
Let q(l) = 2*l**3 - 24*l**2 + 22*l + 2. Let a be q(11). Find i such that 1/4 + i + 3/4*i**a = 0.
-1, -1/3
Let x = -20 + 20. Let o(n) be the third derivative of 0*n**4 + 1/30*n**5 + 1/60*n**6 + x + 0*n**3 + 0*n + 2*n**2. Let o(t) = 0. Calculate t.
-1, 0
Factor -2/15*n**2 + 0*n + 8/15.
-2*(n - 2)*(n + 2)/15
Let b(n) = -1. Let x(w) = -5*w**2 + 10*w - 3. Let i(a) = -3*b(a) + x(a). Let i(d) = 0. What is d?
0, 2
Factor 507/2*d**2 + 6 - 78*d.
3*(13*d - 2)**2/2
Factor 2/9*o**4 + 2/9 + 0*o - 4/9*o**2 + 0*o**3.
2*(o - 1)**2*(o + 1)**2/9
Let t(u) be the third derivative of -5*u**8/336 + 3*u**7/14 - 23*u**6/24 + 7*u**5/12 + 5*u**4 - 40*u**3/3 - 15*u**2. Find i such that t(i) = 0.
-1, 1, 4
Let j = 20 + -19. Suppose 0 = -3*b - u + 6, 4*u + 20 + j = 3*b. Solve 0 + 0*z - 4/7*z**2 - 6/7*z**5 + 8/7*z**4 + 2/7*z**b = 0 for z.
-2/3, 0, 1
Let f(v) be the first derivative of -v**3/9 + v**2/4 - v/6 - 6. Suppose f(q) = 0. What is q?
1/2, 1
Suppose -s = 3 + 1. Let c be (s/(-3))/((-1)/(-3)). Solve 4*g**c - 2*g**4 + 4*g**3 - 2*g**3 = 0.
-1, 0
Suppose 0 = -2*g + 7*g - 20. Suppose 6 - g = b. Solve -1/2*s - 1/2*s**b + 0 = 0.
-1, 0
Let t = -4 + -4. Let q be t/(-10)*2/4. Let 0*p**2 + 4/5*p**3 + 0 + 0*p**4 - q*p - 2/5*p**5 = 0. Calculate p.
-1, 0, 1
Suppose 2*p + 9 = -p. Let k be ((-4)/(-8))/(p/(-2)). Factor 1/3*c + k - 1/3*c**3 - 1/3*c**2.
-(c - 1)*(c + 1)**2/3
Let s(v) = -18*v**2 - 19*v + 9. Let z(w) be the second derivative of 3*w**4/4 + 3*w**3/2 - 2*w**2 + w. Let b(n) = -2*s(n) - 5*z(n). Factor b(d).
-(d + 1)*(9*d - 2)
Factor -d + 2*d**2 - 4*d**2 + d.
-2*d**2
Let z(l) = 11*l**4 - 7*l**3 + 9*l**2 + 9*l - 9. Let t(j) = 5*j**4 - 3*j**3 + 4*j**2 + 4*j 