ose -c = j - 1 - 0, -4*j = c - 16. Let k(u) = -u**3 - 4*u**2 + 7*u - 2. Let s(w) = j*k(w) - 6*f(w). Factor s(h).
(h - 2)*(h - 1)*(h + 1)
Let o(h) be the first derivative of -h**5/15 + h**4/4 - 2*h**3/9 + 11. Solve o(b) = 0.
0, 1, 2
Let q(z) be the second derivative of z**8/2520 + z**7/630 + z**6/540 + z**3/2 + 3*z. Let w(p) be the second derivative of q(p). Factor w(d).
2*d**2*(d + 1)**2/3
Suppose n - u = 3*u + 11, 5*u + 13 = n. Let l be (2 - 1) + (-1)/n. Factor -l*i - 2/3*i**3 + 0 + 4/3*i**2.
-2*i*(i - 1)**2/3
Let d(b) = 2*b + 1. Let j(l) = -l**2 + 1. Let n(p) = -d(p) + j(p). Factor n(m).
-m*(m + 2)
Let j(f) be the second derivative of -f**5/80 + f**4/24 + f**3/24 - f**2/4 + f. Factor j(i).
-(i - 2)*(i - 1)*(i + 1)/4
Let w(o) = -3*o**2 - 2*o - o - 2*o - 1 + 3*o. Let s(h) = 10*h**2 + 6*h + 3. Let c(g) = -2*s(g) - 7*w(g). Factor c(a).
(a + 1)**2
Let q(v) be the third derivative of v**8/8960 - v**7/1120 + v**6/320 - v**5/160 + v**4/3 + 2*v**2. Let m(h) be the second derivative of q(h). Factor m(w).
3*(w - 1)**3/4
Suppose -1 - 8*o + 2*o**2 + 5 + 6*o - 4*o = 0. Calculate o.
1, 2
Suppose 2*a - 3*i - 4 = 0, 5*a + i = -4*i - 15. Let g be (a*4/(-20))/1. Let 0 + 3/5*d**2 - g*d = 0. What is d?
0, 1/3
Let t(q) = 5*q**4 + 12*q**3 + 7*q**2 + 2*q. Let g(o) = -25*o**4 - 61*o**3 - 36*o**2 - 11*o. Let v(n) = 2*g(n) + 11*t(n). Factor v(f).
5*f**2*(f + 1)**2
Let t(m) be the second derivative of m**7/6 - m**6/5 - m**5/10 + m**3/6 - 3*m. Let p(q) = q**5 - q**4. Let b(o) = 6*p(o) - t(o). Determine l so that b(l) = 0.
-1, 0, 1
Let r(h) = h**3 - 11*h**2 + 12*h - 14. Let n be r(10). Let u be 2 - (-5)/((-15)/n). Let -2/7*m**4 + 2/7*m**2 - 2/7*m + u + 2/7*m**3 = 0. What is m?
-1, 0, 1
Suppose 0 = -w - 4*f + 7, 3*w - 3 = 3*f + 3. Solve 0*a**4 + 4*a + 7*a**3 + 4*a**5 + 4*a**4 + 4 - 15*a**w - 8*a**2 = 0.
-1, 1
Let l(b) be the first derivative of -6*b**2 + 18/5*b**5 + 0*b - 1/2*b**6 - 39/4*b**4 + 2 + 12*b**3. Factor l(z).
-3*z*(z - 2)**2*(z - 1)**2
Let z(w) = 2*w + 40. Let a be z(-20). Let -1/2*p**2 + 1/2*p + a = 0. Calculate p.
0, 1
Let f be (-4)/(-18) + 4/(-18). Suppose 14 = 2*g - 5*t - f, -4*g + 18 = -5*t. Factor 22/3*p + 52/3*p**3 + g*p**5 - 4/3 - 28/3*p**4 - 16*p**2.
2*(p - 1)**4*(3*p - 2)/3
Suppose -3*a = a. Let h = -73 + 221/3. Factor -2/3*s + a + h*s**3 + 5/3*s**2 - 5/3*s**4.
-s*(s - 1)*(s + 1)*(5*s - 2)/3
Let i(n) be the second derivative of -n**7/2940 - n**6/630 - n**5/420 - n**3/6 - n. Let r(w) be the second derivative of i(w). Factor r(p).
-2*p*(p + 1)**2/7
Factor 3/5*i - 1/5*i**3 + 2/5 + 0*i**2.
-(i - 2)*(i + 1)**2/5
Let g(a) be the third derivative of 2*a**7/735 + a**6/210 - a**5/35 - a**4/42 + 4*a**3/21 - 9*a**2. Factor g(c).
4*(c - 1)**2*(c + 1)*(c + 2)/7
Let d(c) be the first derivative of -3*c**4 - 7*c**3 - 3*c**2 + 3*c - 29. Solve d(b) = 0.
-1, 1/4
Let j(h) = -3*h - 40. Let b be j(-14). Factor -10/7*s**b - 2*s - 4/7.
-2*(s + 1)*(5*s + 2)/7
Let y = 576841/177 + -3259. Let c = 1585/708 - y. Solve 0 + 3/2*n + c*n**3 + 3/4*n**4 - 3/4*n**5 - 15/4*n**2 = 0.
-2, 0, 1
Let i(f) = -5*f**3 - 3*f**2 - 3*f + 1. Let a(z) = -6*z**3 - 4*z**2 - 4*z + 1. Let c(k) = 6*a(k) - 7*i(k). Solve c(g) = 0.
-1
Find y such that 0*y**2 + 0 + 0*y**3 + 0*y + 1/3*y**4 = 0.
0
Factor -36/5*w - 4/5*w**5 - 64/5*w**2 - 56/5*w**3 - 24/5*w**4 - 8/5.
-4*(w + 1)**4*(w + 2)/5
Suppose -4*c + 92 = -4*k, 70 = -3*k - 0*k + 2*c. Let p be ((-16)/k)/(8/3). Factor 0 - 1/2*d**2 + 1/4*d**3 + p*d.
d*(d - 1)**2/4
Let c = 4 - 2. Let -n**c + n**2 - 3*n**3 + 25*n**4 - 37*n**4 = 0. Calculate n.
-1/4, 0
Suppose a + 2*a = 57. Factor 24*y - y**2 + 1 - 43*y + a*y.
-(y - 1)*(y + 1)
Let g(n) be the second derivative of n**7/21 - n**6/5 + 3*n**5/10 - n**4/6 - 6*n. Factor g(k).
2*k**2*(k - 1)**3
Let d be 38/39 - (-50)/(-75). Factor -2/13*z**2 + 6/13 + d*z.
-2*(z - 3)*(z + 1)/13
Let h = 1389/5 - 277. Factor -6/5*d**2 + 2/5*d**4 + 0 + 0*d**3 - h*d.
2*d*(d - 2)*(d + 1)**2/5
Let b(w) be the second derivative of 1/24*w**4 + 0 - 4*w - 1/2*w**3 + 9/4*w**2. What is s in b(s) = 0?
3
Suppose 3*j - 4 = 4*j + 4*h, 4*h + 4 = 2*j. Factor 2/5*q**3 + 2/5*q**2 + 0 + j*q.
2*q**2*(q + 1)/5
Let 0*g + 0*g**2 + 0 - 1/3*g**3 = 0. What is g?
0
Let l(q) be the second derivative of -3*q**4/4 + 17*q**3/3 - 25*q**2/2 - 6*q. Let d(f) = -3*f**2 + 11*f - 8. Let m(v) = 7*d(v) - 2*l(v). What is i in m(i) = 0?
1, 2
Suppose 2/7*o**4 + 0*o + 0 + 4/7*o**3 + 0*o**2 = 0. What is o?
-2, 0
Let x(j) = 12*j**3 + 3*j**2 - 8*j - 1. Let u(c) be the first derivative of -c + 0*c**3 - 1/4*c**4 + 1 + 0*c**2. Let s(h) = 3*u(h) + x(h). Solve s(z) = 0 for z.
-2/3, 1
Let z(m) be the first derivative of -3/5*m + 6/5*m**3 - 1 + 6/5*m**4 + 9/25*m**5 + 0*m**2. Find x, given that z(x) = 0.
-1, 1/3
Let b(r) = r**3 + 7*r**2 - 8*r + 4. Let x be b(-8). Factor -4*z**4 + z**3 - 2*z + 3*z**5 - z**5 - z**3 + x*z**2.
2*z*(z - 1)**3*(z + 1)
Let b(r) = -12*r**4 - 39*r**3 - 12*r**2 + 15*r + 15. Let m(o) = -3*o**4 - 10*o**3 - 3*o**2 + 4*o + 4. Let k(v) = 4*b(v) - 15*m(v). Factor k(x).
-3*x**2*(x + 1)**2
Suppose -50 = 3*w + 2*w. Let j be (-5)/12 + w/(-15). Factor -1/4*k**3 + 0 + 1/4*k + 1/4*k**2 - j*k**4.
-k*(k - 1)*(k + 1)**2/4
Let y be (2/10)/((-9)/((-135)/6)). Suppose -4*o = 4*u, 2*o - 3 + 7 = -u. Factor -w**u + 0*w**3 - y*w**5 + w**2 + 1/2*w + 0.
-w*(w - 1)*(w + 1)**3/2
Let k(i) be the second derivative of 0*i**2 + i - 1/3*i**4 + 0 + 2/3*i**3. Factor k(o).
-4*o*(o - 1)
Let q = 81 + -81. Let -4/9*i**2 + q + 2/9*i + 2/9*i**3 = 0. Calculate i.
0, 1
Let a(r) be the third derivative of -r**5/15 - r**4/2 - 4*r**3/3 - 8*r**2. Find c, given that a(c) = 0.
-2, -1
Suppose 0 = 4*q - 8, -10*n - 3*q = -15*n - 6. Factor -1/5*d**2 - 1/5*d + 1/5*d**3 + 1/5*d**4 + n.
d*(d - 1)*(d + 1)**2/5
Let s(m) be the first derivative of -m**4/12 + m**3/9 + 2*m**2/3 - 4*m/3 - 22. Factor s(c).
-(c - 2)*(c - 1)*(c + 2)/3
Factor -4*t**3 + 0 + t - 3/2*t**4 - 3/2*t**2.
-t*(t + 1)*(t + 2)*(3*t - 1)/2
Let i(m) = -m**2 - 12*m - 18. Let h(o) = o**2 + 6*o + 9. Let q be 7 + 0*2/4. Let l(a) = q*h(a) + 4*i(a). Factor l(d).
3*(d - 3)*(d + 1)
Suppose 5*f + 2*h - 7*h = -15, -4*h = -12. Let l(y) be the second derivative of -1/24*y**4 - 1/4*y**2 + y - 1/6*y**3 + f. Suppose l(n) = 0. What is n?
-1
Let p = -13 - -11. Let j(f) = f**2 + 2*f. Let m be j(p). Determine l so that 2/5*l**5 + 6/5*l**3 + m*l + 6/5*l**4 + 2/5*l**2 + 0 = 0.
-1, 0
Let u be 16/(-88) - (-24)/11. Factor r**2 + r - r**4 - u*r**3 - 2*r + r**3 + 2*r**3.
-r*(r - 1)**2*(r + 1)
Let n(d) = -d**3 - 12*d**2 + 30*d + 30. Let i be n(-14). Solve 0 + 0*h - 2/5*h**i = 0 for h.
0
Let c = 11 - 6. Suppose -5*u + c*v = -4*u - 4, 2*v = 0. Suppose -g**4 + g**3 + g**3 + 3*g**u = 0. Calculate g.
-1, 0
Factor 5/2*n**2 - 5*n + 5/2.
5*(n - 1)**2/2
Let g(j) be the first derivative of -j**5/5 - 5*j**4 - 50*j**3 - 250*j**2 - 625*j + 4. Factor g(f).
-(f + 5)**4
Factor -1/2*r - 1/4*r**2 + 0 + 1/4*r**3.
r*(r - 2)*(r + 1)/4
Let o(b) be the third derivative of b**7/70 + 3*b**6/40 + b**5/10 + 9*b**2. Suppose o(f) = 0. Calculate f.
-2, -1, 0
Let h(a) be the second derivative of a**6/255 - a**4/34 - 2*a**3/51 - 9*a. What is t in h(t) = 0?
-1, 0, 2
Let b(j) be the third derivative of -j**7/5880 + j**6/630 - j**5/168 + j**4/84 + j**3/6 + j**2. Let a(y) be the first derivative of b(y). Solve a(q) = 0.
1, 2
Suppose -4*c + 16 = -3*y + 6, -2*y = -4. Factor 3 + 2*r**5 + 6*r**2 - 9*r**c + 3*r**5 - 9*r + 6*r**3 - 2*r**5.
3*(r - 1)**4*(r + 1)
Let d be 170/60 + 2/(1 + 3). Let f(k) be the second derivative of 0 + d*k**3 + 1/2*k**4 - 2*k - 9/20*k**5 + 4*k**2. Factor f(x).
-(x - 2)*(3*x + 2)**2
Let k(j) be the third derivative of -j**7/210 + j**6/12 - 3*j**5/5 + 9*j**4/4 - 9*j**3/2 - 3*j**2. Factor k(s).
-(s - 3)**3*(s - 1)
Let j(z) = 3*z - 9. Let t be j(3). Factor 2/7*s**2 + 2/7*s + t.
2*s*(s + 1)/7
Factor 8/5*a**2 + 2*a + 4/5 + 2/5*a**3.
2*(a + 1)**2*(a + 2)/5
Let g be -1 - (1 - (-20)/(-4)). Factor 4*b**3 + 5*b - b**2 - g*b + 4 - 3*b**2 - 6*b.
4*(b - 1)**2*(b + 1)
Factor 1/9*r**2 + 4/9 + 4/9*r.
(r + 2)**2/9
Let u(i) be the second derivative of -i**5/30 - 2*i**4/9 - 4*i**3/9 + i. Determine c, given that u(c) = 0.
-2, 0
Let d be ((-1)/(-7))/(-8 - 17/(-2)). Determine q, given that -d - 2/7*q**2 + 4/7*q = 0.
1
Let z = 38 + -34. Let l(q) be the second derivative of 0*q**3 + 1/60*q**6 - 1/24*q**z - 2*q + 0*q**2 + 0 +