uppose -l + 11 - 6 = 0. Let n(k) be the third derivative of 1/420*k**6 + 1/735*k**7 + 0 - 2*k**2 - 1/210*k**l + 0*k + 0*k**3 - 1/84*k**4. Factor n(b).
2*b*(b - 1)*(b + 1)**2/7
Let a(s) be the first derivative of s**7/1260 - s**6/270 + s**5/180 + 4*s**3/3 + 4. Let r(v) be the third derivative of a(v). Let r(t) = 0. Calculate t.
0, 1
Let z(m) be the second derivative of -m**7/126 - m**6/90 + m**5/30 + m**4/18 - m**3/18 - m**2/6 - 31*m. Factor z(d).
-(d - 1)**2*(d + 1)**3/3
Let d(q) = q**2. Let v(i) = i**3 + i**2. Let o(c) = 2*d(c) - v(c). Find x, given that o(x) = 0.
0, 1
Let w(h) be the third derivative of -h**6/1140 + h**5/570 + h**4/114 - 8*h**2. Factor w(o).
-2*o*(o - 2)*(o + 1)/19
Suppose 2*r = 5*r - 6. Determine y so that r*y**4 - 2*y**5 + 2*y**2 - 4*y**2 + 0*y**4 + 2*y**3 = 0.
-1, 0, 1
Factor i**2 - 1 + 2*i**3 - 4*i**5 + i**2 + 3*i**5 - i - i**4.
-(i - 1)**2*(i + 1)**3
Factor -6*i**2 + 4*i**3 + 0*i**3 - 5*i**3 + 3*i**3 + 4*i.
2*i*(i - 2)*(i - 1)
Suppose 30 = -5*l - 5*y, 2*l + 3*y = -13 - 1. Let c = 8 + l. Determine r, given that 0 + 0*r**2 + 0*r - 1/3*r**5 - 2/3*r**c - 1/3*r**3 = 0.
-1, 0
Suppose -4*c = -3*u - 6, -4*c + 2*u = u - 2. Factor -2/7*f**4 + c*f**3 + 2/7*f**2 + 0 + 0*f.
-2*f**2*(f - 1)*(f + 1)/7
Factor 30 - 324*u + 4*u**2 + 2*u**2 + 261*u.
3*(u - 10)*(2*u - 1)
Let m(q) be the second derivative of -5*q**5/16 + 5*q**4/16 + 3*q**3/8 + q**2/8 + 2*q. Solve m(a) = 0 for a.
-1/5, 1
Let w be (-2)/(-12) - 2/((-54)/63). Let x be -2 - (-1 + 2/(-2)). Suppose 0 + 2*b**4 + 1/2*b**2 + x*b - w*b**3 = 0. What is b?
0, 1/4, 1
Let r be -1 + 5 + 8/(-2). Let p(i) be the first derivative of r*i - 4 + 4/7*i**2 + 1/14*i**4 - 8/21*i**3. Factor p(t).
2*t*(t - 2)**2/7
Let p(u) = -u**5 + 19*u**4 - 7*u**3 + 7. Let f(y) = 6*y**4 - 2*y**3 + 2. Let w(q) = -q + 2. Let c be w(4). Let r(k) = c*p(k) + 7*f(k). What is s in r(s) = 0?
-2, 0
Let a = -787 + 787. Factor 0*c**2 + 1/7*c - 1/7*c**3 + a.
-c*(c - 1)*(c + 1)/7
Let m = -57 - -115/2. Solve m + 1/2*b**2 + b = 0.
-1
Let j(o) = -o**3 - 4*o**2 - o + 4. Let c be j(-3). Let l be -2 - (6/c - 1). What is m in -l*m**2 - 1 + 0*m**2 + m**2 - 2*m = 0?
-1
Let c be (-3)/((-6)/2)*-3. Let n be (-5)/10*(-3 - c). Factor 1/4*b**3 + n*b + 0*b**2 - 1/4*b**4 + 0.
-b**3*(b - 1)/4
Let j(o) be the third derivative of -o**6/468 - o**5/390 + o**3 - 3*o**2. Let i(z) be the first derivative of j(z). Factor i(u).
-2*u*(5*u + 2)/13
Let v be -2 - (1 + 0/1). Let p = -1 - v. Factor -1 + m**2 - m**p + m**2.
(m - 1)*(m + 1)
Let c(u) = -15*u**4 - 36*u**3 - 246*u**2 - 336*u - 135. Let q(m) = -m**4 + m**3 - m**2 + 1. Let s(x) = c(x) - 12*q(x). Let s(f) = 0. What is f?
-7, -1
Let r = 61 - 239/4. Find w, given that 1 + r*w**2 - 1/4*w**3 - 2*w = 0.
1, 2
Let s(g) be the first derivative of -g**5/90 - g**4/54 - 3*g + 3. Let a(l) be the first derivative of s(l). Suppose a(x) = 0. Calculate x.
-1, 0
Let h(m) be the third derivative of m**5/75 + m**4/30 - 4*m**3/15 + 5*m**2. Solve h(b) = 0.
-2, 1
Let b(i) be the third derivative of i**9/30240 + i**8/13440 - i**4/12 + 4*i**2. Let o(w) be the second derivative of b(w). Suppose o(j) = 0. Calculate j.
-1, 0
Let w(q) be the third derivative of q**6/30 - q**4/6 + 4*q**2. Factor w(u).
4*u*(u - 1)*(u + 1)
Let c(s) be the third derivative of 1/70*s**7 + 1/40*s**6 + 0*s**3 - 1/20*s**5 - s**2 + 0*s + 0 - 1/8*s**4. Factor c(f).
3*f*(f - 1)*(f + 1)**2
Let s(n) = -3*n**2 + 7. Suppose -g = -4*k + 2 + 10, -8 = g - 3*k. Let f(m) = 12*m**2 - 27. Let q(l) = g*f(l) + 15*s(l). Factor q(r).
3*(r - 1)*(r + 1)
Let n = -14 + 44. Suppose -11 = -4*y + 3*b, 3*y + 0*b = -5*b + n. Factor -2/3*s**3 + s - 2/3*s**2 - 1/3*s**y + s**4 - 1/3.
-(s - 1)**4*(s + 1)/3
Let t(z) = z**2 - 12*z - 11. Let j be t(13). What is q in -4*q**4 + j*q**3 - 6 + 6 - 2*q + 1 + 3*q**4 = 0?
-1, 1
Suppose 0 + 2/5*h**2 - 4/5*h = 0. What is h?
0, 2
Let x(w) be the first derivative of w**6/3 - 16*w**5/5 + 11*w**4 - 16*w**3 + 9*w**2 - 8. Suppose x(o) = 0. Calculate o.
0, 1, 3
Let f = 142 - 139. Suppose 4/3*w**3 + 5/3*w**5 - f*w - 10/3*w**2 + 4*w**4 - 2/3 = 0. Calculate w.
-1, -2/5, 1
Let x(p) be the second derivative of 1/120*p**5 + 1/480*p**6 + 0*p**3 + 0 - 1/2*p**2 + p + 0*p**4. Let b(m) be the first derivative of x(m). Solve b(l) = 0.
-2, 0
Determine n so that -2*n**3 + 13*n**4 + 50*n**3 - 40*n**2 + 4*n**5 + 12*n - 37*n**4 = 0.
0, 1, 3
Suppose g - 3*p = -8*p + 25, 0 = -2*g - 3*p + 15. Suppose -k + 1 + 1 = g. Factor 3/2 + 24*j**k - 12*j.
3*(4*j - 1)**2/2
Let h = 11 - 11. Find r, given that 4 + h*r**2 - 3*r**2 + 5*r**2 + 6*r = 0.
-2, -1
Determine s so that 21*s**2 + 4*s - 17*s**2 + 16*s - 56 = 0.
-7, 2
Let t be (-16)/24*(10 - 1). Let z = -64/11 - t. What is o in 6/11*o - 8/11*o**2 + z = 0?
-1/4, 1
Let u(k) = 45*k**4 + 20*k**3 + 5*k**2 - 30*k + 30. Let v(y) = y**4 - y + 1. Let b(x) = u(x) - 30*v(x). Find r, given that b(r) = 0.
-1, -1/3, 0
Solve -1/2*q**4 + 0 - 6*q**2 - 4*q - 3*q**3 = 0.
-2, 0
Let l(c) be the first derivative of -2/5*c - 2/25*c**5 - 2/5*c**2 - 2/15*c**6 + 4/15*c**3 + 2/5*c**4 + 1. Find d such that l(d) = 0.
-1, -1/2, 1
Let g(h) be the second derivative of 5/66*h**4 - 4/165*h**6 + 1/11*h**3 + 5*h - 1/11*h**2 - 3/110*h**5 + 0. Find x such that g(x) = 0.
-1, 1/4, 1
Suppose 0 = 5*m - 2*m + 5*m. Factor m + 1/2*d**2 - 1/2*d**4 - 1/4*d + 0*d**3 + 1/4*d**5.
d*(d - 1)**3*(d + 1)/4
Let w = -2/387 + 788/2709. Solve 0 - w*x**3 + 0*x**2 + 2/7*x = 0.
-1, 0, 1
Let b(f) be the second derivative of f**7/441 + f**6/35 + f**5/7 + 23*f**4/63 + 11*f**3/21 + 3*f**2/7 - 12*f. Factor b(p).
2*(p + 1)**3*(p + 3)**2/21
Suppose 6*r**4 + r**3 + 6*r - 11*r**2 - 7*r**4 + 5*r**3 = 0. What is r?
0, 1, 2, 3
Let o = -42 - -44. Factor -2/3*v**o + 2*v - 4/3.
-2*(v - 2)*(v - 1)/3
Let w be (-3)/(-6) + (-10)/(-4). Factor 5 + 6*g**w + 2*g**5 + 6*g**4 - 5 + 2*g**2.
2*g**2*(g + 1)**3
Let g(u) be the first derivative of -u**3/3 - 2*u**2 - 4*u + 8. Let g(b) = 0. Calculate b.
-2
Let z(r) be the first derivative of r**5/10 + r**4/8 - r**3/2 - r**2/4 + r + 5. Determine k, given that z(k) = 0.
-2, -1, 1
Let k(d) be the third derivative of d**6/70 - d**5/140 - d**4/14 + d**3/14 + 7*d**2. Suppose k(g) = 0. Calculate g.
-1, 1/4, 1
Factor 60*m**2 - 1 + 0*m - 2*m + 4 - 61*m**2.
-(m - 1)*(m + 3)
Let m = -10/13 + 96/91. Factor 6/7*n**2 + m*n + 0.
2*n*(3*n + 1)/7
Let s be ((-4)/(-8))/1 + 4/(-16). Factor -1/4 + 1/4*z**2 + s*z - 1/4*z**3.
-(z - 1)**2*(z + 1)/4
Let j(w) = -3*w**2 - 3*w + 4. Let u(i) = -4*i**2 - 4*i + 5. Let a(n) = -3*j(n) + 2*u(n). Factor a(x).
(x - 1)*(x + 2)
Let w(s) be the first derivative of -s**4/7 + 10*s**3/21 - 4*s**2/7 + 2*s/7 - 4. Solve w(p) = 0 for p.
1/2, 1
Let c = 291 - 6110/21. Let w(z) be the third derivative of 0*z - 4/21*z**3 + c*z**4 + 0 - 1/210*z**5 + z**2. Factor w(r).
-2*(r - 2)**2/7
Suppose v + 6 = -0. Let y(j) = j + 6. Let m be y(v). Factor -2/7 + m*u + 2/7*u**2.
2*(u - 1)*(u + 1)/7
Let m be (-284)/(-52) + 6 + -11. Factor -2/13*d**4 + m*d**2 + 4/13*d + 0 + 0*d**3.
-2*d*(d - 2)*(d + 1)**2/13
Factor -1/3 - 1/3*g**2 + 2/3*g**4 - g**3 + g.
(g - 1)**2*(g + 1)*(2*g - 1)/3
Let n(r) = r**2 + 2*r + 2. Let q be n(-2). Factor 8*u**3 + 4*u + 11*u + 1 + 1 + 18*u**q - 3*u.
2*(u + 1)**2*(4*u + 1)
Let a(b) be the second derivative of 0*b**3 + 0 - 6*b**2 - 3/20*b**5 + 3/4*b**4 + 2*b. Factor a(t).
-3*(t - 2)**2*(t + 1)
Let v(j) = -j + 3 - 5 + 4 - 4. Let i be v(-5). Suppose 2*m + m**5 + 4*m**2 - 4*m**4 - i*m**5 + 0*m**5 = 0. Calculate m.
-1, 0, 1
Let w(f) be the second derivative of -f**6/2 - f**5 - 5*f**4/12 + 15*f. Suppose w(m) = 0. Calculate m.
-1, -1/3, 0
Let s be 180/(-40)*2*(-4)/30. Determine x so that s*x - 1/5 + 8/5*x**3 - 12/5*x**2 = 0.
1/2
Let v(u) = -4*u**4 - 4*u**3 + 4*u**2 + 9*u. Let z(w) = -14*w + 3*w**4 + 3*w**4 - 27*w**2 + 21*w**2 + 6*w**3. Let j(b) = -8*v(b) - 5*z(b). Factor j(d).
2*d*(d - 1)*(d + 1)**2
Let a(s) = -13*s**5 + 8*s**4 + 8*s**3 - 16*s**2 - 4*s - 1. Let k(h) = -3*h**5 + 2*h**4 + 2*h**3 - 4*h**2 - h. Let l(o) = 2*a(o) - 9*k(o). Factor l(b).
(b - 2)*(b - 1)**2*(b + 1)**2
Suppose 0 = -4*t + 2*o - 8, 0 = 4*t - 0*t + 5*o - 20. Factor t - 4/5*d + 2/5*d**2.
2*d*(d - 2)/5
Let y(d) = -10*d**2 + 12*d + 14 + 0*d**2 + 0*d - d**3. Let f be y(-11). Let 1/3*k**5 - 1/3 - k - 2/3*k**2 + 2/3*k**f + k**4 = 0. What is k?
-1, 1
Suppose -4*g - 2*x - 50 = 0, 0 = -3*g - 0*x - 3*x -