, 1/3, 2
Let u be 0/(7 - 5 - 4). Factor 3/4*o**5 + u*o + 0*o**2 + 1/2*o**3 + 0 - 5/4*o**4.
o**3*(o - 1)*(3*o - 2)/4
Let x(t) be the second derivative of 2*t**7/21 - 8*t**6/15 + t**5/5 + 10*t**4/3 - 8*t**3/3 - 16*t**2 + 6*t. Solve x(s) = 0 for s.
-1, 2
Suppose -2*z + 0 - 13 = -5*i, -3*i = -5*z - 4. Let c(n) be the third derivative of 0*n**i + 1/36*n**4 - n**2 + 1/90*n**5 + 0 + 0*n. What is u in c(u) = 0?
-1, 0
Let 9/4*l - 3/4*l**2 + 0 = 0. Calculate l.
0, 3
Let s = 8 + -5. Factor -5*h**3 - 15*h**2 - 4*h - 2*h + 0*h - 4*h**s.
-3*h*(h + 1)*(3*h + 2)
Let k = -144 - -146. Let m(t) be the first derivative of 1/5*t**5 + 0*t**2 + 0*t**4 + 0*t + k - 1/3*t**3. Suppose m(d) = 0. Calculate d.
-1, 0, 1
Let h(x) be the first derivative of -4/21*x**3 - 1/7*x**2 - 2 - x - 1/105*x**6 - 1/7*x**4 - 2/35*x**5. Let n(s) be the first derivative of h(s). Factor n(z).
-2*(z + 1)**4/7
Let p = 40 + -40. Factor 3/4*k**4 + 1/4*k**3 - 3/4*k**2 - 1/2*k + 1/4*k**5 + p.
k*(k - 1)*(k + 1)**2*(k + 2)/4
Let b(l) be the third derivative of -l**8/1512 - l**7/945 + l**6/180 + l**5/270 - l**4/54 + 13*l**2. Solve b(i) = 0.
-2, -1, 0, 1
Let h = 45/169 + 13633/845. Let j = h - 16. Find p such that 0*p**2 - j*p**4 + 0 + 0*p + 2/5*p**3 = 0.
0, 1
Suppose 3*r + 7 = -2*m, 5*r + 7*m = 2*m - 20. Let w = 5 - r. Suppose 18*b - 22*b - w + 0 - b**2 = 0. What is b?
-2
Suppose -4*m - 21 + 1 = 0. Let n(y) = -y**2 - 7*y - 6. Let g be n(m). Factor -3*q**5 + 4*q**5 + 2*q**4 - 3*q**g.
q**4*(q - 1)
Suppose 5*r = 19 + 6. Let v be ((-4)/r)/(2/(-5)). Factor -2*w**4 + w**v + 0*w**2 - 2 + 3*w**2.
-2*(w - 1)**2*(w + 1)**2
Let r(m) = -7*m**2 + 11*m - 5. Let l(s) = -s**2 + s - 1. Let x(h) = 5*l(h) - r(h). Factor x(q).
2*q*(q - 3)
Let r(m) be the first derivative of 2/45*m**5 + 0*m**2 + 0*m**4 - 2/27*m**3 + 0*m + 1. Determine w so that r(w) = 0.
-1, 0, 1
Suppose 2*f + f - d = 41, -5*f = -5*d - 65. Let q = f + -8. Factor 3*i**4 - 5*i**2 - 4*i**4 + q*i**2.
-i**2*(i - 1)*(i + 1)
Let a(p) = 0*p + 0*p**3 + 3 + p + 5*p**2 - 3*p**4 - p**3. Let y(v) = 4*v**4 + v**3 - 7*v**2 - v - 4. Let h(l) = 7*a(l) + 5*y(l). Factor h(g).
-(g - 1)*(g + 1)**3
Let -6/17*k + 2/17 + 4/17*k**2 = 0. Calculate k.
1/2, 1
Let y(w) be the third derivative of -w**5/45 + 11*w**4/24 - 4*w**3/9 - 12*w**2. Factor y(k).
-(k - 8)*(4*k - 1)/3
Solve 0 + 8/5*n**4 + 0*n - 6/5*n**3 - 2/5*n**2 = 0.
-1/4, 0, 1
Let k(t) be the second derivative of 3*t**7/14 - 29*t**6/30 + 33*t**5/20 - 5*t**4/4 + t**3/3 + 14*t + 1. Find m, given that k(m) = 0.
0, 2/9, 1
Let y(g) be the first derivative of -g**6/180 - g**5/40 - g**4/24 + g**3/3 + 4. Let j(k) be the third derivative of y(k). Find s such that j(s) = 0.
-1, -1/2
Let b(g) be the first derivative of 2*g**6/3 + 12*g**5/5 + g**4 - 4*g**3 - 4*g**2 + 14. Find u, given that b(u) = 0.
-2, -1, 0, 1
Let n(m) be the third derivative of m**8/840 + 2*m**7/525 - m**6/150 - 2*m**5/75 + m**4/60 + 2*m**3/15 + 3*m**2. Find d, given that n(d) = 0.
-2, -1, 1
Let j(v) be the third derivative of v**7/630 + v**6/120 - v**4/18 + 18*v**2. Factor j(p).
p*(p - 1)*(p + 2)**2/3
Let i(z) be the second derivative of z**8/3360 - z**7/3780 - z**6/360 + z**5/180 - z**4/4 - 2*z. Let d(j) be the third derivative of i(j). Factor d(w).
2*(w - 1)*(w + 1)*(3*w - 1)/3
Let d be 2*8 - (-9)/(-3). Let f = d - 4. Factor f*z + 2 - 6 - 2 + 15*z**2.
3*(z + 1)*(5*z - 2)
Let a(u) be the third derivative of 1/3*u**4 + 0*u + 2/15*u**5 + 0 + 2*u**2 + 0*u**3 + 1/60*u**6. Determine k, given that a(k) = 0.
-2, 0
Let d(l) be the third derivative of l**6/40 - l**4/8 - l**2. Factor d(b).
3*b*(b - 1)*(b + 1)
Let y(o) = 2 - 6*o + o - o**2 + 4. Let a be y(-6). Factor 8/9*f - 2/3*f**3 - 2/9*f**4 + 0*f**2 + a.
-2*f*(f - 1)*(f + 2)**2/9
Let o(n) be the first derivative of n**4/15 - n**3/3 + 2*n**2/5 + 2*n - 5. Let x(t) be the first derivative of o(t). Factor x(f).
2*(f - 2)*(2*f - 1)/5
Suppose -7 = 5*m + 53. Let z be m/8*(-4)/3. Factor -2/5*h**z + 0 + 2/5*h.
-2*h*(h - 1)/5
Let y(v) = -5*v**2 + v - 3. Let g be ((-4)/8)/((-2)/12). Let f(z) = 4*z**2 + 2. Let j(i) = g*f(i) + 2*y(i). Factor j(p).
2*p*(p + 1)
Let l(w) = 10*w + 72. Let y be l(-7). Factor 0 - 1/6*b + 1/2*b**3 + 0*b**y - 1/3*b**4.
-b*(b - 1)**2*(2*b + 1)/6
Factor -1/3*v**3 + 1/3*v - 1/3 + 1/3*v**2.
-(v - 1)**2*(v + 1)/3
Let i(l) = -2*l**2 - l + 1. Let c be 2/(-4)*(-12 - -2). Let b(r) = 4*r**2 + r - 3. Let k(s) = c*i(s) + 3*b(s). Factor k(f).
2*(f - 2)*(f + 1)
Let k be 10/(-6)*(676/(-65) - -10). Let -16/3*l**2 + 4/3 - 10/3*l**3 - k*l = 0. Calculate l.
-1, 2/5
Suppose 0 = -2*y + 4*y - 10. Let b = -3 + y. Factor d**2 - 3*d**b + 0 + 4*d - 2.
-2*(d - 1)**2
Let d(f) = -f**3 - f**2 + f + 1. Let n(l) = -9*l**3 - 3*l**2 + 18*l + 12. Let b(a) = -12*d(a) + n(a). Solve b(y) = 0.
-2, -1, 0
Let x(d) be the first derivative of d**4/16 + d**3/12 - d**2/8 - d/4 + 9. Solve x(p) = 0 for p.
-1, 1
Suppose p + 1 = -0*p. Let r = 3 + p. Factor t**r + 2*t - 1 - 5*t**2 + 3*t**2.
-(t - 1)**2
Let x(o) be the third derivative of -3*o**7/140 - o**6/20 + o**5/60 + o**4/12 - o**3/12 - 7*o**2. Factor x(d).
-(d + 1)**2*(3*d - 1)**2/2
Let t(l) = l**4 - l**3 + l**2 + 3*l - 2. Suppose -10 = 2*f + 2. Let y(c) = 8*c**4 - 8*c**3 + 9*c**2 + 25*c - 17. Let d(i) = f*y(i) + 51*t(i). Factor d(n).
3*n*(n - 1)**2*(n + 1)
Suppose 4*n + 6*n - 20 = 0. Solve 0*m + 1/4*m**n + 0 = 0.
0
Let q be 3/2 - (-4)/8. Factor -7*t**2 + 5*t**q + 8 + 0*t**2.
-2*(t - 2)*(t + 2)
Let y(d) = 97 - 97 - 6*d**2 - 12*d. Let x(h) = 9*h**2 + 18*h. Let u(m) = -5*x(m) - 8*y(m). Factor u(i).
3*i*(i + 2)
Let u = -16 - -16. Factor 1/3*y**4 - 1/3*y + 1/3*y**3 + u - 1/3*y**2.
y*(y - 1)*(y + 1)**2/3
Let r(h) = -h**3 - 7*h**2 + 8*h + 5. Let z be r(-8). Factor -1/3*i**z + 0 + 0*i - 1/3*i**2 - i**3 - i**4.
-i**2*(i + 1)**3/3
Let j(t) = t**3 + t**2 - t - 1. Let s(w) = -3*w**4 + 2*w**3 + 4*w**2 - 4*w - 4. Let a(d) = 4*j(d) - s(d). Factor a(q).
q**3*(3*q + 2)
Suppose -3*l - 3 = -4*l. Suppose -10 = l*c - 8*c. Solve -d**4 + 2*d**4 - 10*d**3 + 4 - 6*d**2 + 24*d**c - 14*d + d**4 = 0.
1, 2
Let k = 7 - 2. Let g(l) be the third derivative of 0*l - 1/21*l**4 + 11/210*l**k - 3/245*l**7 - 2*l**2 + 0 - 4/21*l**3 + 1/70*l**6. Factor g(r).
-2*(r - 1)**2*(3*r + 2)**2/7
Let j = 149 + -147. Let k(b) be the third derivative of 0*b**3 - 1/300*b**5 + 1/300*b**6 - 4*b**j + 0*b**4 - 1/1050*b**7 + 0*b + 0. Find l, given that k(l) = 0.
0, 1
Let y(q) be the first derivative of -2/21*q**3 - 7 + 0*q**2 + 0*q - 1/14*q**4. Determine f so that y(f) = 0.
-1, 0
Let f(d) be the second derivative of -d**5/4 + d**4/4 + 2*d**3/3 + 2*d**2 - d. Let a(g) = -g**3 + g**2 + g + 1. Let l(x) = -4*a(x) + f(x). Factor l(c).
-c**2*(c + 1)
Let d(k) = k**3 + 5*k**2 - 6*k + 3. Let y be d(-6). Factor 3 - 5*g**4 - 36*g**2 + 2*g**4 + 20*g**y - 11 + 28*g - g**4.
-4*(g - 2)*(g - 1)**3
Let s(r) be the second derivative of r**6/30 - 3*r**5/5 + 9*r**4/2 - 18*r**3 + 5*r**2 + 10*r. Let c(x) be the first derivative of s(x). Factor c(g).
4*(g - 3)**3
Let h be (-7)/14*32/(-1). Let r be (2 + (-36)/h)/(-1). Factor 1/2*i**2 - r*i**5 - 3/4*i**4 - 1/2*i**3 + 3/4*i + 1/4.
-(i - 1)*(i + 1)**4/4
Let k = -106 - -108. Factor 0 + 0*r - 14/5*r**3 - 4/5*r**k.
-2*r**2*(7*r + 2)/5
Let a(c) be the third derivative of c**5/12 + 3*c**4/8 - c**3/3 + 9*c**2. Factor a(h).
(h + 2)*(5*h - 1)
Let h(j) be the third derivative of j**6/24 + j**5/6 + 5*j**4/24 - 12*j**2. Determine i, given that h(i) = 0.
-1, 0
Let w(a) be the second derivative of 5*a**7/21 + a**6/5 - 7*a**5/10 - a**4/2 + 2*a**3/3 + 12*a. What is f in w(f) = 0?
-1, 0, 2/5, 1
Suppose -1/6 - 1/6*n**2 + 1/3*n = 0. Calculate n.
1
Let j(r) be the second derivative of r**6/55 + 23*r**5/110 + 20*r**4/33 - 16*r**3/33 + 10*r. Factor j(f).
2*f*(f + 4)**2*(3*f - 1)/11
Suppose 4*k = -k + 5. Suppose -x + 5 = k. Factor -2*d**x + 3*d**4 - 3*d**2 + 0*d + 2*d.
d*(d - 1)**2*(d + 2)
Let c(w) be the second derivative of -w**5/10 + 3*w**4/2 - 9*w**3 + 27*w**2 - 8*w. Determine d so that c(d) = 0.
3
Let d(y) = y + 1. Let v be d(5). Let x be ((-5)/(15/v))/(-6). Factor 0*n + 0*n**2 - 1/3*n**3 - x*n**4 + 0 + 2/3*n**5.
n**3*(n - 1)*(2*n + 1)/3
Suppose 7*w = 2*w + 20. Suppose w*a = -a. Solve a*s**3 + 0*s**2 + 2/7*s**5 + 0 + 0*s**4 + 0*s = 0.
0
Let q(t) be the third derivative of 0 + 0*t**7 + 0*t + 0*t**3 + 0*t**5 - 3*t**2 + 1/150*t**6 - 1/840*t**8 - 1/60*