uch that h(m) = 0.
-1, -1/2, 0, 2/9
Let f = 18 - 15. Suppose 0 = f*k - 0*k. Suppose 8/3*g**4 + 8/3*g**2 - 2/3*g - 2/3*g**5 - 4*g**3 + k = 0. What is g?
0, 1
Let z = 147 - 138. Solve 0 + 0*m**2 - 9*m**4 - 4/3*m + z*m**3 = 0.
-1/3, 0, 2/3
Let b(l) be the first derivative of -l**8/336 + 2*l**7/105 - l**6/40 - l**5/15 + l**4/6 - l**2/2 + 3. Let w(r) be the second derivative of b(r). Factor w(u).
-u*(u - 2)**2*(u - 1)*(u + 1)
Let c(v) be the third derivative of 16*v**7/231 + 38*v**6/165 - 9*v**5/110 - 5*v**4/33 + 4*v**3/33 - 2*v**2. What is o in c(o) = 0?
-2, -2/5, 1/4
Let o(b) be the third derivative of 0*b + 0*b**3 + 1/56*b**8 + 0 - 1/120*b**6 + 1/210*b**7 + 0*b**4 - 2*b**2 + 0*b**5. Solve o(c) = 0 for c.
-1/2, 0, 1/3
Factor -z**2 + 2*z - 2 - 5*z + 0*z.
-(z + 1)*(z + 2)
Let k(v) be the first derivative of v**4/17 - 10*v**3/51 + v**2/17 + 4*v/17 + 20. Factor k(u).
2*(u - 2)*(u - 1)*(2*u + 1)/17
Let w be 1 - (-1 + (-16)/(-9)). Let y = 283/6 + -89/2. Suppose y*x + 8/9 + 4/3*x**3 + 26/9*x**2 + w*x**4 = 0. What is x?
-2, -1
Let p(l) be the third derivative of l**5/60 - l**4/4 - 7*l**3/6 + 2*l**2. Let r be p(7). Factor 1/2*b**2 + r*b - 1/2.
(b - 1)*(b + 1)/2
Factor 8/5*y + 3/5*y**3 + 4/5 - 11/5*y**2.
(y - 2)**2*(3*y + 1)/5
Let n be 54/(-45)*(-5)/2. Factor -2*p**n + 9/2*p - 3/2*p**2 - 1.
-(p - 1)*(p + 2)*(4*p - 1)/2
Let c be 6/(-15) - 17/(-5). Let i be ((-3)/(-4))/((-27)/(-6)). Find g such that -i*g**c - 1/6*g + 1/3*g**2 + 0 = 0.
0, 1
Let f = 444/5 + -88. Let b = 19/35 - 1/7. What is a in -2/5*a**2 + f*a - b = 0?
1
Let x(r) be the second derivative of -r**6/720 - r**5/40 - 3*r**4/16 + r**3/3 - 3*r. Let p(h) be the second derivative of x(h). Let p(t) = 0. Calculate t.
-3
Let m(b) be the second derivative of 0 - 1/4*b**3 - 1/4*b**2 + 1/6*b**4 - 4*b. Factor m(g).
(g - 1)*(4*g + 1)/2
Let l(w) be the first derivative of -20*w**3/3 - 95*w**2/2 + 25*w + 24. Find p such that l(p) = 0.
-5, 1/4
Factor -1/5*s**4 + 1/5*s**3 + 0 + 0*s + 2/5*s**2.
-s**2*(s - 2)*(s + 1)/5
Let h(w) = w**4. Let i be (-2)/5 + 9/(-15). Let a(q) = -4*q**4 + 51*q**3 - 119*q**2 + 93*q - 18. Let j(k) = i*a(k) + 3*h(k). Let j(d) = 0. Calculate d.
2/7, 1, 3
Let x(j) be the third derivative of -j**8/112 - 2*j**7/35 - 3*j**6/20 - j**5/5 - j**4/8 - 10*j**2. Solve x(u) = 0 for u.
-1, 0
Let g(o) = 5*o**2 - 1. Suppose b - 5 = -4. Let i be g(b). Factor 0 + 1/2*y**2 + 0*y - 1/2*y**5 + 1/2*y**3 - 1/2*y**i.
-y**2*(y - 1)*(y + 1)**2/2
Let w(i) be the second derivative of -i**7/49 - 2*i**6/35 - 3*i**5/70 + 18*i. Factor w(o).
-6*o**3*(o + 1)**2/7
Factor 0 + 2/5*w + 2*w**2.
2*w*(5*w + 1)/5
Let a(k) be the first derivative of k**8/1344 - k**7/420 + k**6/480 + 7*k**2/2 + 5. Let m(h) be the second derivative of a(h). Solve m(l) = 0.
0, 1
Let w(a) be the second derivative of a**5/110 + a**4/22 + a**3/11 + a**2/11 + 3*a. Factor w(m).
2*(m + 1)**3/11
Let n(b) = b**3 + 3*b**2 - 2*b - 5. Let h be n(-2). Let p(t) be the third derivative of 1/42*t**4 + 1/210*t**5 - 3*t**2 + 0 + 0*t + 1/21*t**h. Factor p(o).
2*(o + 1)**2/7
Let z(o) be the third derivative of 1/108*o**4 - 2*o**2 - 1/27*o**3 + 1/270*o**5 + 0 - 1/540*o**6 + 0*o. Find p, given that z(p) = 0.
-1, 1
Let y(p) be the third derivative of 1/525*p**7 + 0*p**3 + 0*p + 0*p**4 - 1/75*p**5 - 1/300*p**6 - 2*p**2 + 0. Factor y(o).
2*o**2*(o - 2)*(o + 1)/5
Solve -20*b - 8*b**5 - b**4 + 0*b**2 + 8 + 28*b**3 - 3*b**2 - b**2 - 3*b**4 = 0.
-2, -1, 1/2, 1
Factor -1 - 27*l - 4*l**2 + 11*l - 8*l - 35.
-4*(l + 3)**2
Suppose 4*d = 4*f - 20, f + d + 7 = -2*d. Let h = 2 - f. Factor 2/9*c**4 + h + 8/3*c**2 - 4/3*c**3 - 16/9*c.
2*c*(c - 2)**3/9
Let z(p) be the first derivative of 0*p + 2 + 2/5*p**2 - 2/25*p**5 - 2/3*p**3 + 2/5*p**4. Determine a, given that z(a) = 0.
0, 1, 2
Factor 1944 + 1296*n + 3/2*n**4 + 324*n**2 + 36*n**3.
3*(n + 6)**4/2
Factor -1/5*b**4 + 0*b**2 + 2/5*b**3 + 1/5 - 2/5*b.
-(b - 1)**3*(b + 1)/5
Suppose h + 3*h - 8 = 0. Let g be -1*(-3 + 2/h). Factor 56/3*u**g + 3*u**4 + 16/3 - 16*u - 32/3*u**3 - 1/3*u**5.
-(u - 2)**4*(u - 1)/3
Let 21*j - 4 + 8*j**2 - j - 6*j = 0. What is j?
-2, 1/4
Let c(t) = -t**3 + 7*t**2 - 3*t + 21. Let l be c(7). Find j such that -8/5*j**2 - 2*j**4 - 16/5*j**3 + 0*j + l - 2/5*j**5 = 0.
-2, -1, 0
Suppose 19*q = q + 54. Factor 0 + 2/5*z**q + 0*z**2 + 0*z + 2/5*z**4.
2*z**3*(z + 1)/5
Let j(p) be the first derivative of -p**6/15 + 3*p**5/25 + p**4/10 - p**3/5 - 12. Suppose j(x) = 0. What is x?
-1, 0, 1, 3/2
Let o = 131 + -1585/12. Let q = o + 7/4. What is y in q*y**2 + 0*y - 2/3 = 0?
-1, 1
Let y be 6 + -5 - (-8)/(-10). Let m be ((-6)/(-20))/3*2. Solve 1/5*g + m*g**2 - y*g**3 - 1/5 = 0 for g.
-1, 1
Let n be (-2948)/10 + (-6)/(-2). Let i = n + 293. Let 2/5 + 6/5*o**2 - i*o - 2/5*o**3 = 0. Calculate o.
1
Let p(s) be the third derivative of -s**5/60 + 3*s**4/8 - s**3 - s**2. Let a be p(8). Factor -4*c**2 + 4*c**a - 4*c + c + 3*c**2.
3*c*(c - 1)
Let y(h) = -h + 3. Let g be y(0). Let v(k) = 2*k**2 - 2. Let i(z) = -z**2 - z. Let s(t) = g*v(t) + 3*i(t). Determine r, given that s(r) = 0.
-1, 2
Factor -9/7*f + 3/7*f**3 - 6/7 + 0*f**2.
3*(f - 2)*(f + 1)**2/7
Factor 0 + 2/7*z**3 - 1/7*z - 1/7*z**2.
z*(z - 1)*(2*z + 1)/7
Let b(s) = 2*s**2 - s + 1. Let a be b(1). Solve 162*i**a - 32*i - 9*i + 8 - 31*i = 0.
2/9
Let y = 0 + 1. Let v(k) = 5 - y + k**2 - k - 5. Let b(z) = -5*z**2 + 6*z + 1. Let p(r) = -b(r) - 2*v(r). Factor p(c).
(c - 1)*(3*c - 1)
Suppose 0 = 4*l - 57 - 23. Suppose -3*m - g = -2*g + 5, 4*m - l = -4*g. Factor m*q + 0 - 2/5*q**2.
-2*q**2/5
Let b = 3 + 1. Factor 2*r**3 + 2*r**2 + 1 + r**5 - 3*r**b + r + 0*r - 4*r.
(r - 1)**4*(r + 1)
Suppose -4*h + 20 = -n, 0 = 5*n - 2*h - 2*h + 20. Suppose 0 = 5*m + 10, b + 6 = -n*m - 4*m. Solve 16/9 + 8/3*x + 2/9*x**3 + 4/3*x**b = 0 for x.
-2
Let z(g) = -g**3 + g**2 - g + 2. Let d(o) = 21*o**3 + 34*o**2 + 21*o - 22. Let s(m) = d(m) + 6*z(m). Factor s(y).
5*(y + 1)*(y + 2)*(3*y - 1)
Let f(g) = -2*g**2 - 22*g - 48. Let a be f(-8). Factor 2/7*w**5 + 0*w**2 + a + 0*w**4 - 4/7*w**3 + 2/7*w.
2*w*(w - 1)**2*(w + 1)**2/7
Suppose 0 = 19*i - 20*i. Let o be 4/(-14) + (-26)/(-42). Factor -1/3*c**4 - 2/3*c**3 + 0*c + i - o*c**2.
-c**2*(c + 1)**2/3
Let z(f) be the first derivative of -f**7/210 - f**6/90 + f**5/180 + f**4/36 + f**2/2 + 1. Let u(p) be the second derivative of z(p). Let u(t) = 0. Calculate t.
-1, 0, 2/3
Let r(a) be the first derivative of -a**6/3 + 2*a**5/5 + a**4/2 - 2*a**3/3 + 57. Solve r(g) = 0 for g.
-1, 0, 1
Let q(y) = 13*y**3 - 7*y**2 - 3*y. Let c(v) = -40*v**3 + 20*v**2 + 8*v. Let j(b) = -3*c(b) - 8*q(b). Factor j(k).
4*k**2*(4*k - 1)
Suppose -2*w + 3 = -3*w, -4*w = 5*u + 2. Let l(r) be the first derivative of 2/9*r - 1 + 0*r**3 - 1/3*r**u + 2/9*r**4. Let l(g) = 0. Calculate g.
-1, 1/2
Let y = 3/8 - 11/72. Let c be (-5*(-5)/25)/((-2)/(-8)). Suppose 2/9*b**c + 0 + 2/3*b**2 - y*b - 2/3*b**3 = 0. Calculate b.
0, 1
Let v(g) be the first derivative of -1/3*g**2 + 0*g**5 + 0*g**3 + 3 - 1/9*g**6 + 1/3*g**4 + 0*g. What is z in v(z) = 0?
-1, 0, 1
Let l(j) be the first derivative of -7*j**3/6 + 5*j**2/4 + j - 13. Factor l(o).
-(o - 1)*(7*o + 2)/2
Suppose -2*j - 1 = -7. Let r(v) = 6*v. Let s be r(j). Factor -s*b**4 - 40*b - 74*b**2 - 5 - 4 + 1 - 60*b**3.
-2*(b + 1)**2*(3*b + 2)**2
Let v(a) be the second derivative of 0*a**2 - 1/66*a**4 + 0 + 1/33*a**3 - 3*a. What is x in v(x) = 0?
0, 1
Let z(n) be the first derivative of n**5/5 - n**4/2 + n**3/3 + 5. Find c such that z(c) = 0.
0, 1
Suppose 2*k + 3*u - 7 = 0, -2*k + 4*u + 4 = 2*k. Suppose a + k*a = 12. Let a*n + 0*n**4 - n**2 - 3*n + n**4 - n**3 = 0. Calculate n.
-1, 0, 1
Factor 7/6*c - 3/2*c**2 - 1/6*c**4 - 1/3 + 5/6*c**3.
-(c - 2)*(c - 1)**3/6
Let y(w) = w**5 + 10*w**4 - 3*w**3 - 4*w. Let t(u) = 9*u**4 - 3*u**3 - 3*u. Let q(x) = -4*t(x) + 3*y(x). Factor q(a).
3*a**3*(a - 1)**2
Suppose -8 = -4*y + 2*z, -z + 8 - 15 = -3*y. Factor -2*x - 1/3*x**2 - y.
-(x + 3)**2/3
Factor -11*q**2 + 6*q**2 + q**2 - 20*q.
-4*q*(q + 5)
Let w(p) be the second derivative of -1/8*p**3 - 1/8*p**2 + 0 - 2*p - 1/80*p**5 - 1/16*p**4. Factor w(m).
-(m + 1)**3/4
Let d(y) be the third derivative of y**8/336 + y**7/105 + y**6/120 - 7*y**2. Factor d(o).
o**3*(o + 1)**2
Let m(z) = -5*z**2 + 1 + 4*z**2 + z + 0*z**3 - z**3. Let h(j) = 16*j**3 + 36*j**2 - 72*j + 36. Let n(v) = 2*h(v) + 36*m(v). Determ