i(h). Factor g(a).
2*(a - 1)*(a + 3)
Let m be (1/2 - 2/(-4))*2. Let a(d) be the first derivative of -2/21*d**3 + 2 + 4/7*d + 1/7*d**m. Factor a(q).
-2*(q - 2)*(q + 1)/7
Let a(o) be the second derivative of o**6/150 + 3*o**5/100 + o**4/30 - 9*o. Suppose a(t) = 0. Calculate t.
-2, -1, 0
Suppose 4*t - 5*g + 24 = 0, 2*g = 4*t + 3*g. Let k be ((-4)/84)/(t/6). Determine c, given that 0 + 0*c + 0*c**2 + 10/7*c**4 - 8/7*c**5 - k*c**3 = 0.
0, 1/4, 1
Let x be 10/45 + 97/9. Let v = x - 7. Factor -3*r - 5*r + 6*r**4 - 5*r**3 + 38*r**2 - 14*r + v - 21*r**3.
2*(r - 2)*(r - 1)**2*(3*r - 1)
Let f(c) be the second derivative of -1/6*c**3 + 0 + 4*c - 1/2*c**2. Let l(q) = 3*q**2 - 9*q. Let d(u) = -3*f(u) + l(u). Determine w, given that d(w) = 0.
1
Let o(s) = -2*s + 5. Let a be o(4). Let w be -1 - (-2 + 4) - a. Suppose -1/4*h**2 + w + 0*h - 1/4*h**3 = 0. Calculate h.
-1, 0
Let u(k) = k + 6. Let g be u(-6). Suppose -5*i - 3*s = 7, -2*s + 1 = 4*i + 5. What is o in 0*o + o**2 + g*o + i + 2*o = 0?
-1
Let z = 8 - 5. Factor -4 + 2*k**3 + 13*k + 5*k**2 - k**3 + 2*k**z - 17*k.
(k - 1)*(k + 2)*(3*k + 2)
Suppose 3*a + a = 0. Suppose -13 = -5*g - m - a, -3*m - 1 = -5*g. Factor 5/3*s - 2/3 - s**g.
-(s - 1)*(3*s - 2)/3
Suppose 7*j + 12 = 3*j, -4*j = 5*q - 13. Suppose q*k**2 + 0*k**2 - 3*k**2 - k**2 = 0. What is k?
0
Let p = 81 - 79. Find q such that 1/2*q**3 + 0 + 0*q + 0*q**p - 1/2*q**5 + 0*q**4 = 0.
-1, 0, 1
Let v(j) be the first derivative of 6*j**5/55 - 2*j**4/11 - 10*j**3/33 + 2*j**2/11 - 5. Let v(y) = 0. Calculate y.
-1, 0, 1/3, 2
Suppose -4*v + 2*z - 52 = -50, v - 2*z = -8. Factor 4/5 + 126/5*t**v + 38/5*t + 162/5*t**3 + 54/5*t**4.
2*(t + 2)*(3*t + 1)**3/5
Let y(g) be the second derivative of g**5/160 + g**4/96 - g**3/48 - g**2/16 - 11*g. Factor y(k).
(k - 1)*(k + 1)**2/8
Let m be (-5 - -2)/3 - -4. Solve -36*f - 10*f**m - 39*f**2 - 16*f**3 - 12 + 8*f**3 - 3*f**4 = 0.
-2, -1
Let u = -206 + 206. Let -1/3 + 1/3*v**2 + u*v = 0. Calculate v.
-1, 1
Suppose 0 = -4*c - 7*c + 3*c. Find l such that 4/7*l**3 + 0 + 2/7*l**4 + 0*l + c*l**2 = 0.
-2, 0
Let c = 25 - 13. Let p be 9/c - (-14)/8. Let -1/2*b**3 - 2 - 4*b - p*b**2 = 0. Calculate b.
-2, -1
Suppose 2*l = -4*k + l, 2*k + 3*l = 0. Let j(c) be the third derivative of 1/24*c**4 - 2*c**2 - 1/60*c**5 + 0*c + 1/3*c**3 + k. Factor j(a).
-(a - 2)*(a + 1)
Suppose -115*k = -102*k. Factor -3/7*c**3 + k*c + 3/7*c**2 + 0.
-3*c**2*(c - 1)/7
Factor 1/2*c**3 + 3/2*c - 1/2 - 3/2*c**2.
(c - 1)**3/2
Let a(k) be the third derivative of k**6/120 - k**5/30 + k**4/24 - 9*k**2. Determine o, given that a(o) = 0.
0, 1
Let q(c) = -2*c**2 + c + 1. Let b be q(-1). Let k(z) = -4*z - 4. Let t be k(b). Let 0*u**2 - 4/3*u**3 + 4/3*u + 2/3*u**t - 2/3 = 0. What is u?
-1, 1
Suppose 15 = 2*j - 9. Find l such that 19*l**4 - 5*l**4 - j*l**5 - 2*l**2 + 0*l**2 = 0.
-1/3, 0, 1/2, 1
Let h(p) = p**2 + 20*p + 38. Let t be h(-18). Suppose 14/5*d**4 + 0*d**t + 4/5*d**3 + 2*d**5 + 0*d + 0 = 0. What is d?
-1, -2/5, 0
Let d(f) be the third derivative of -7*f**2 - 1/12*f**3 - 1/32*f**4 - 1/240*f**5 + 0*f + 0. Let d(b) = 0. What is b?
-2, -1
Suppose 0 = 4*l - 8 - 4. Determine g so that 3*g**2 - g**4 - 4*g**2 + 2*g**3 - 2*g**4 - g**5 - 5*g**l = 0.
-1, 0
Let m(f) = -62*f**3 + 72*f**2 - 32*f - 8. Let a(d) = 21*d**3 - 24*d**2 + 11*d + 3. Let l(s) = 8*a(s) + 3*m(s). Find y, given that l(y) = 0.
0, 2/3
Let r = 1 + -5/3. Let i = r + 1. Factor -1/2*j + 1/6*j**2 + i.
(j - 2)*(j - 1)/6
Let f be 13/13*(0 - -2). Suppose f*k - 3*p - 7 = -1, -k - 5*p - 10 = 0. Determine y so that 0*y + k + 0*y**3 - 1/5*y**2 + 1/5*y**4 = 0.
-1, 0, 1
Let b(o) be the third derivative of o**5/15 - 2*o**4/3 + 2*o**3 + 3*o**2. Let b(k) = 0. What is k?
1, 3
Let r be 6/((-1)/(4/(-6))). Let z(i) be the first derivative of -3/8*i**r - 2 - 5/4*i**2 - 7/6*i**3 - 1/2*i. Solve z(x) = 0.
-1, -1/3
Let t(u) be the third derivative of 0*u**3 + 1/140*u**5 + 0*u**4 - 6*u**2 + 0*u + 1/280*u**6 + 0. Let t(r) = 0. What is r?
-1, 0
Let p = 2/373 + 3347/1865. Solve -p*t**2 + 2/5 - 7/5*t = 0 for t.
-1, 2/9
Let b(t) be the first derivative of -t**3/7 + 3*t**2/7 + 24*t/7 + 3. Suppose b(k) = 0. What is k?
-2, 4
Determine m, given that -4/7*m**2 - 2/7*m - 2/7*m**3 + 0 = 0.
-1, 0
Let y(p) = p**3 + 8*p**2 - p - 8. Let n be y(-8). Suppose n*m - 4*m = -8. Factor -z**m + 2*z**2 + z**2.
2*z**2
Let k(g) be the first derivative of -5*g**4/4 + 15*g**2/2 + 10*g + 22. Solve k(i) = 0 for i.
-1, 2
Let o(d) be the second derivative of 0*d**2 - 1/60*d**5 + 1/180*d**6 + 0 + 2*d + 0*d**4 - 1/6*d**3. Let g(b) be the second derivative of o(b). Factor g(l).
2*l*(l - 1)
Suppose -n + 112 = -5*h, -4*n - n + 3*h = -494. Factor n*d**3 + 76/5*d - 8/5 + 25*d**5 - 80*d**4 - 278/5*d**2.
(d - 1)**2*(5*d - 2)**3/5
Let k(v) = 4*v**3 - 4*v**2 + 2*v - 2. Let q = -2 - -1. Let x be (-2)/3*(2 - q). Let m(u) = 5*u**3 - 5*u**2 + 3*u - 3. Let h(i) = x*m(i) + 3*k(i). Factor h(y).
2*y**2*(y - 1)
Let u(a) = 5*a**5 - 6*a**4 + 5*a**3 + 9*a**2 - 4*a + 3. Let x(f) = 6*f**5 - 6*f**4 + 6*f**3 + 10*f**2 - 4*f + 4. Let v(r) = 4*u(r) - 3*x(r). Factor v(w).
2*w*(w - 2)*(w - 1)**2*(w + 1)
Suppose -4 = -f - f. Factor 4 - 4 + q**2 - f - q.
(q - 2)*(q + 1)
Let b(u) be the third derivative of 1/24*u**4 - 1/30*u**5 + 1/2*u**3 + 2*u**2 + 0 + 0*u. What is g in b(g) = 0?
-1, 3/2
Let d be (-2)/(-4)*(-1 - (-9 + 7)). Let 7*v**3 - d + 3*v**2 + 11/2*v**4 - 1/2*v + 3/2*v**5 = 0. Calculate v.
-1, 1/3
Let f = 3 + -1. Suppose -f*d = -5*i + 1, -4*i = d - 2 - 4. Find k, given that k**5 - k**4 - 2 - k**4 + k**3 + d = 0.
0, 1
Suppose -10/13*m**4 + 16/13*m - 36/13*m**2 + 32/13*m**3 - 2/13 = 0. What is m?
1/5, 1
Let u be ((-16)/(-2) - 4) + -2. Find q, given that 5*q**2 + 3 - 9*q**u + q**2 = 0.
-1, 1
Let a(b) be the third derivative of b**5/30 + b**4/24 - b**3/6 + b**2. Let l be a(1). Factor -4*p**2 + 6 - 5*p - 7*p + 2*p**l - 24.
-2*(p + 3)**2
Factor -3/2*h**3 + 0*h**2 + 0 + 3/4*h + 3/4*h**5 + 0*h**4.
3*h*(h - 1)**2*(h + 1)**2/4
Suppose 5*a - 5 = 2*p + 9, -a - p = -7. Factor -6/7*q + 3/7 + 0*q**2 + 6/7*q**3 - 3/7*q**a.
-3*(q - 1)**3*(q + 1)/7
Let a be ((-6)/10)/(1/(-15)). Let q = a + -6. Factor -3*x**2 - 1 - 6 - 6*x + 1 + q.
-3*(x + 1)**2
Let f(t) be the third derivative of 5*t**2 + 2/21*t**3 + 0*t - 1/140*t**6 + 1/28*t**4 - 1/30*t**5 + 0 + 1/147*t**7. Let f(m) = 0. What is m?
-1, -2/5, 1
Let r(x) = -x**2 - x + 12. Let o be r(-4). Let m(f) be the third derivative of 1/210*f**5 - 3*f**2 - 1/21*f**3 + 0*f**4 + 0*f + o. Let m(g) = 0. Calculate g.
-1, 1
Suppose -2*n - 4*b + 10 = 0, -5*b = -3*b. Let k(d) be the third derivative of 0 + 0*d**3 + 0*d**4 - 1/60*d**n - d**2 + 0*d. Factor k(h).
-h**2
Let d be 1/(-6)*9/(-756). Let c(g) be the third derivative of 0*g**4 + 1/180*g**6 + 0*g**7 + 0*g**5 + 0*g**3 + 0 - d*g**8 + 3*g**2 + 0*g. Factor c(m).
-2*m**3*(m - 1)*(m + 1)/3
Let z(n) be the third derivative of -15*n**8/28 - n**7/42 + 55*n**6/12 + 25*n**5/4 - 5*n**4/6 - 10*n**3/3 - n**2. Solve z(v) = 0.
-1, -1/4, 2/9, 2
Let d(y) be the first derivative of 4 + 0*y**2 + 1/14*y**4 + 2/21*y**3 + 0*y. Factor d(b).
2*b**2*(b + 1)/7
Let x(a) = 4*a - 5. Let i be x(10). Factor i*d**2 + 1 + 18*d**2 - 17*d**2 - 12*d.
(6*d - 1)**2
Let f(d) be the second derivative of -d**7/84 - d**6/20 - 3*d**5/40 - d**4/24 - 2*d. Solve f(b) = 0.
-1, 0
What is m in 18/5 + 6/5*m**3 - 3*m**2 - 3/5*m = 0?
-1, 3/2, 2
Let u(y) be the second derivative of -y**5/4 - 5*y**4/12 - 25*y. Factor u(o).
-5*o**2*(o + 1)
Solve -31 - 5*s - 5*s**3 + 106 - 45 - 20*s**2 = 0 for s.
-3, -2, 1
Suppose 5*a + 31 = 3*u, -3*u - 8 + 29 = -3*a. Let p = u - -3. Determine n, given that 1 + 5*n**5 - 4*n**p + 5*n + 5*n**4 + 10*n**2 + 4*n**3 + 6*n**3 = 0.
-1
Let i(l) be the second derivative of -1/35*l**6 + 1/70*l**5 + 1/21*l**4 + 0 + 0*l**3 + 0*l**2 + 5*l. Let i(j) = 0. Calculate j.
-2/3, 0, 1
Suppose -n + 0 = -4. Factor 0 + 2*w**2 - 8*w + 2*w + n + 0*w**2.
2*(w - 2)*(w - 1)
Let a(h) be the first derivative of h**4/4 + 8*h**3/3 - h**2/2 - 5*h - 1. Let y be a(-8). Factor -2*m**2 + m + 2*m**4 - m**y + m**2 - m**4.
m*(m - 1)**2*(m + 1)
Let c(j) be the third derivative of -j**8/5880 - j**7/2940 + j**3/3 + 3*j**2. Let u(a) be the first derivative of c(a). Factor u(r).
-2*r**3*(r + 1)/7
Let q(w) be the second derivative of w**5/40 - w**4/6 + w**3/4 - 8*w. Find y such that q(y) = 0.
0, 1,