d + 1)**2/4
Let u(i) be the first derivative of -2*i**5/5 + 5*i**4/2 - 16*i**3/3 + 4*i**2 - 68. Solve u(a) = 0 for a.
0, 1, 2
Let h = 10 + -9. Let a be -1 - 1/h*-3. Solve 2/3*y**a + 0*y + 2/3*y**4 - 4/3*y**3 + 0 = 0 for y.
0, 1
Suppose -v**4 + v**2 - 2*v**4 - 7*v**3 - 5*v**2 + 2*v**2 = 0. What is v?
-2, -1/3, 0
Suppose -2*t + 5*g + 1 = 0, -t - 2*g - 7 = 3*g. Let s be 1 + t + -12 + 16. What is i in 1/5*i - i**2 + 2/5 + 3/5*i**4 - 1/5*i**s = 0?
-1, -2/3, 1
Suppose -6/7*o**2 - 6 + 48/7*o = 0. What is o?
1, 7
Solve -3*b**3 + 4*b**2 + 6*b - 5*b**3 - 4*b**4 + 0*b**3 + 2*b = 0 for b.
-2, -1, 0, 1
Factor -98/15*k**4 + 0*k - 56/15*k**3 + 0 - 8/15*k**2.
-2*k**2*(7*k + 2)**2/15
Let r(y) be the third derivative of -1/9*y**3 + 0 + 1/72*y**4 + 1/180*y**5 + 0*y - y**2. Factor r(x).
(x - 1)*(x + 2)/3
Let j(c) be the first derivative of -3*c**4/10 - 4*c**3/15 + 3*c**2/5 + 4*c/5 - 13. Suppose j(q) = 0. Calculate q.
-1, -2/3, 1
Factor 4/5*b**3 + 0*b + 0*b**2 + 0 + 4/5*b**5 + 8/5*b**4.
4*b**3*(b + 1)**2/5
Let a be (0 + 1)*4/672. Let m(h) be the third derivative of 1/60*h**6 + h**2 - a*h**8 + 0*h**4 + 1/70*h**7 - 1/15*h**5 + 0*h + 1/6*h**3 + 0. Factor m(u).
-(u - 1)**3*(u + 1)*(2*u + 1)
Let v(w) be the first derivative of -w**5/240 - w**4/48 - w**3/24 + 7*w**2/2 - 2. Let d(i) be the second derivative of v(i). Factor d(a).
-(a + 1)**2/4
Let l(h) = -h**3 + h**2 + 1. Let i(b) = 3*b**4 - 9*b**3 + 6. Let a(x) = i(x) - 6*l(x). Find k such that a(k) = 0.
-1, 0, 2
Let w(j) be the first derivative of -2*j - 2/3*j**3 + 3 - 2*j**2. Find n, given that w(n) = 0.
-1
Suppose 3*p = 3*q + 12, 3*q + 14 = -3*p + 2. Let k(v) be the first derivative of p*v + 1/2*v**3 + 4 + 0*v**2. Factor k(r).
3*r**2/2
Let i(l) = -2*l - 1. Let c be i(-2). Determine m, given that -m**4 - c*m**5 - 2*m + 6*m**2 - 4 - m + 6*m**3 - 2*m**4 + 1 = 0.
-1, 1
Let v(d) be the first derivative of 2*d**6/3 + 8*d**5/5 - 4*d**4 - 8*d**3/3 + 6*d**2 + 18. Solve v(z) = 0.
-3, -1, 0, 1
Let k be (1/(-3))/((-7)/42). Suppose -n + 2*n - k = 0. Factor -1/3 + 1/3*o + 2/3*o**n.
(o + 1)*(2*o - 1)/3
Let v(t) be the second derivative of 2*t**6/15 + t**5/5 - t**4/3 - 2*t**3/3 - 11*t. Factor v(h).
4*h*(h - 1)*(h + 1)**2
Suppose 8 = m + 4. Factor 3*i**4 - 2*i + 6*i**2 - 7*i**m + 2*i**3 - 2*i**4.
-2*i*(i - 1)*(i + 1)*(3*i - 1)
Let t(q) be the third derivative of -q**6/80 + q**5/120 + q**4/16 - q**3/12 - 6*q**2. Let t(v) = 0. Calculate v.
-1, 1/3, 1
What is q in 11*q**4 - 11*q**3 - 6*q**5 - 8*q**4 + 14*q**3 = 0?
-1/2, 0, 1
Let o = 140 - 1258/9. Solve 0 - o*q**2 - 4/9*q = 0 for q.
-2, 0
Let p be 2*(2/24)/(4/12). Let -2*o - 2*o**5 - p + o**2 - 1/2*o**4 + 4*o**3 = 0. What is o?
-1, -1/4, 1
Let d(f) = f + f + 2 - 3*f. Let o be d(0). Factor -2*h - 2*h**3 + 2*h**2 + o*h.
-2*h**2*(h - 1)
Suppose c - 2*h - 7 = 0, 2*h - 5*h = 0. Let r = c - 2. Let -4*w**r + 4*w**5 + 2*w**5 - 4*w**5 = 0. Calculate w.
0
Let m = -2/137 - -554/411. Let v(t) be the third derivative of 2*t**2 - 1/3*t**4 - m*t**3 + 0*t + 0 - 1/30*t**5. Factor v(y).
-2*(y + 2)**2
Suppose 0*m - 8/9*m**2 + 0 + 4/9*m**4 - 4/9*m**3 = 0. Calculate m.
-1, 0, 2
Let o(n) be the third derivative of n**8/1344 + n**7/210 + n**6/120 + 26*n**2. Suppose o(c) = 0. Calculate c.
-2, 0
Factor 0*f - 12/5*f**2 + 0 + 3/5*f**3.
3*f**2*(f - 4)/5
Suppose -4/5*i + 2/5*i**2 - 6/5 = 0. What is i?
-1, 3
Let n = 8 - 4. Let l(i) = -n*i**2 + 13 + i + 8*i + 0*i**2. Let v(q) = q**2 - 3*q - 4. Let f(a) = -2*l(a) - 7*v(a). Factor f(o).
(o + 1)*(o + 2)
Determine g so that -11/5*g**4 + 2/5*g + 0 - 1/5*g**2 - 3/5*g**5 - 11/5*g**3 = 0.
-2, -1, 0, 1/3
Let j(q) be the second derivative of -1/84*q**7 - 1/4*q**5 + 0 - 5/12*q**3 - 5/12*q**4 - q - 1/4*q**2 - 1/12*q**6. Determine t so that j(t) = 0.
-1
Determine g so that -2*g**3 + 0*g**2 - 4*g**2 + 16*g + 2*g**4 - 16*g = 0.
-1, 0, 2
Let s be 3 - (0 - (-1 + 4)). Let k be (-9)/(1/(-8)*s). Solve 0*o**3 - k*o**2 + 7*o**3 + 2*o + 2 - 2*o + 3*o = 0.
-2/7, 1
Let o(p) be the third derivative of -p**8/3920 + p**7/1260 + p**6/630 - p**5/12 + p**2. Let w(x) be the third derivative of o(x). Factor w(a).
-4*(a - 1)*(9*a + 2)/7
Let j(g) be the second derivative of 4*g**4/39 + g**3/13 - g. Find d such that j(d) = 0.
-3/8, 0
Let x(n) be the second derivative of -n**6/90 - n**5/90 + n**4/36 + 3*n**2/2 - 2*n. Let j(m) be the first derivative of x(m). Factor j(r).
-2*r*(r + 1)*(2*r - 1)/3
Let s(q) = q**2 - q. Let p(y) = 8*y**2 - 3*y**2 - 4 - 4*y**2 + 5*y**2 - 2*y. Let w(v) = -p(v) - 4*s(v). Factor w(a).
-2*(a - 1)*(5*a + 2)
Let m be 1/(-4) + (-6)/(-120)*5. Determine c, given that -4/9*c**2 + 2/9*c**3 + 2/9*c + m = 0.
0, 1
Let k(i) = -i + 11. Let m be k(9). Suppose m + 0*y**2 + 8*y**2 + 3*y - 7*y - 6*y**2 = 0. Calculate y.
1
Let y(m) = m**3 + 23*m**2 + 22*m - 48. Let n(j) = 24*j**2 + 21*j - 48. Let b(i) = -2*n(i) + 3*y(i). Factor b(w).
3*(w - 1)*(w + 4)**2
Let p be ((-12)/21)/(20/(-14)). Factor p*r**2 + 2/5 - 4/5*r.
2*(r - 1)**2/5
Suppose 4*i = 2*i + 6. Factor -3/2*z**4 + i*z**3 + 0 + 0*z - 3/2*z**2.
-3*z**2*(z - 1)**2/2
Suppose 6*b - b = -80. Let a be 6/(-4)*b/21. Solve -10/7*s - 2/7 - a*s**2 = 0 for s.
-1, -1/4
Let s(x) be the first derivative of x**6/360 - x**5/40 + x**4/12 - 5*x**3/3 - 4. Let v(w) be the third derivative of s(w). Solve v(y) = 0.
1, 2
Suppose -3*g - 10 + 1 = 3*a, -5*g + 3 = -4*a. Let l be ((-8)/(0 - a))/(-1). Factor w**5 - w**2 + 5*w + w**l - w**3 - 5*w.
w**2*(w - 1)*(w + 1)**2
Let j be 1 + (-6)/(-5) - 1/(-5). Suppose 12/5*u**4 + j*u**2 - 3/5*u**5 - 18/5*u**3 + 0 - 3/5*u = 0. Calculate u.
0, 1
Let o(h) be the first derivative of -3*h**4/44 - 8*h**3/33 - 7*h**2/22 - 2*h/11 - 19. Suppose o(u) = 0. Calculate u.
-1, -2/3
Let g be (-4 - (-4 - 3/6))/27. Let n(t) be the second derivative of 0*t**2 + g*t**4 - 2/27*t**3 - 4*t + 0. Determine p so that n(p) = 0.
0, 2
Let v = 23 + -43/2. Factor 6 - 6*o + v*o**2.
3*(o - 2)**2/2
Let b(o) = o - 5. Let r be b(7). Solve -14*j + 1 + 12*j + 2*j**2 - j**r = 0 for j.
1
Let s(l) be the second derivative of l**9/30240 + l**8/6720 - l**7/5040 - l**6/720 + 7*l**4/12 - 3*l. Let v(w) be the third derivative of s(w). Factor v(f).
f*(f - 1)*(f + 1)*(f + 2)/2
Let a(j) be the second derivative of j**4/12 + j**3/2 - 25*j. Find i such that a(i) = 0.
-3, 0
Let u = 967 - 72523/75. Let z = 32/75 - u. Factor z*w + 2/5*w**2 + 0.
2*w*(w + 1)/5
Let s(c) be the third derivative of -c**7/15 + c**6/2 - 6*c**5/5 + 2*c**4/3 + 3*c**2. Factor s(k).
-2*k*(k - 2)**2*(7*k - 2)
Let v(y) = -2*y**2. Let n be v(-1). Let k be (1 - n)/((-9)/(-6)). Factor -6*c + 4 + 6*c**2 - k - 2*c.
2*(c - 1)*(3*c - 1)
Suppose j**3 + 18*j - 20*j + j**3 = 0. What is j?
-1, 0, 1
Suppose 20 = -9*c + 14*c. Let f(d) be the second derivative of -4/3*d**c + 0 + 4/5*d**5 + 5/6*d**3 - 1/4*d**2 + d. Let f(i) = 0. What is i?
1/4, 1/2
Let c(t) be the second derivative of 3*t**5/20 + 15*t**4/4 + 75*t**3/2 + 375*t**2/2 - 8*t. Find x such that c(x) = 0.
-5
Let x = -18 - -30. Let l be ((-8)/x)/(4/(-30)). Factor n**4 + n + n**2 + l*n**2 - 5*n - 4*n**3 + 1.
(n - 1)**4
Factor -1/2*p**3 - 3/2*p - 1/2 - 3/2*p**2.
-(p + 1)**3/2
Let b(n) = n**2 - 4*n + 3. Suppose k - u + 11 = 4*k, -3*k + 4*u + 16 = 0. Let v be b(k). Factor -v*t**3 - t**3 - 3*t + 9*t**2 - 3*t + 1.
-(t - 1)**2*(4*t - 1)
Factor 41*y - 66*y + 29*y - y**3 + 3*y**2.
-y*(y - 4)*(y + 1)
Suppose 0 = -52*y + 64*y - 24. Find i such that 0 + 1/6*i**y - 1/6*i**3 - 1/6*i**4 + 1/6*i = 0.
-1, 0, 1
Suppose -3*u = -4*u + 7. Let r = -5 + u. Factor -4*i**4 - 2*i**4 + 3*i + 6*i**r + 0*i**2 - 3*i**5.
-3*i*(i - 1)*(i + 1)**3
Let r(a) = -5*a**3 + 9*a**2. Let u(c) = c**3 - 2*c**2. Let p(b) = 4*r(b) + 18*u(b). Factor p(h).
-2*h**3
Factor 2*t - 1/3 - 3*t**2 + 4/3*t**3.
(t - 1)**2*(4*t - 1)/3
Factor 32*h**2 - 14*h**2 - 36*h**3 - 2*h + 10*h**2 - 4*h**5 - 6*h + 20*h**4.
-4*h*(h - 2)*(h - 1)**3
Let c(v) be the first derivative of -2*v**5/25 + v**4/5 + 8*v**3/15 - 8*v**2/5 - 10. Find k such that c(k) = 0.
-2, 0, 2
Suppose -2*z + 3*z + 15 = 0. Let g be 10/z*2/(-4). Factor 1/3*i**3 - 1/3 + 1/3*i**2 - g*i.
(i - 1)*(i + 1)**2/3
Let y(w) = -w. Let b(i) = -3*i**3 + i. Let v be b(1). Let l be y(v). Factor 0*f**l - 1/3*f**4 + 0*f + 0 - 1/3*f**3.
-f**3*(f + 1)/3
Factor -1/2*z**2 + 0 - z.
-z*(z + 2)/2
Let v(c) = c + 1. Let p be v(2). Let u(s) be the second derivative of 0 - 1/6*s**4 + s + 0*s*