, 2
Factor -3/2*l**3 + 0 + 3/2*l + 0*l**2.
-3*l*(l - 1)*(l + 1)/2
Let s(w) be the second derivative of w**6/60 + w**5/20 + w**4/24 - 2*w. Factor s(o).
o**2*(o + 1)**2/2
Suppose 4*v + 5*p - 7 = 0, -v + p + 5 = -p. Factor l**v - 4*l**2 + 3*l**2 - l**3 + l**4.
l**2*(l - 1)*(l + 1)
Let s be (-12)/(-15) - (-16)/5. Let i(c) be the second derivative of 0 + 7/3*c**3 - 1/3*c**4 - s*c - 7/10*c**5 + 2*c**2. Factor i(g).
-2*(g - 1)*(g + 1)*(7*g + 2)
Let u(k) = -k**2 - 9*k + 2. Let a be u(-9). Factor -a*q - 52*q**2 + 18*q + 64*q**3 + 4 + 148*q**2 + 20*q.
4*(q + 1)*(4*q + 1)**2
Let b(g) be the third derivative of -g**6/100 - 3*g**5/100 + g**3/10 + 16*g**2 - g. Factor b(a).
-3*(a + 1)**2*(2*a - 1)/5
Let l(q) be the first derivative of q**5/10 - q**3/3 - q + 1. Let m(j) be the first derivative of l(j). Factor m(b).
2*b*(b - 1)*(b + 1)
Factor 4*t - 6 - 12*t**2 + 5*t + 9*t**2.
-3*(t - 2)*(t - 1)
Suppose 144 = 2*u - 6*u. Let z be (-2 - u/28) + 1. Factor -z*q + 0 - 2/7*q**2.
-2*q*(q + 1)/7
Let p(g) = -g**2 + g**2 + 2*g + 4*g**2. Let y = 6 + -8. Let k(r) = -9*r**2 - 3*r + 1. Let x(i) = y*k(i) - 5*p(i). Solve x(a) = 0.
-1
Let l(z) be the third derivative of 0*z**3 - 10*z**2 + 0*z**6 + 1/18*z**4 + 0 - 1/315*z**7 + 0*z + 1/30*z**5. Suppose l(f) = 0. What is f?
-1, 0, 2
Factor -4*f**5 + f**3 - 3*f**3 + 4*f**3 - 4*f + 6*f**3.
-4*f*(f - 1)**2*(f + 1)**2
Let q be 3676/234 - (2 - (-192)/(-104)). Factor -98/9*j**3 - 16/9 - q*j**2 + 104/9*j.
-2*(j + 2)*(7*j - 2)**2/9
Let c(v) = 3*v**2 + 20*v + 81. Let u(l) = -13*l**2 - 81*l - 324. Let t(s) = -18*c(s) - 4*u(s). Factor t(q).
-2*(q + 9)**2
Factor -8/9*h**3 + 2/9 + 2/9*h**4 - 8/9*h + 4/3*h**2.
2*(h - 1)**4/9
Let n(c) be the second derivative of 2*c**4/21 + 4*c**3/21 + c**2/7 - 8*c. Factor n(j).
2*(2*j + 1)**2/7
Let j = -2/37 - -43/111. Let k(u) be the first derivative of u**2 + 0*u - j*u**3 - 2. Suppose k(x) = 0. What is x?
0, 2
Find a, given that 0*a + 1/3*a**2 + 1/3*a**4 + 0 - 2/3*a**3 = 0.
0, 1
Let u(n) be the third derivative of 8*n**7/315 - 2*n**6/45 - n**5/15 + 2*n**4/9 - 2*n**3/9 + 25*n**2. Let u(w) = 0. Calculate w.
-1, 1/2, 1
Suppose 4*m - 5*n - 68 = 0, 34 = 2*m - 3*n - 2. Let k = -1 - -5. Factor u**3 + u**k + m - 12.
u**3*(u + 1)
Let p(s) be the second derivative of s**8/840 + 2*s**7/525 - s**5/75 - s**4/60 - 3*s**2/2 + 2*s. Let v(y) be the first derivative of p(y). Factor v(k).
2*k*(k - 1)*(k + 1)**3/5
Factor -3 - 1/4*g + 1/4*g**2.
(g - 4)*(g + 3)/4
Let b be 0 - (0 - 15/3). Let y(p) = -p**3 + 4*p**2 + 5*p + 3. Let s be y(b). Factor -1 + 3 - 2*o**s - o**2 + 2*o - o**2.
-2*(o - 1)*(o + 1)**2
Let c be (-3)/(-5)*(-15)/(-3). Let j = c - -1. Let -2*w**j - 2 + 7*w**3 - 4*w**2 - 8*w**2 + 8*w + w**3 = 0. Calculate w.
1
Let p(w) be the first derivative of -w**3/9 - 2*w**2/3 - 4*w/3 + 13. Factor p(t).
-(t + 2)**2/3
Let l(v) = -12*v**4 + 3*v**3 + 9*v**2 + 15*v + 15. Let x(b) = -b**4 + b**2 + b + 1. Let y(h) = l(h) - 15*x(h). Factor y(s).
3*s**2*(s - 1)*(s + 2)
Let p = 2 - -6. Factor p*j**3 - 10*j**3 - 2*j**2 + 4*j**3.
2*j**2*(j - 1)
Let t(k) be the first derivative of -3 - 1/4*k**4 - 1/5*k**2 + 7/15*k**3 + 0*k. Let t(m) = 0. What is m?
0, 2/5, 1
Factor 4*z**2 + z**4 - 2*z + 12*z**3 - z - 9*z - 8 + 3*z**4.
4*(z - 1)*(z + 1)**2*(z + 2)
Let r = -269 - -271. Suppose 2/9*c**5 + 0*c**4 + 0*c**r + 0 + 0*c**3 + 0*c = 0. Calculate c.
0
Let w(u) be the third derivative of -u**9/3780 + u**8/3360 + u**7/630 - u**6/360 + u**4/12 - 6*u**2. Let j(m) be the second derivative of w(m). Factor j(k).
-2*k*(k - 1)*(k + 1)*(2*k - 1)
Find j, given that 2/7*j**4 + 0 - 4/7*j**2 + 2/7*j**3 + 0*j = 0.
-2, 0, 1
Let y = 4/15 + 103/120. Let i(l) be the first derivative of -3/2*l - 1 - y*l**2 - 1/4*l**3. Factor i(w).
-3*(w + 1)*(w + 2)/4
Let i(d) be the third derivative of -d**7/630 + d**6/120 + d**5/20 + 5*d**4/72 + 38*d**2. Determine v so that i(v) = 0.
-1, 0, 5
Suppose -3*m + 27 = 5*c, 7 + 4 = 2*m + c. Suppose -3*k + 11 = v, 7*k - 15 = -3*v + m*k. Factor 8/5*z**v - 4/5 + 6/5*z**3 - 2*z.
2*(z - 1)*(z + 2)*(3*z + 1)/5
Let n(t) be the first derivative of -2*t**5/5 - 2*t**4 - 2*t**3/3 + 6*t**2 - 41. Suppose n(a) = 0. Calculate a.
-3, -2, 0, 1
Let c(g) be the first derivative of -1 - 1/7*g**2 - 2/21*g**4 - 5/21*g**3 - 2*g. Let i(o) be the first derivative of c(o). Factor i(u).
-2*(u + 1)*(4*u + 1)/7
Let i = -110 + 112. What is w in -2*w**3 + 0 + 0*w - 4/9*w**i = 0?
-2/9, 0
Let n = -3 - -8. Suppose 12 = n*v + 2. Suppose v + 4*k**3 - 7*k**3 + k + 2*k - 2*k**2 = 0. Calculate k.
-1, -2/3, 1
Suppose 4*k - 20 = -k. Suppose -4*p = k, 5*j - 1 = 2*p + 16. Factor 4*y + 6 - 6*y**2 - 2*y + 3*y**j - 5*y.
3*(y - 2)*(y - 1)*(y + 1)
Let k be ((-10)/2)/(-1 - 0). Suppose y - 3*y = -2*i + 8, -y - 12 = -k*i. Suppose -3*v**3 + 3*v**3 - i*v**2 + 2*v**3 - 4*v**3 + 2*v**4 + 2*v = 0. Calculate v.
-1, 0, 1
Let m be (-93)/(-7) + (-8)/28. Suppose -u - 3*v + m = 1, 0 = 2*u + 4*v - 16. Let 2*q**2 + u + 2/3*q**4 - 2*q**3 - 2/3*q = 0. Calculate q.
0, 1
Let j(x) = -x**4 + 10*x**3 - 5*x**2 - 4*x - 3. Let v(q) = -3*q**4 + 19*q**3 - 9*q**2 - 7*q - 5. Let o(i) = 10*j(i) - 6*v(i). Solve o(d) = 0.
-1/4, 0, 1
Let f = -18/59 - -203/472. Factor 0*h + 0 - f*h**4 - 1/4*h**3 - 1/8*h**2.
-h**2*(h + 1)**2/8
Let q = -1 - -3. Suppose -2*p**2 - 6*p - 10 + 14*p + q = 0. Calculate p.
2
Let m(c) be the third derivative of -c**8/126 + c**7/315 + c**6/45 - c**5/90 + 51*c**2. Let m(l) = 0. What is l?
-1, 0, 1/4, 1
Let b = 23 - 21. Let t(j) be the first derivative of 0*j**2 - b + 1/4*j**4 + 0*j - 1/6*j**3. Find s such that t(s) = 0.
0, 1/2
Factor 2/21*n**2 + 2/7*n + 0.
2*n*(n + 3)/21
Let j be (-35)/20 + (-4)/(-2). Factor 1/4*l**2 + 0 - j*l.
l*(l - 1)/4
Let v(n) be the first derivative of n**3/5 - 3*n**2/10 - 18*n/5 + 33. Suppose v(z) = 0. Calculate z.
-2, 3
Let l = 10 - 8. Let z(p) be the first derivative of 1/3*p**3 + 0*p + 1/2*p**2 + l. Factor z(w).
w*(w + 1)
Let p(t) = t**3 + t + 3. Let m be p(0). Factor 8/7*a**m + 0 + 6/7*a**4 + 2/7*a**2 + 0*a.
2*a**2*(a + 1)*(3*a + 1)/7
Find q, given that -1 + 1 + 56*q**2 - 60*q**2 - 16*q = 0.
-4, 0
Factor 0*i + 0*i**3 + 1/3*i**4 - 1/3*i**2 + 0.
i**2*(i - 1)*(i + 1)/3
Let n be (-2)/4 - (-6)/8. Let r be ((-5)/20)/((-11)/(-6) + -2). Factor -1/4*s - s**2 + 0 - n*s**5 - s**4 - r*s**3.
-s*(s + 1)**4/4
Factor 0*s + 0 - 18/7*s**3 + 2*s**4 + 4/7*s**2.
2*s**2*(s - 1)*(7*s - 2)/7
Let y = -87 - -92. Let w(u) be the second derivative of -u - 1/3*u**3 + 1/10*u**y - 1/6*u**4 + 1/15*u**6 + 0*u**2 + 0. Determine k, given that w(k) = 0.
-1, 0, 1
Suppose -5*f = -231 + 921. Let u be f/(-33) + (-8)/44. Factor -b**5 + b**5 + 3*b**3 + b**2 + 2*b**4 + b**5 + b**u.
b**2*(b + 1)**3
Let p be 272/255 + 2/(-5). Let 2/3*m + 0 + 4/3*m**2 + p*m**3 = 0. Calculate m.
-1, 0
Let f(i) = 16*i**2 + 4*i - 5. Let s(b) = 8*b**2 + 2*b - 3. Let d = 11 - 16. Let h(a) = d*s(a) + 3*f(a). Factor h(q).
2*q*(4*q + 1)
Suppose -3*k - 10 = -2*c - k, 0 = 4*c + k - 15. Suppose -4*q = 4*p - 12, 6*q + 2 = 2*p + c*q. Factor 2*h**3 + p + 0 - 2.
2*h**3
Suppose 5*p = 2*v + 51, -2*p + 19 = -p + 4*v. Suppose 0 = -4*o + p + 1. Factor -3*u**4 + 3*u**4 - 3*u**2 + 6*u**o - 3*u**4.
-3*u**2*(u - 1)**2
Let o(a) be the second derivative of 1/75*a**6 + 4*a + 3/50*a**5 + 0*a**3 + 0*a**2 + 0 + 1/15*a**4. What is j in o(j) = 0?
-2, -1, 0
Factor -5*z**5 - z**4 + z**5 - 3*z**4.
-4*z**4*(z + 1)
Let t be 1*(0 - (-58)/44). Let v = -9/11 + t. Solve 1/2*m**3 - m**2 + 0 + v*m = 0.
0, 1
Suppose -372 = -9*y - 345. Factor -1/2*j + 0 + 1/2*j**4 - 1/2*j**2 + 1/2*j**y.
j*(j - 1)*(j + 1)**2/2
Let b = -11 + 13. Let i(c) be the third derivative of 2/525*c**7 - 1/60*c**4 + 0 + 0*c**3 + 0*c + 2*c**b + 0*c**5 + 1/100*c**6. Find x such that i(x) = 0.
-1, 0, 1/2
Suppose 2/5*c - c**2 + 0 = 0. What is c?
0, 2/5
Factor 0 + 1/2*k - 1/4*k**2.
-k*(k - 2)/4
Let b(n) be the third derivative of -2*n**7/735 + n**6/70 - n**5/105 - n**4/14 + 4*n**3/21 + 37*n**2. Suppose b(y) = 0. Calculate y.
-1, 1, 2
Suppose -6 = 3*f - 5*f. Factor -23*o**f - 12*o - 6*o**2 + 13*o**3 + 24 + 13*o**3.
3*(o - 2)**2*(o + 2)
Suppose w = 5, 2*h = -2*w - 5 + 27. Suppose -3*o = -3*m, -2*o + 0*o - h = -4*m. Factor 1/2*k**4 + 1/2*k**m + 0 - 1/2*k - 1/2*k**2.
k*(k - 1)*(k + 1)**2/2
Let f(c) be the first derivative of c**4/6 + 2*c**3/9 - 2*c**2/3 - 8. Factor f(g).
2*g*(g - 1)*(g + 2)/3
Suppose -3*n - 34 = -3*