0.
-1, 0, 1
Suppose 0 = -4*k + 5*h + 28, k - 3*h + 1 = 15. Let m(c) be the third derivative of 0*c + 1/90*c**5 - 2*c**k + 0*c**3 + 0 + 1/54*c**4. Factor m(n).
2*n*(3*n + 2)/9
Let d be (-1)/(-5)*(-1384)/(-4). Let r = d - 69. Suppose 1/5*w + 0 - r*w**2 = 0. Calculate w.
0, 1
Let r(v) be the first derivative of 4*v**7/735 - v**6/420 - 2*v**5/105 + v**4/84 - v**2 - 4. Let p(i) be the second derivative of r(i). Solve p(g) = 0.
-1, 0, 1/4, 1
Let d(k) be the first derivative of -k**5 - 5*k**4 + 10*k**3/3 + 30*k**2 - 45*k + 8. Find c such that d(c) = 0.
-3, 1
Let k(q) be the first derivative of -3 - 1/30*q**5 + 0*q**4 - q**2 + 0*q + 1/105*q**7 + 0*q**3 + 0*q**6. Let a(n) be the second derivative of k(n). Factor a(x).
2*x**2*(x - 1)*(x + 1)
Factor 0 + 1/10*p**4 - 3/10*p**3 + 0*p**2 + 2/5*p.
p*(p - 2)**2*(p + 1)/10
Let p(c) be the first derivative of c**4/24 + c**3/6 + c**2/4 - 4*c + 4. Let l(s) be the first derivative of p(s). Factor l(t).
(t + 1)**2/2
Determine g, given that -2/7*g**4 + 0 - 2/7*g**5 + 2/7*g**3 + 2/7*g**2 + 0*g = 0.
-1, 0, 1
Let w = -30 - -15. Let x be (6/25)/((-1)/w). What is j in -x*j + 4/5 + 18/5*j**3 + 14/5*j**2 - 18/5*j**4 = 0?
-1, 1/3, 2/3, 1
Let t be 20/(-6)*(-9)/6. Suppose 3*v - 5*v - 17 = t*i, -3*i - 35 = -5*v. Factor 4*n + 2 + 4*n**3 - 2*n**v - 2*n**3 - 6*n**3.
-2*(n - 1)*(n + 1)**3
Let -2/3*o**2 + 0 + 0*o = 0. What is o?
0
Let l(m) be the third derivative of -7*m**7/150 - 7*m**6/200 + 61*m**5/150 - m**4/2 + 4*m**3/15 - 16*m**2. Suppose l(q) = 0. What is q?
-2, 2/7, 1
Let t(b) = -b - 8. Let i be t(-10). Let 0*j**3 + 4*j**4 - 7*j**4 - 9*j**i - 9*j**3 - 3*j = 0. Calculate j.
-1, 0
Suppose -5*s = k - 383, 79 = s - 0*s + k. Suppose -7*u + 2*u - 5*t + 95 = 0, -4*u + 4*t = -s. Factor -16*a - u*a - 5*a + 8 + 50*a**2.
2*(5*a - 2)**2
Let q(v) be the second derivative of -v**4/90 + 17*v**3/45 - 16*v**2/15 + 2*v + 12. What is y in q(y) = 0?
1, 16
Let r(j) = 4*j + 40. Let k be r(-9). Let m(i) be the first derivative of -1 + 1/4*i**k - 1/5*i**5 + i + 7/4*i**2 + 4/3*i**3 - 1/12*i**6. Factor m(g).
-(g - 2)*(g + 1)**4/2
Let j = -102 + 104. Determine p so that 1/4 - 1/2*p + 1/4*p**j = 0.
1
Let d(y) be the second derivative of -3*y**5/4 - y**4/2 - 8*y. Let d(v) = 0. Calculate v.
-2/5, 0
Factor 0 - 5/3*g**2 + 25/6*g + 1/6*g**3.
g*(g - 5)**2/6
Suppose 4*m - 9 = -1. Solve 8*i - i**m - 4 - 5*i**4 - 8*i**3 + 5*i**2 + 4*i**2 + i**2 = 0 for i.
-2, -1, 2/5, 1
Let l(k) = k + 1. Let m(d) = -d**3 - 2*d**2 + 8*d + 9. Let u(q) = -18*l(q) + 2*m(q). Factor u(c).
-2*c*(c + 1)**2
Let u(d) be the first derivative of 125*d**6/27 - 40*d**5 + 1585*d**4/18 - 2236*d**3/27 + 116*d**2/3 - 80*d/9 - 21. Determine l so that u(l) = 0.
2/5, 1, 5
Factor 0 + 1/2*t + 1/2*t**2.
t*(t + 1)/2
Let d(r) be the first derivative of -1/3*r**3 + 0*r**2 + 1/210*r**5 + 1 - 1/1260*r**6 - 1/84*r**4 + 0*r. Let q(z) be the third derivative of d(z). Factor q(g).
-2*(g - 1)**2/7
Let f be (-8 + 4)*1/(-1). Suppose 0 = i + 3*i + 2*a - 20, 4*i = 2*a + f. Solve 0 + 1/4*x**i - 1/4*x + 0*x**2 = 0 for x.
-1, 0, 1
Suppose -6*u + u = -25. Suppose -7 = -4*x - 5*y, -2*y = -x - 4*y + 1. Factor 1 + 5*k + k**u - k**4 + 6*k**4 + 6*k**x + 10*k**2 + 4*k**3.
(k + 1)**5
Let j(k) be the first derivative of 0*k**2 - 5 - 4*k + 4/3*k**3. Factor j(x).
4*(x - 1)*(x + 1)
Let m be 1 + (1 - (-56)/(-36)). What is p in 0*p**2 + m - 2/9*p**3 + 2/3*p = 0?
-1, 2
Let n(l) = 6*l**3 - 4*l - 4. Let d(x) = x**3. Let q(v) = 4*d(v) - n(v). Let s(g) = g**4 - 7*g**3 + 16*g + 17. Let a(y) = 9*q(y) - 2*s(y). Factor a(b).
-2*(b - 1)*(b + 1)**3
Let o(a) be the second derivative of -a**7/105 + a**6/45 - a**5/90 + a**2/2 - 5*a. Let d(p) be the first derivative of o(p). Find c such that d(c) = 0.
0, 1/3, 1
Let t(c) be the first derivative of -2*c**3/3 + 3*c**2 + 2*c - 1. Let z(p) = 7*p**2 - 23*p - 1 - 3 - 4. Let o(a) = 22*t(a) + 6*z(a). What is j in o(j) = 0?
-2, -1
Let b(f) be the third derivative of f**7/35 - f**6/60 - f**5/15 + 21*f**2. Factor b(r).
2*r**2*(r - 1)*(3*r + 2)
Let p = -7 + 2. Let t(q) = -6*q**4 + 9*q**3 - 8*q**2 - 9*q + 4. Let f(w) = 7*w**4 - 10*w**3 + 9*w**2 + 10*w - 4. Let h(x) = p*f(x) - 6*t(x). Factor h(d).
(d - 2)**2*(d - 1)*(d + 1)
Let t be 4/(-14) + (-2886)/(-4515). Let c = 2/43 + t. Factor -2/5*q**3 + 0 - 2/5*q**4 + 0*q + 2/5*q**2 + c*q**5.
2*q**2*(q - 1)**2*(q + 1)/5
Factor -32/19 - 2/19*s**2 + 20/19*s.
-2*(s - 8)*(s - 2)/19
Let w(n) = 2*n. Let u be w(1). Let 0*z**u + 0*z**4 + 0*z + 2/9*z**5 + 0 - 2/9*z**3 = 0. What is z?
-1, 0, 1
Suppose n + 13 = m - 4*m, 0 = -2*n - 5*m - 21. Factor -f**4 + f**3 + n*f**2 + f**5 - 4*f + 5*f - 3*f**3 - 1.
(f - 1)**3*(f + 1)**2
Let q(z) be the third derivative of -z**5/270 + z**4/36 + 4*z**3/27 + 7*z**2. Determine n, given that q(n) = 0.
-1, 4
Let d be 9/(-15)*(1 + -6). Solve -2/3*o - 4/3*o**d + 5/3*o**2 + 0 + 1/3*o**4 = 0.
0, 1, 2
Factor 3/5*x**2 + 0 + 1/5*x.
x*(3*x + 1)/5
Let c = -26509/25254 + 145/414. Let j = -2/61 - c. Let -j*d**3 + 0 - 1/3*d**2 - 1/3*d**4 + 0*d = 0. What is d?
-1, 0
Find y, given that -4/3*y**2 + 0 + 2/3*y**5 + 4/3*y**4 + 0*y**3 - 2/3*y = 0.
-1, 0, 1
Let v(t) be the second derivative of -1/20*t**5 + 1/60*t**6 + 0 + 0*t**3 + 0*t**4 + 0*t**2 - 3*t. Find c, given that v(c) = 0.
0, 2
Let g(z) be the first derivative of 2*z**3/15 - 2*z**2/5 + 2. Suppose g(i) = 0. What is i?
0, 2
Suppose 4*k - 3*q - 9 = 0, k - 5*q - 7 = -3*k. What is o in 6 + 2*o + 2*o**4 + 0 + 2*o**5 - 4*o**2 - k - 4*o**3 - 1 = 0?
-1, 1
Let f = 29 + -79/3. Let m = -28/15 + f. Factor -2/5*q**5 - m*q**2 + 6/5*q + 6/5*q**4 - 2/5 - 4/5*q**3.
-2*(q - 1)**4*(q + 1)/5
Let s(o) be the third derivative of 2*o**7/105 - 7*o**6/120 + o**5/30 + o**4/24 - 10*o**2. Suppose s(w) = 0. Calculate w.
-1/4, 0, 1
Let j(h) = -h - 6. Let a be j(-6). Let n = 4 - 3. Suppose 5*b**2 + a - 4*b**2 - n = 0. What is b?
-1, 1
What is r in 2/3 + 32*r**2 - 8*r - 128/3*r**3 = 0?
1/4
Solve -5*r**3 - 26 - 19 + 15*r**2 + 47 - 22 = 0.
-1, 2
Find t, given that 24*t**2 - 40*t**2 - t**3 + 19*t**2 = 0.
0, 3
Let f(x) = 6*x**2 - 6*x. Let m(y) = 5*y**2 - 5*y. Let i = -9 - -14. Suppose 4*n - i + 25 = 0. Let s(g) = n*m(g) + 4*f(g). Determine w, given that s(w) = 0.
0, 1
Let q be 0*(14/4 - 3). Let i be (q - 3) + 0 - -7. Factor 3*k**5 + 20*k**i + 22*k**2 + k + 26*k**2 + 48*k**3 + 15*k.
k*(k + 2)**3*(3*k + 2)
Let i(b) = 2*b**4 + 19*b**3 + 3*b**2 - 25*b - 11. Let t(m) = -m**4 - m**3 - m - 1. Let r(k) = -i(k) + 3*t(k). Let r(v) = 0. What is v?
-4, -1, -2/5, 1
Suppose 15 = 2*d + 3*d. Let z be (-2)/8*(3 - 3). Factor 1/4*w + z - 1/4*w**d + 1/4*w**2 - 1/4*w**4.
-w*(w - 1)*(w + 1)**2/4
Factor 3/5*u**4 - 6/5*u**2 + 0*u + 0 + 3/5*u**3.
3*u**2*(u - 1)*(u + 2)/5
Let o(k) = -k**2 + 7*k - 12. Let q be o(4). Factor -2/5*l**2 - 2/5*l**5 + q*l - 6/5*l**4 + 0 - 6/5*l**3.
-2*l**2*(l + 1)**3/5
Let w(d) be the third derivative of 0*d + 0 + 4/3*d**3 - 7*d**2 + 1/3*d**5 + 7/6*d**4. Factor w(k).
4*(k + 1)*(5*k + 2)
Let c(v) = -25*v**2 - 4*v + 13. Let u(x) = -6*x**2 - x + 3. Let q(k) = 6*c(k) - 26*u(k). Factor q(s).
2*s*(3*s + 1)
Let z = -12 - -12. Let p(q) be the third derivative of -1/270*q**5 + 0 + 0*q**4 + 0*q - q**2 + 0*q**3 + 1/945*q**7 + z*q**6. Solve p(o) = 0.
-1, 0, 1
Let m = 1057/18 + -117/2. Let z(k) be the first derivative of 2 + m*k**3 + 0*k - 1/3*k**2. Factor z(s).
2*s*(s - 1)/3
Factor 55 + 46*i - 3*i**3 + 89 + 39*i**2 - 36 - 190*i.
-3*(i - 6)**2*(i - 1)
Let g be (-4)/6 - ((-100)/(-15))/(-5). Determine w so that -2/3*w + 0 + 4/3*w**2 - g*w**3 = 0.
0, 1
Let n(k) = -15*k**5 - 7*k**4 + 23*k**3 - k + 7. Let g(v) = -3 - 11*v**3 + 7*v**5 + v + 0*v + 2*v**4 + v**4 + 0*v**5. Let r(i) = -7*g(i) - 3*n(i). Factor r(c).
-4*c*(c - 1)**2*(c + 1)**2
Let d be (0 - 0)/(-3 + 2). Let u(p) be the first derivative of d*p + 7/12*p**4 - 2/9*p**3 + 2 + 0*p**2 - 1/3*p**5. Solve u(o) = 0.
0, 2/5, 1
Let t(i) be the first derivative of -i**5/5 - i**4 - i**3 + 9. Solve t(w) = 0.
-3, -1, 0
Let l(s) be the first derivative of 2*s**5/5 - 4*s**3/3 + 2*s - 23. Factor l(f).
2*(f - 1)**2*(f + 1)**2
Let d(v) = 2*v - 2. Let k(c) = c**2 + 5*c - 6. Suppose 33 = 3*z + 12. Let f(i) = z*d(i) - 2*k(i). Let f(o) = 0. What is o?
1
Let j(f) be the first derivative of -2*f**3/27 - f**2/3 - 4*f/9 - 8. Factor j(w).
-2*(w + 1)*(w + 2)/9
Let b(m) be the first derivative of -5*m**3/3 - 5*m**2 - 11. Factor b(y