1
Factor -19*g**4 - 12*g**4 - 210*g**3 - 132*g**2 - 24*g - 44*g**4.
-3*g*(g + 2)*(5*g + 2)**2
Suppose 0 = -m + 3*h - 5, 4*m + 5*h = 2 - 5. Let d be (-2 + -1)*m/3. Solve 15*j**3 + d*j**3 + 4*j**2 - 3*j**3 = 0 for j.
-2/7, 0
Let u(f) be the second derivative of f**7/2100 + f**3/2 + 2*f. Let y(a) be the second derivative of u(a). Let y(x) = 0. What is x?
0
Let w(z) be the first derivative of z**7/420 - z**6/60 + z**5/30 + z**3 + 4. Let q(s) be the third derivative of w(s). Solve q(g) = 0.
0, 1, 2
Let l(s) be the third derivative of 1/18*s**4 + 1/945*s**7 - 1/3*s**3 + 0*s - 8*s**2 - 1/90*s**6 + 4/135*s**5 + 0. Let l(y) = 0. Calculate y.
-1, 1, 3
Solve -8/3*w + 2/3*w**2 + 0 = 0 for w.
0, 4
Factor 2/7*h**2 - 2/7*h**3 - 2/7 + 2/7*h.
-2*(h - 1)**2*(h + 1)/7
Let y(l) be the first derivative of -l**3/7 + 9*l**2/14 - 6*l/7 + 6. Find x such that y(x) = 0.
1, 2
Let c(j) = -j**3 - j**2 - 2*j. Let o(z) = 5*z**3 + 11*z. Let s(f) = -4*c(f) - o(f). Suppose s(x) = 0. Calculate x.
0, 1, 3
Let g(t) = t**3 + t**2. Let j(w) = 10*w**5 + 5*w**4 - 10*w**3 + 5*w. Let b(v) = -5*g(v) + j(v). What is x in b(x) = 0?
-1, 0, 1/2, 1
Let f(x) = 4*x**3 + 10*x**2 - 3*x + 4. Let k(u) = u**3 + u**2 + u. Let a(i) = -2*f(i) + 10*k(i). Solve a(b) = 0 for b.
1, 2
Let a(f) = -3*f**2 - f - 10. Let v(m) be the first derivative of 2*m**3/3 + m**2/2 + 7*m + 2. Let o(c) = -5*a(c) - 7*v(c). Factor o(n).
(n - 1)**2
Let r(t) be the first derivative of t**3 - 33*t**2 + 363*t + 9. Factor r(v).
3*(v - 11)**2
Let q(s) be the third derivative of -s**5/360 + s**4/144 + 2*s**2. Factor q(m).
-m*(m - 1)/6
Let k = -33 + 35. Let n(p) be the first derivative of 7/16*p**4 - 1 + 1/4*p**5 - 7/8*p**k - 1/4*p**3 - 1/2*p. Let n(b) = 0. Calculate b.
-1, -2/5, 1
Suppose -5*p + 0*s + 15 = -5*s, 2*p - 2 = 4*s. Suppose -3*l = 3*m + 15, -10 = -p*l - 0*l + 2*m. Find o such that 1/2 - 1/2*o**2 + l*o = 0.
-1, 1
Let r(a) be the third derivative of a**10/201600 - a**8/26880 - a**5/15 - a**2. Let y(g) be the third derivative of r(g). Solve y(i) = 0 for i.
-1, 0, 1
Let b(f) = -7*f**3 + 3*f**2 + f - 3. Let k(j) = -64*j**3 + 28*j**2 + 8*j - 28. Let v(c) = 28*b(c) - 3*k(c). Suppose v(r) = 0. What is r?
-1, 0, 1
Let u(c) = -8*c**3 + 15*c**2 + 5*c - 12. Let q(i) = 65*i**3 - 120*i**2 - 40*i + 95. Let r(k) = 3*q(k) + 25*u(k). Let r(y) = 0. What is y?
-1, 1, 3
Let p be (-20)/1100*((-5)/6 - 0). Let z(u) be the second derivative of 0*u**3 + u - p*u**4 + 0 + 1/11*u**2. Factor z(y).
-2*(y - 1)*(y + 1)/11
Let u(o) be the second derivative of -o**5/240 + o**3/6 + o**2/2 + 6*o. Let q(l) be the first derivative of u(l). Suppose q(f) = 0. What is f?
-2, 2
Let i = -10 - -10. Suppose -3*y + 2*y + 4 = i. Let -2/11*j**2 + 4/11*j**3 + 0 + 2/11*j**y - 4/11*j = 0. What is j?
-2, -1, 0, 1
Let u(m) be the second derivative of -5*m**4/3 + 15*m**3/2 - 5*m**2 + 4*m. Factor u(n).
-5*(n - 2)*(4*n - 1)
Let m be 24/(-30)*4/(-8). Let u = 298 - 1481/5. Factor m*k + u*k**2 + 3*k**3 + 11/5*k**4 + 0 + 3/5*k**5.
k*(k + 1)**3*(3*k + 2)/5
Let z be (-66)/(-14) + (-2)/(-7). Let -4*u**3 + 0*u**3 + z*u**3 - u**4 = 0. Calculate u.
0, 1
Let a(w) be the second derivative of 2/5*w**5 + 0*w**2 + 0 + 1/3*w**3 + 3*w + 2/3*w**4. Find r, given that a(r) = 0.
-1/2, 0
Let j(q) be the second derivative of -q**4/16 + 2*q**3 - 24*q**2 + 4*q. Find w such that j(w) = 0.
8
Let y be 4/8*2/2. Let o = 24/13 + -83/52. Suppose -3/4*z**3 - y*z**2 + 0*z + 0 - o*z**4 = 0. What is z?
-2, -1, 0
Let b(x) = -x**2 + 5*x - 4. Let p(a) = a. Let l(g) = b(g) - p(g). Factor l(i).
-(i - 2)**2
Let h(s) be the second derivative of s**5/5 + 4*s**4 + 32*s**3 + 128*s**2 - 17*s. Find z, given that h(z) = 0.
-4
Let b(f) = -f**2 + f + 4. Let k(y) = y**2 - 7*y + 6. Let w be k(6). Let u be b(w). Solve -u*a**2 - a + 6*a**2 - 3*a**2 = 0.
-1, 0
Factor 9*i**4 - 6*i**5 + 0*i + 0 + 3/8*i**2 - 27/8*i**3.
-3*i**2*(i - 1)*(4*i - 1)**2/8
Let a be 0/((9 + -1)/(-4)). Let i(u) be the first derivative of 2 + 0*u**5 - 1/15*u**6 + 1/10*u**4 + 0*u**3 + 0*u + a*u**2. Let i(m) = 0. Calculate m.
-1, 0, 1
Let t(q) be the third derivative of 3/40*q**4 + 1/15*q**3 + 1/350*q**7 + 0 + 11/600*q**6 + 0*q + 2*q**2 + 1/20*q**5. Suppose t(c) = 0. What is c?
-1, -2/3
Suppose 4*c = -4*x + 24, -x + 18 = x + 5*c. Suppose -t = x*t. Solve t + 2/7*k - 2/7*k**2 = 0 for k.
0, 1
Let k(v) be the first derivative of v**5/30 - v**4/12 - 2*v**3/3 - 3*v**2/2 - 3. Let i(c) be the second derivative of k(c). Suppose i(s) = 0. What is s?
-1, 2
Let g(y) = -5*y**2 - 20*y + 12. Let b be 4/10 + (-154)/10. Let h = b + 23. Let x(d) = 3*d**2 + 13*d - 8. Let s(p) = h*x(p) + 5*g(p). Let s(c) = 0. Calculate c.
2
Let d(h) = 10*h**2 - 5*h - 7. Let y be d(-3). Let 0*z**2 - 70*z**4 + 3*z**3 + y*z**5 - 2*z**2 - 29*z**3 = 0. Calculate z.
-1/7, 0, 1
Let o(c) be the second derivative of c**4/4 - c**3 + 3*c**2/2 + 16*c. Factor o(d).
3*(d - 1)**2
Let d(h) be the third derivative of 0*h**5 + 0*h**7 + 1/40*h**4 + 0 - 2*h**2 + 0*h + 1/560*h**8 + 0*h**3 - 1/100*h**6. Find z, given that d(z) = 0.
-1, 0, 1
Let d(c) be the first derivative of 6*c**5/65 + c**4/26 - 6*c**3/13 - 9*c**2/13 - 4*c/13 + 8. Find o, given that d(o) = 0.
-1, -1/3, 2
Let k = -705 - -38071/54. Let z(g) be the second derivative of 0 - k*g**4 + 1/9*g**2 + g + 0*g**3. Let z(v) = 0. What is v?
-1, 1
Let 6*l**3 + 12*l**3 + 36*l**2 + 30*l + 9 + 92*l**4 - 89*l**4 = 0. What is l?
-3, -1
Let l(k) be the third derivative of -4*k**7/735 - k**6/140 + k**5/210 + 8*k**2. Determine h, given that l(h) = 0.
-1, 0, 1/4
Let n be -2 + -1 - (-899)/195. Let r = -16/39 + n. Factor 4/5 - r*g + 2/5*g**2.
2*(g - 2)*(g - 1)/5
Let l be 12/(-9)*6/(-14). Let a = 2153/7 - 307. Factor 0*f**3 + 2/7*f - 2/7*f**5 + 0 + l*f**4 - a*f**2.
-2*f*(f - 1)**3*(f + 1)/7
Solve -21/4*i**5 + 0 + 0*i + 21/4*i**3 - 3/2*i**2 + 3/2*i**4 = 0 for i.
-1, 0, 2/7, 1
Let v(p) be the third derivative of p**7/42 + 5*p**6/24 + 3*p**5/4 + 35*p**4/24 + 5*p**3/3 + 15*p**2. Suppose v(r) = 0. What is r?
-2, -1
Let j(i) = i + 1. Let f be j(-1). Let t(w) be the second derivative of 0*w**3 + 1/135*w**6 + f*w**2 - 1/45*w**5 + 0 + 1/54*w**4 + w. Find q such that t(q) = 0.
0, 1
Suppose -17*z + 16*z + 3 = 0. Let w(h) be the third derivative of -1/18*h**4 - 1/360*h**6 + 0*h + 4*h**2 + 0 - 1/45*h**5 + 0*h**z. Factor w(b).
-b*(b + 2)**2/3
Let v(c) = 2*c**2 + 6*c - 6. Let t be v(-4). Let h(m) be the first derivative of t + 1/2*m**2 + 1/4*m**4 - 1/2*m**3 - 1/4*m - 1/20*m**5. Factor h(x).
-(x - 1)**4/4
Let z(x) = 2*x**3 - x**2 + 5*x + 3. Let w(d) = -d**3 - d - 1. Let j(o) = -3*w(o) - z(o). Factor j(v).
v*(v - 1)*(v + 2)
Let k(n) = n**2 + 3*n + 3. Let v = -3 - 1. Let g be k(v). Find z, given that -g*z + z - 4 + 2*z**3 + 0*z**3 = 0.
-1, 2
Let c be (-1)/2 - (-52)/8. Let q(r) be the third derivative of 0 + 0*r**3 + 1/30*r**4 - 1/150*r**5 - 1/100*r**c + 0*r - r**2. Let q(z) = 0. What is z?
-1, 0, 2/3
Factor -25*t - 4 + 20*t**2 + 4 + 40*t + 5*t**3.
5*t*(t + 1)*(t + 3)
Let y(d) be the first derivative of -d**5/30 - d**4/6 - d**3/3 + d**2 + 1. Let v(z) be the second derivative of y(z). Factor v(c).
-2*(c + 1)**2
Let v(n) = -n**2 + 6*n - 4. Suppose j = 5*j - 16. Let s be v(j). Factor -6*l**s + 4*l**4 - l**4 + 2*l**3 + 1 + 2*l**4 - 2*l.
-(l - 1)**3*(l + 1)
Factor 1/11*q**2 + 5/11 + 6/11*q.
(q + 1)*(q + 5)/11
Let f = 662 - 13237/20. Let z(n) be the second derivative of -1/2*n**3 + 2*n + 0 + f*n**5 - 1/2*n**4 + 3*n**2. Factor z(a).
3*(a - 2)*(a - 1)*(a + 1)
Let m(z) be the first derivative of -2*z**5/5 - z**4/2 + 2*z**3/3 + z**2 + 25. Suppose m(t) = 0. What is t?
-1, 0, 1
Factor 2/9*p - 2/9*p**2 + 0.
-2*p*(p - 1)/9
Let j(o) be the first derivative of 3/4*o**4 + 3 - 1/3*o**3 - 3/5*o**5 + 0*o**2 + 1/6*o**6 + 0*o. Factor j(c).
c**2*(c - 1)**3
Let w = 21 + -14. Let a = 15/2 - w. Find f, given that -a + 0*f + 1/2*f**2 = 0.
-1, 1
Let t be 7/4 + (-2)/(-8). Let i(a) be the second derivative of 0 + 1/36*a**4 + 0*a**5 - 1/90*a**6 + t*a + 0*a**2 + 0*a**3. Factor i(w).
-w**2*(w - 1)*(w + 1)/3
Let g(z) = -5*z**3 + z**2 + z - 3. Let d(r) = r**3 + 1. Let j(x) = -6*d(x) - 2*g(x). Determine y, given that j(y) = 0.
-1/2, 0, 1
Let r(c) be the third derivative of c**8/112 + 3*c**7/70 + 3*c**6/40 + c**5/20 + 5*c**2. Factor r(u).
3*u**2*(u + 1)**3
Let o(p) be the first derivative of -2 + p**2 + 2/3*p**3 + 0*p. Solve o(r) 