y.
-1, 1
Factor -5 + 2*p**4 - 2*p**3 - 4*p**2 + 5 + 0*p**2.
2*p**2*(p - 2)*(p + 1)
Factor 2/3*p**3 + 2/3*p**5 + 0*p**2 + 0*p + 0 + 4/3*p**4.
2*p**3*(p + 1)**2/3
Let o(z) = -z**2 - z + 1. Let w(x) = -5*x**3 - 25*x**2 - 25*x + 25. Let k(m) = -30*o(m) + w(m). Factor k(d).
-5*(d - 1)**2*(d + 1)
Factor -2/3*n + 1/3*n**2 + 1/3.
(n - 1)**2/3
Let y(b) = b - 7. Let n be 27*(4 - 44/12). Let q be y(n). Factor 4/3*s**q + 0 + 2/3*s**3 + 2/3*s.
2*s*(s + 1)**2/3
Let z**5 + 5 - 4*z - 4*z**5 - 50*z**3 + 25*z**4 - 21*z - 2*z**5 + 50*z**2 = 0. Calculate z.
1
Let o be (-6)/9*((-30)/12 - 2). Suppose 0 + 0*v**2 + 0*v**4 - 1/4*v**5 - 1/4*v + 1/2*v**o = 0. What is v?
-1, 0, 1
Let k(v) be the first derivative of -v**5/270 - v**4/36 - 2*v**3/27 + v**2/2 + 2. Let h(n) be the second derivative of k(n). Let h(u) = 0. What is u?
-2, -1
Let s(a) be the second derivative of 5*a**7/147 - a**6/35 - a**5/35 + 6*a. Factor s(l).
2*l**3*(l - 1)*(5*l + 2)/7
Let z(a) be the third derivative of -2/45*a**7 + 0*a + 1/10*a**6 + 0*a**3 + 4/15*a**5 - 2/9*a**4 + 0 - 2*a**2. Solve z(o) = 0.
-1, 0, 2/7, 2
Let i(g) be the first derivative of g**6/18 + 2*g**5/15 + g**4/12 - 6. Suppose i(t) = 0. What is t?
-1, 0
Let b(t) be the first derivative of -2*t**3/21 + 12*t**2/7 - 72*t/7 + 7. Let b(q) = 0. Calculate q.
6
Let r be -1*1/(-1 - 4)*1. Factor -2/5 + r*f + 3/5*f**2.
(f + 1)*(3*f - 2)/5
Factor -2/11*x**4 - 2/11*x**2 + 0*x + 0 - 4/11*x**3.
-2*x**2*(x + 1)**2/11
Let z(j) be the third derivative of 0*j - 4*j**2 + 11/30*j**6 - 1/3*j**4 + 0*j**3 + 0 - 3/5*j**5. Factor z(g).
4*g*(g - 1)*(11*g + 2)
Let a be (1/(-3))/(16/(-60)). Factor 0 - 3/4*t**4 - 1/4*t**2 + a*t**3 - 1/4*t.
-t*(t - 1)**2*(3*t + 1)/4
Factor 3 + 5*u**5 + 0*u**5 - 6*u**3 + 3*u**4 + 2*u**2 - 8*u**2 + 3*u - 2*u**5.
3*(u - 1)**2*(u + 1)**3
Let r(j) be the third derivative of j**8/1344 + j**7/280 + j**6/480 - j**5/80 - j**4/48 - j**2. Factor r(o).
o*(o - 1)*(o + 1)**2*(o + 2)/4
Let c(k) be the second derivative of -k**7/21 + k**6/5 + k**5/5 - k**4 - k**3/3 + 3*k**2 - 31*k. What is y in c(y) = 0?
-1, 1, 3
Let v(p) be the first derivative of -p**4/16 - 5*p**3/12 - 3*p**2/8 + 9*p/4 - 16. Determine k so that v(k) = 0.
-3, 1
Let x(s) be the third derivative of s**2 + 0*s**3 + 0*s + 0 - 2/75*s**6 - 1/25*s**5 - 1/60*s**4. Suppose x(o) = 0. Calculate o.
-1/2, -1/4, 0
Let r(h) be the second derivative of -h**4/12 - h**3/3 - h**2/2 - 6*h. Solve r(f) = 0.
-1
Let y(u) = -4*u**2 - u - 1. Let f(b) be the second derivative of -7*b**4/12 - b**3/3 - b**2/2 + 2*b. Let g(k) = 6*f(k) - 10*y(k). Factor g(d).
-2*(d - 1)*(d + 2)
Let w(z) = z**2 + z. Let j be (-10)/(-8) - 4/16. Let r(a) = 4*a**2 + 14*a - 8. Let q(d) = j*r(d) - 6*w(d). Solve q(k) = 0 for k.
2
Let h(q) be the second derivative of -5*q + q**4 + 8/3*q**3 + 0 + 2/15*q**6 - 4/5*q**5 - 8*q**2. Let h(v) = 0. What is v?
-1, 1, 2
Let g(r) be the first derivative of -r**5/15 - 3*r**4/8 - r**3/3 + r**2/2 - 7. Let k(m) be the second derivative of g(m). Factor k(d).
-(d + 2)*(4*d + 1)
Suppose -4*k + 4 = -4. Let g be 6/4*(-16)/(-6). Determine p so that -k*p**3 - p**g - 5 - p**2 + 5 = 0.
-1, 0
Let g(m) be the second derivative of -m**6/75 + m**5/50 - 22*m. Factor g(s).
-2*s**3*(s - 1)/5
Let s = 2/657 + 215/1314. Determine g, given that -s*g**4 + 0*g**2 + 0 + 1/6*g**3 + 0*g = 0.
0, 1
Let t = -80/9 + 82/9. Factor t*j**2 + 0*j + 0.
2*j**2/9
Let l(f) = -17*f**2 - 42*f - 12. Let m(r) = 0*r**2 + 21*r + 9*r**2 + 4*r**2 + 6 - 4*r**2. Let q(p) = -6*l(p) - 13*m(p). Factor q(k).
-3*(k + 1)*(5*k + 2)
Let x(o) = o**3 - o**2 + 1. Let t = -4 - 0. Let v(b) = -4*b**3 - 12*b**2 - 2*b + 3. Let h(m) = t*v(m) + 12*x(m). Find r such that h(r) = 0.
-1, -2/7, 0
Let s(x) be the first derivative of x**4 + 28. Factor s(d).
4*d**3
Let g = 1907309/105 - 18165. Let u = 2/15 - g. Solve 0*m**2 + 0 + 0*m**4 - 4/7*m**3 + 2/7*m + u*m**5 = 0.
-1, 0, 1
Let z(h) be the first derivative of 1/5*h**5 - 3 - 3/4*h**4 + 0*h + 0*h**2 + 2/3*h**3. Factor z(t).
t**2*(t - 2)*(t - 1)
Let o(f) = -1. Let t(n) = -15*n**2 - 27*n - 8. Let l(w) = -4*o(w) - t(w). Factor l(p).
3*(p + 1)*(5*p + 4)
Let z be 5 + -24*6/45. Factor 12/5*v + 0 + 0*v**2 - z*v**3 + 3/5*v**4.
3*v*(v - 2)**2*(v + 1)/5
Suppose -3*d = -5*p + 11, p - 5*p + 2*d + 10 = 0. Factor -b**3 + 0*b**p - 2*b - b**4 + b**2 + 3*b.
-b*(b - 1)*(b + 1)**2
Let h = 26 - 23. Suppose 0 = 4*s - u - 6, -h*u = s - u - 6. What is y in -1/4*y**3 - 1/4 - 3/4*y - 3/4*y**s = 0?
-1
Let r(h) be the third derivative of 0*h**3 - 1/180*h**5 + 1/144*h**4 + 0*h + 1/720*h**6 + 0 - 7*h**2. Suppose r(v) = 0. What is v?
0, 1
Let i(d) = 4*d**3 - 6*d - 4. Let a(u) = -17*u**3 + 24*u + 16. Let k(v) = 4*a(v) + 18*i(v). Factor k(n).
4*(n - 2)*(n + 1)**2
Let z be (-8)/6 + (-8)/(-6). Let p = -3/23 + 29/46. Find j such that -5/4*j**2 - 1/4*j**4 + j**3 + z + p*j = 0.
0, 1, 2
Let d = 3/20 + 29/40. Let z(s) be the second derivative of 2*s + 0 - 1/4*s**4 + 3/4*s**2 - d*s**3. Let z(m) = 0. Calculate m.
-2, 1/4
Suppose -3*w + 5 = -c, 4*c = -w - 2*w + 25. Let f be -1*3/(-1 + 0). Factor 2*v**4 + 2*v**2 + 5*v**f - 2*v**w + v**3.
2*v**2*(v + 1)**2
Let x = -10 + 10. Suppose 5*h = 4*s + 23, -3*h - 4*s = -x*h - 1. Find f, given that -h*f - 4*f**3 - 7 + 9 + 5*f**3 = 0.
-2, 1
Let t(s) be the first derivative of s**5/5 + s**4/2 + s**3/3 - 22. Factor t(r).
r**2*(r + 1)**2
Let i(n) be the first derivative of -n**4/4 + 2*n**3/3 - n**2/2 - 5. Factor i(s).
-s*(s - 1)**2
Let f(w) be the third derivative of -w**7/1260 - w**6/540 + w**3/2 - 3*w**2. Let h(v) be the first derivative of f(v). Factor h(i).
-2*i**2*(i + 1)/3
Let w(k) = k**5 + k**4 + k**3 + k. Let o(s) = 6*s**5 + 2*s**4 + 7*s**3 + 5*s. Let c(j) = -o(j) + 5*w(j). Suppose c(g) = 0. What is g?
0, 1, 2
Let j(w) = -2*w - 6. Let i be j(-3). Let r(x) be the third derivative of 0 + 7/120*x**5 + i*x**3 + 0*x - 1/24*x**4 + 4*x**2. Factor r(h).
h*(7*h - 2)/2
Let o(q) be the third derivative of q**8/672 - q**7/252 + q**6/360 - 10*q**2. Find m such that o(m) = 0.
0, 2/3, 1
Let c = -489/5 - -98. Find k such that -4/5*k**2 - c + 4/5*k = 0.
1/2
Let s(c) be the first derivative of -5*c**3/3 - 5*c**2/2 - 5. Suppose s(f) = 0. Calculate f.
-1, 0
Let u be 535/75 - (2 + 1). Let q = u + -19/5. Solve -1/2*t + 1/6*t**3 + 0*t**2 - q = 0 for t.
-1, 2
Let g(m) be the second derivative of m**5/40 - m**3/12 - 19*m. Factor g(l).
l*(l - 1)*(l + 1)/2
Let q(a) be the third derivative of -a**8/1344 + a**6/240 - a**4/96 + 5*a**2. Factor q(r).
-r*(r - 1)**2*(r + 1)**2/4
Let n(x) be the second derivative of -x**6/12 - x**5/5 - x**4/24 + x**3/6 + 4*x. Determine l, given that n(l) = 0.
-1, 0, 2/5
Suppose 0 = -5*v + 19 - 4. Let y(p) be the second derivative of 5/36*p**4 + 0 + 1/18*p**v + 0*p**2 + 1/15*p**5 + 2*p. Suppose y(c) = 0. Calculate c.
-1, -1/4, 0
Let u = -2 + 2. Let p be (38/(-14) - -3) + 17 + -17. Factor -p*g**2 - 2/7*g + u.
-2*g*(g + 1)/7
Let a(n) = 4*n**2 - 18*n + 34. Let s(u) = -9*u**2 + 37*u - 69. Let y(j) = -10*a(j) - 4*s(j). Let y(r) = 0. Calculate r.
4
Let o(t) be the first derivative of -1/7*t**2 - 2/21*t**3 + 2/7*t - 2 + 1/14*t**4. Factor o(c).
2*(c - 1)**2*(c + 1)/7
Determine v, given that 22/9*v**2 - 26/9*v**4 + 26/9*v + 56/9*v**5 + 4/9 - 82/9*v**3 = 0.
-1, -2/7, -1/4, 1
Let d(m) be the first derivative of m**4/6 - 2*m**3/3 + m**2 + 2*m + 2. Let v(u) be the first derivative of d(u). Factor v(r).
2*(r - 1)**2
Let h be 29/9 - (-4)/(-18). Let s be 2/(-6) - (-1 - (-130)/(-75)). Solve -11/5*x**2 + 2/5*x + 0 + s*x**h + 1/5*x**4 - 4/5*x**5 = 0 for x.
-2, 0, 1/4, 1
Let r be -2 + 8 - 476/85. Let -14/5*b**2 - 4/5*b**3 + r - 3/5*b + 7/5*b**5 + 12/5*b**4 = 0. Calculate b.
-1, 2/7, 1
Determine x so that -3/7*x + 0 + 1/7*x**2 = 0.
0, 3
Let b(p) = -p**2 + 3*p. Let w(f) be the third derivative of -3*f**5/20 + 5*f**4/4 + 6*f**2. Let s(r) = -21*b(r) + 2*w(r). Solve s(k) = 0 for k.
0, 1
Let y(b) be the second derivative of -2*b**7/21 + 6*b**6/5 - 31*b**5/5 + 17*b**4 - 80*b**3/3 + 24*b**2 + b - 14. Determine h so that y(h) = 0.
1, 2, 3
Let n be (76/24)/19*3/1. Let b + 1/2*b**2 + n = 0. What is b?
-1
Let o(v) be the third derivative of -v**6/120 - v**5/10 - 5*v**4/24 + 8*v**2. Let h be o(-5). Solve m**3 + 1/3*m - 1/3*m**4 + h - m**2 = 0 for m.
0, 1
Let i(f) = -6*f**4 - 24*f**3 - 18*f**2 - 9*f - 3. Let k(m) = m**4 + m**2 - m - 1. Let r(g) = -i(g