- 1/120*h**6 + 0*h**3 + 2*h**2. Determine i, given that t(i) = 0.
0, 1
Let n(m) = -2*m**2 - 4*m + 2. Let z(l) = l**2 + 1. Let d(y) = -n(y) + 2*z(y). Factor d(w).
4*w*(w + 1)
Let d(u) = 7*u**2 + 2*u - 3 + u**3 + u + 0*u**3 + 2*u. Let k be d(-6). Solve 5*r**2 - r**2 - 2*r**k - r**2 - 4 + r**2 + 2*r = 0 for r.
-1, 1, 2
Let u(b) = 4*b**2 + 32*b + 20. Let x(w) = -w**3 + 5*w**2 + 31*w + 19. Let y(p) = -3*u(p) + 4*x(p). Determine a so that y(a) = 0.
-1, 4
Determine u, given that -48/5*u + 8/5 + 98/5*u**2 - 16/5*u**4 - 66/5*u**3 + 24/5*u**5 = 0.
-2, 1/2, 2/3, 1
What is s in -s**4 + 4*s + 68*s**3 + 3 - 6*s**2 - 4 - 64*s**3 = 0?
1
Let v(a) be the second derivative of -a**8/840 + a**7/1470 - a**3/3 - 4*a. Let l(j) be the second derivative of v(j). Factor l(m).
-2*m**3*(7*m - 2)/7
Let b(s) be the second derivative of s**4/20 - s**3/2 + 6*s**2/5 - 24*s. Factor b(i).
3*(i - 4)*(i - 1)/5
Let q(x) be the second derivative of -x**5/20 + x**4/4 - x**3/3 - 4*x. Factor q(j).
-j*(j - 2)*(j - 1)
Let m(n) = -5*n**4 - 11*n**3 + 11*n**2 + 5*n - 6. Let q(d) = -5*d**4 - 12*d**3 + 12*d**2 + 5*d - 7. Let f(i) = 7*m(i) - 6*q(i). Factor f(c).
-5*c*(c - 1)*(c + 1)**2
Let v(d) be the third derivative of d**6/40 + 3*d**5/20 + 3*d**4/8 + d**3/2 + 9*d**2. Factor v(f).
3*(f + 1)**3
Let b(x) be the third derivative of -x**8/26880 - x**4/12 - x**2. Let h(t) be the second derivative of b(t). Determine j so that h(j) = 0.
0
Let p = 80/147 - -6/49. Let i = 248/369 - 2/369. Factor i*k**3 + 0 + p*k**2 + 0*k.
2*k**2*(k + 1)/3
Let o = 10 - 10. Suppose -2*f + 1 = v - 4, 4*v - 4 = o. Factor 0 - 2/7*i**f - 2/7*i.
-2*i*(i + 1)/7
Let l = -241 - -243. Let -3/5*d + 0 - 3/5*d**l = 0. Calculate d.
-1, 0
Suppose 4*c = 3*c + 4. Let b be (c/(-16))/(-1)*1. Determine f, given that -3/4*f - 1/4*f**3 - b - 3/4*f**2 = 0.
-1
Let o(y) = y + 6. Let m be o(-4). Solve 4*q**2 + 0*q - q - q - m*q**3 = 0.
0, 1
Suppose 2 = -d + 4. Let v(l) be the second derivative of -1/12*l**4 + 0 + 1/30*l**6 + 0*l**2 + 1/6*l**3 - 1/20*l**5 + d*l. Factor v(f).
f*(f - 1)**2*(f + 1)
Let r(a) = -a**3 - a. Let s(h) = -h**3 - 2*h**2 - h. Let g be 19/(-38) - 10/(-4). Let z(x) = g*r(x) - s(x). Let z(m) = 0. What is m?
0, 1
Suppose -4*m + 6*y = y - 6, 0 = 3*m + 3*y - 18. Find a, given that -12/7*a**5 - 44/7*a**3 + 38/7*a**m + 0 + 22/7*a**2 - 4/7*a = 0.
0, 1/2, 2/3, 1
Let r = -61 - -65. Factor -5/2*p**2 + 2 + r*p.
-(p - 2)*(5*p + 2)/2
Let x = -16 + 18. Factor -2*u + x*u**3 + 5*u - 5*u.
2*u*(u - 1)*(u + 1)
Let b(j) be the first derivative of -j**4/14 - 2*j**3/7 - 3*j**2/7 - 2*j/7 - 18. Factor b(a).
-2*(a + 1)**3/7
Let b(z) be the first derivative of -6 - 1/3*z**2 + z - 1/9*z**3. Factor b(s).
-(s - 1)*(s + 3)/3
Let u(b) be the second derivative of b**6/160 - b**5/240 - b**4/48 - b**2 + 4*b. Let n(t) be the first derivative of u(t). Factor n(d).
d*(d - 1)*(3*d + 2)/4
Let q(y) be the second derivative of -y**7/147 + 2*y**6/105 + y**5/35 - 4*y**4/21 + y**3/3 - 2*y**2/7 + y. Find h such that q(h) = 0.
-2, 1
Factor -89*z - 30*z**2 + 110*z + z**2 - 3*z**4 + 2*z**2 - 6 + 15*z**3.
-3*(z - 2)*(z - 1)**3
Let i(o) be the third derivative of o**6/180 - o**3/2 - 3*o**2. Let x(k) be the first derivative of i(k). Factor x(y).
2*y**2
Let h(p) be the second derivative of -2*p**6/105 - 17*p**5/140 - 5*p**4/21 - 2*p**3/21 + 5*p. Factor h(i).
-i*(i + 2)**2*(4*i + 1)/7
Let u = 17 - 17. Suppose -5*c - 5*w + 20 = u, -c - 15 = -5*c - 3*w. Suppose -2/5*f**2 - 4/5*f**5 + 1/5*f**4 + 8/5*f**c + 1/5 - 4/5*f = 0. Calculate f.
-1, 1/4, 1
Let j be 4/12 + 10/6. Determine r so that 4*r**2 - 11 + 3*r**3 - r**j + 8 - 3*r = 0.
-1, 1
Suppose 39 = 7*l + 25. Factor 0*t + 1/5*t**3 + 0*t**l + 0.
t**3/5
Let b(o) be the second derivative of 0 - 4*o - 9*o**2 + 5/4*o**4 - 13/2*o**3. Factor b(i).
3*(i - 3)*(5*i + 2)
Let y(j) be the first derivative of 1/4*j**6 + 0*j**3 - 3/10*j**5 - 6 - 3/4*j**4 + 0*j + 0*j**2. Determine d so that y(d) = 0.
-1, 0, 2
Let q(p) = 3*p**4 - 37*p**3 - 16*p**2 + 101*p + 72. Let w(j) = -8*j**4 + 92*j**3 + 40*j**2 - 252*j - 180. Let t(o) = 12*q(o) + 5*w(o). Factor t(r).
-4*(r - 3)**2*(r + 1)**2
Let d(v) = -v**2 + 2*v + 3. Let f be d(3). Suppose f = -14*i + 11*i. Let 2/9*o**4 + i*o - 2/9*o**2 + 2/9*o**5 - 2/9*o**3 + 0 = 0. Calculate o.
-1, 0, 1
Let u(z) be the second derivative of -z**2 + z + 1/24*z**3 + 1/60*z**5 - 5/96*z**4 + 0. Let c(q) be the first derivative of u(q). What is r in c(r) = 0?
1/4, 1
Let l = 11 + -8. Factor 4/9 + 2/9*u**l + 10/9*u + 8/9*u**2.
2*(u + 1)**2*(u + 2)/9
Let r(k) be the third derivative of k**7/210 - k**6/40 + k**5/60 + k**4/8 - k**3/3 - 8*k**2. Factor r(f).
(f - 2)*(f - 1)**2*(f + 1)
Let u be 90/21 + 2/(-7). Suppose x + 4 = -2*r, 0 = 4*x + 4*r + r + u. Factor -4/7*o**x - 2*o + 16/7*o**2 + 2/7*o**5 - 4/7*o**3 + 4/7.
2*(o - 1)**4*(o + 2)/7
Find z, given that 4*z**2 + 12*z + 0*z**2 - 8 + 8*z - 16*z = 0.
-2, 1
Let p(b) be the second derivative of -b**5/50 + 2*b**4/15 - b**3/3 + 2*b**2/5 - 10*b. Factor p(m).
-2*(m - 2)*(m - 1)**2/5
Let p(b) be the second derivative of -b**7/840 + b**6/180 + b**3/3 + b. Let u(r) be the second derivative of p(r). Suppose u(w) = 0. What is w?
0, 2
Let c(o) be the second derivative of o**4/36 + o**3/18 + 5*o. Factor c(u).
u*(u + 1)/3
Let i(m) be the second derivative of -m**6/90 + m**5/12 - 2*m**4/9 + 2*m**3/9 - 13*m. Let i(v) = 0. Calculate v.
0, 1, 2
Let h be 1/14*4*7. Let l be -1 + -1 + 0 - (-40)/12. Suppose 8/3*k**3 + 2/3 + 8/3*k**4 - l*k - 2*k**h = 0. Calculate k.
-1, 1/2
Let m(i) be the first derivative of i**6/2 + 9*i**5/5 + 3*i**4/2 + 1. Determine g so that m(g) = 0.
-2, -1, 0
Factor -2/19*z**3 - 6/19*z + 0 + 10/19*z**2 - 2/19*z**4.
-2*z*(z - 1)**2*(z + 3)/19
Let k be (-24)/(-60) - ((-22)/(-60) + 0). Let w(y) be the second derivative of -1/5*y**2 + 0 + 2*y + k*y**4 + 0*y**3. Determine n so that w(n) = 0.
-1, 1
Let q(n) be the first derivative of 3*n**5/20 - n**3/2 + 3*n/4 - 7. Determine r so that q(r) = 0.
-1, 1
Let x(d) be the second derivative of d**7/6300 - d**6/450 + d**5/75 - d**4/6 - 2*d. Let i(q) be the third derivative of x(q). What is h in i(h) = 0?
2
Let u = -9 + 15. Let z be u/(-21) + 2/7. Factor 1/4*q**2 + 0*q + z.
q**2/4
Let t(h) = h**3 - 4*h**2 + 2*h - 6. Let y be t(4). Find c such that 7*c**2 - 6*c**2 - y*c**2 + 2*c = 0.
0, 2
Let u(o) = 6*o - 14. Let c be u(3). Find m such that -1/3*m**2 + 1/3*m**5 + 0*m - m**c + 0 + m**3 = 0.
0, 1
Let k = 45 - 31. Suppose 0 = 5*x - k - 1. Factor 6/7*n**2 + 0 - 8/7*n**x + 2/7*n.
-2*n*(n - 1)*(4*n + 1)/7
Suppose -4*f = 3*d - 0*f - 31, 4*f = 4*d - 32. Find h such that 4*h**2 + 3*h**5 - 9*h**2 + 5*h**2 + d*h**4 + 6*h**3 = 0.
-2, -1, 0
Let j(b) be the first derivative of -2*b**5/5 - b**4 + 2*b**3 + 4*b**2 - 8*b - 2. Factor j(y).
-2*(y - 1)**2*(y + 2)**2
Factor 0*x + 9/4*x**3 + 0 - 1/2*x**2 - x**4.
-x**2*(x - 2)*(4*x - 1)/4
Let k(g) be the third derivative of -g**5/75 + 2*g**4/15 - 2*g**3/5 - 14*g**2. Factor k(a).
-4*(a - 3)*(a - 1)/5
Let g = 2009/460 - -3/92. Factor 34/5*i**3 - 4/5 - 42/5*i**2 - 2*i**4 + g*i.
-2*(i - 1)**3*(5*i - 2)/5
Suppose -2/13*q**2 - 4/13*q + 4/13*q**3 + 2/13 = 0. Calculate q.
-1, 1/2, 1
Let n(z) = -3*z**4 - 14*z**3 - 14*z**2 + 2*z - 2. Let f(i) = -3*i**4 - 15*i**3 - 15*i**2 + 3*i - 3. Let s(v) = -2*f(v) + 3*n(v). Factor s(j).
-3*j**2*(j + 2)**2
Let z(q) be the third derivative of q**5/300 - 2*q**3/15 + 36*q**2. Solve z(m) = 0 for m.
-2, 2
Let r = 3 + -1. Determine d, given that 2*d - 5*d**2 + 4*d**2 - d**2 + 2 - r*d**3 = 0.
-1, 1
Determine t so that -4/5*t**2 + 8/15*t + 16/15 - 2/15*t**4 - 2/3*t**3 = 0.
-2, 1
Let j = 6 + -4. Let h(n) = -7*n - 18. Let o be h(-3). Factor 0*s + 2/11*s**j + 0 - 2/11*s**o.
-2*s**2*(s - 1)/11
Let p = -14/31 + 278/341. Factor -2/11 + p*z - 2/11*z**2.
-2*(z - 1)**2/11
Let q(g) = -2*g**3 + 3*g - 7. Suppose -5*n - 31 = -4*h, 3*n + 14 = 5*h + 5*n. Let t(i) = -2*i**3 - 5 - 3 + i + i. Let m(f) = h*q(f) - 3*t(f). Factor m(y).
-2*(y - 1)**2*(y + 2)
Let c = -2/81 - -125/1782. Let n(u) be the first derivative of -2 + 0*u + 0*u**3 - c*u**4 + 1/11*u**2. Suppose n(b) = 0. What is b?
-1, 0, 1
Factor 1 + 6*f**2 - 4 + 3 - 2*f**3.
-2*f**2*(f - 3)
Let z(i) be the second derivative of i**6/210 + 3*i**5/70 - 2*i**4/21 - i**3/7 + i**2/2 - 6*i. Factor z(x).
(x - 1)**2*(x + 1)*(x + 7)/7
Let h be (2 + -6)/120*(-10)/16. Let z(x