. Let o(j) = h*l(j) + 2*b(j). Factor o(c).
-(c - 1)*(c + 1)**2
Let k(j) be the third derivative of -j**8/10080 + j**7/2520 + j**5/12 - 2*j**2. Let m(o) be the third derivative of k(o). Find d such that m(d) = 0.
0, 1
Let a(n) = 3*n - 1. Let l = -5 + 6. Let u be a(l). Let 2/9 + 2/9*x**u + 4/9*x = 0. What is x?
-1
Let r be 12/14*756/486. Determine a, given that -r*a - 2/3*a**2 + 2/3*a**3 + 0 = 0.
-1, 0, 2
Suppose 5*t + 0*t = 130. Suppose 0 = -5*x - 1 + t, s - 2*x + 10 = 0. Determine k, given that s + 1/2*k**2 - 1/2*k = 0.
0, 1
Let w(u) be the first derivative of 4*u**3/3 + 14*u**2 - 32*u + 41. Factor w(g).
4*(g - 1)*(g + 8)
Let m(r) be the third derivative of 0*r**5 + r**2 + 0 + 2/15*r**3 + 1/20*r**4 - 1/300*r**6 + 0*r. Let m(t) = 0. Calculate t.
-1, 2
Suppose 0 + 7*k**2 - 49*k - 1/4*k**3 = 0. What is k?
0, 14
Let a(o) be the third derivative of -1/35*o**5 + 0*o**3 - 1/245*o**7 + 0*o + 0 - 4*o**2 + 0*o**4 - 11/420*o**6. Factor a(d).
-2*d**2*(d + 3)*(3*d + 2)/7
Let c(v) be the third derivative of -2*v**7/35 - 13*v**6/40 - 3*v**5/4 - 7*v**4/8 - v**3/2 + 5*v**2. Factor c(i).
-3*(i + 1)**3*(4*i + 1)
Suppose 4*d**3 + 27*d + 3*d**4 - 27*d + 2*d**3 = 0. Calculate d.
-2, 0
Let s = 4 - 1. Suppose p = 4*f - 4, -2*p = -3*p + 4. Factor -14*w**4 + 8*w**5 - 2*w**3 + 4*w**3 + 0*w**s + f*w**2 + 2*w**3.
2*w**2*(w - 1)**2*(4*w + 1)
Factor 54/7 - 2/7*s**3 + 18/7*s**2 - 54/7*s.
-2*(s - 3)**3/7
Factor 4/3*l**3 + 0 + 2*l**2 - 4/3*l.
2*l*(l + 2)*(2*l - 1)/3
Let w = 405 - 209. Find n, given that -3*n**2 + 19*n**2 + 2*n**3 - w*n**4 - 2*n**3 = 0.
-2/7, 0, 2/7
Let y(k) = k**2 + 7*k + 12. Let g be y(-5). Let z(i) be the first derivative of -2*i - 2/3*i**3 - g*i**2 - 1. Let z(d) = 0. What is d?
-1
Let k = 6 - 4. Factor 0 + 1/4*r - 1/4*r**k.
-r*(r - 1)/4
Let l(t) be the first derivative of t**5/5 - t**4/2 + t**2 - t - 7. Factor l(k).
(k - 1)**3*(k + 1)
Let r(o) be the second derivative of o**5/20 - o**3/6 - 32*o. Factor r(w).
w*(w - 1)*(w + 1)
Let h = 48 - 48. Let c(k) be the second derivative of -k + 0*k**3 + 0*k**5 + h*k**2 + 0*k**4 + 1/30*k**6 + 0. Factor c(v).
v**4
Let h = 1/54 + 101/378. Factor h*d**3 - 1/7*d**4 + 0 + 0*d + 0*d**2.
-d**3*(d - 2)/7
Let q(v) be the second derivative of 0*v**3 + 7*v - 1/45*v**6 + 0 - 1/15*v**5 + 0*v**2 - 1/18*v**4. Let q(o) = 0. Calculate o.
-1, 0
Let p(b) = 3*b**4 - 4*b**3 - 9*b**2 + 2*b + 4. Let o(n) = n**3 + n - 1. Let j(d) = -4*o(d) - p(d). Suppose j(y) = 0. Calculate y.
-2, 0, 1
Let q(b) = b**3 - b - 6. Let x be q(0). Let a be 4/(-12) - 20/x. Factor -2*d**a + d**5 + 5*d**2 - 3*d**2 - 1 - d**4 + d + 0*d.
(d - 1)**3*(d + 1)**2
Suppose 0 = -2*z - 237 + 245. Find r, given that 3/2*r**3 + 0 - 9/4*r**z + 9/4*r**2 - 3/2*r = 0.
-1, 0, 2/3, 1
What is b in -1/2*b**4 + 1/2*b**2 + 0 + 1/2*b - 1/2*b**3 = 0?
-1, 0, 1
Factor -6*a**4 + 2*a**5 + 16 - 16 + 8*a**2.
2*a**2*(a - 2)**2*(a + 1)
Let k(f) be the first derivative of -1/6*f**3 - 3 - 9/2*f - 3/2*f**2. Factor k(b).
-(b + 3)**2/2
Find f, given that -29*f - 5 - 7 + 31*f + 2*f**2 = 0.
-3, 2
Let n be 6/(-9) + -8 + 64/6. Factor -3/2*x**n + 1/2*x**4 + 2*x - x**3 + 2.
(x - 2)**2*(x + 1)**2/2
Let g(b) be the third derivative of b**7/210 + b**6/120 - b**5/60 - b**4/24 + 7*b**2. Factor g(r).
r*(r - 1)*(r + 1)**2
Let p be 16 - 12 - 2*2. Let a(g) be the first derivative of 2 + p*g + 0*g**2 - 1/18*g**4 + 2/27*g**3. Determine n, given that a(n) = 0.
0, 1
Let v be (20/24)/((-10)/(-9)). Find w, given that -v*w**2 - 1/2*w**3 + 0 + 1/2*w + 3/4*w**4 = 0.
-1, 0, 2/3, 1
Suppose -17*d - 3*r + 12 = -14*d, d - 16 = -4*r. Factor d - 2/13*f**3 - 2/13*f**2 + 0*f.
-2*f**2*(f + 1)/13
Let w be 287/(-39)*(-14)/77. Let f = -2/429 + w. Factor 1/3*d + 1/3*d**5 - 4/3*d**2 + 0 - f*d**4 + 2*d**3.
d*(d - 1)**4/3
Let g(r) be the second derivative of 3*r**5/20 - r**4/2 + r**3/2 - 5*r. Factor g(n).
3*n*(n - 1)**2
Let 21/4*r**2 + 0 + 3/4*r**3 + 9/2*r = 0. Calculate r.
-6, -1, 0
Let r(s) be the third derivative of s**7/525 + s**6/300 - s**5/75 + 50*s**2. Solve r(o) = 0.
-2, 0, 1
Let v(t) be the third derivative of t**7/2520 + t**6/360 + t**5/120 - t**4/12 + 3*t**2. Let o(b) be the second derivative of v(b). Let o(h) = 0. What is h?
-1
Let f = -4 + 8. Factor 0*r**2 - 9*r**4 + 8*r**2 + 37*r**f + 36*r**3.
4*r**2*(r + 1)*(7*r + 2)
Let b(s) = -2*s**3 - s**2 - s - 1. Let o be b(-1). Let 0 - o - 1 + 1 - 3*v**2 + v**3 + 3*v = 0. What is v?
1
Let l be (1/(-2))/((-1)/9). Let a(k) = k**2 - 3*k + 4. Let y be a(2). Factor -l*q**y + 7/2*q + 1.
-(q - 1)*(9*q + 2)/2
Let k(v) = v - 10. Let f be k(13). Factor -1/2*w + 1/2*w**f + 1/2 - 1/2*w**2.
(w - 1)**2*(w + 1)/2
What is u in 0*u + 0 - 1/5*u**2 = 0?
0
Let i(x) = -x - 5. Let l be i(-10). Find f such that 2 + 6*f - 5*f**2 + 15*f**2 + f - l*f**2 = 0.
-1, -2/5
Factor -5*j + 3 - 2 + 5*j - 2*j**3 + 2*j - j**4.
-(j - 1)*(j + 1)**3
Let s be ((-30)/(-675))/((-3)/(30/(-2))). Factor -2/9*m**2 + s + 0*m.
-2*(m - 1)*(m + 1)/9
Factor 0*m + m**2 - 1/2 - 1/2*m**4 + 0*m**3.
-(m - 1)**2*(m + 1)**2/2
Let t = -1 + 1. Factor -1/4*f**2 + t + 1/4*f.
-f*(f - 1)/4
Let d be 0/(-5 + 3) + 50. Suppose -48*p**3 + 2*p**2 + 2*p**2 + d*p**3 + 2*p = 0. What is p?
-1, 0
Factor 2/3 - 2/3*m - 2/3*m**2 + 2/3*m**3.
2*(m - 1)**2*(m + 1)/3
Let u be 8/(-44) + 194/(-22). Let n be 2/u*-24 - 4. Let -4/3 - 2/3*j**3 + 2/3*j + n*j**2 = 0. Calculate j.
-1, 1, 2
Let p(y) = 2*y**4 - 2*y**2 + 4. Let c(t) = 2*t**4 - 3*t**2 - t + 3. Let w(j) = -4*c(j) + 3*p(j). Determine v so that w(v) = 0.
-1, 0, 2
Find l such that 0 + 2/3*l**2 + 2/3*l = 0.
-1, 0
Let r(y) = -3*y**2 + 3*y + 3. Let s(d) be the first derivative of d**4/4 - d**2/2 - d + 5. Let n(i) = r(i) + 3*s(i). Factor n(f).
3*f**2*(f - 1)
Let w(y) be the second derivative of y**4/4 - 3*y**2/2 + 6*y. Factor w(m).
3*(m - 1)*(m + 1)
Let u(h) be the third derivative of -1/30*h**5 + 0*h - 2*h**2 + 2/3*h**3 + 0 + 1/12*h**4 + 1/180*h**6. Let q(j) be the first derivative of u(j). Factor q(k).
2*(k - 1)**2
Let a(o) be the third derivative of o**5/15 + o**4/3 - 2*o**3 - 11*o**2. Factor a(m).
4*(m - 1)*(m + 3)
Let y(h) = 28*h + 86. Let m be y(-3). Solve -2/3*j + 2/3*j**m - 4/3 = 0.
-1, 2
Let a(t) be the second derivative of -3*t**5/40 - 5*t**4/24 + t**3/3 + t**2 + 13*t. Factor a(g).
-(g - 1)*(g + 2)*(3*g + 2)/2
Let o(a) be the second derivative of a**7/84 + a**6/60 - a**5/40 - a**4/24 - 2*a. Determine f so that o(f) = 0.
-1, 0, 1
Let v(z) be the second derivative of -2/15*z**3 + 0*z**4 + 1/25*z**5 + 1/5*z**2 - 2*z - 1/75*z**6 + 0. Factor v(i).
-2*(i - 1)**3*(i + 1)/5
Let y be 6/(-2) - (-70)/30 - -4. Solve -y*d - 2/3*d**3 - 8/3*d**2 - 4/3 = 0 for d.
-2, -1
Find m such that 1/5 - 2/5*m + 1/5*m**2 = 0.
1
Let v be (3/(-4)*-1)/3. Let a be 2 + -5 + (-51)/(-12) - 1. Factor -v*w**2 + 0 + 1/4*w - a*w**3 + 1/4*w**4.
w*(w - 1)**2*(w + 1)/4
Let 5*p**2 - 9*p + 4*p**3 - 9*p**2 + p**2 - 2 = 0. Calculate p.
-1, -1/4, 2
Let c(j) be the third derivative of j**5/90 + j**4/36 + j**2. Factor c(i).
2*i*(i + 1)/3
Determine b so that 4*b**3 - 12*b**2 - 9*b + 0*b - 4*b - 8 + 4*b**4 - 7*b = 0.
-1, 2
Suppose 3*i + 6 = -3*y, 5*i + 2*y - 2 = 4*i. Let w be (-2)/(1/(i/3)). Suppose -2*n - 2*n**2 + 4*n**3 + w*n**4 + n**5 - 4 - 5*n + 2*n + 2 = 0. Calculate n.
-2, -1, 1
Suppose -22/7*s - 4/7 - 10/7*s**2 = 0. Calculate s.
-2, -1/5
Factor -10*q - q**2 - q + 6*q - 6.
-(q + 2)*(q + 3)
Let q be 1*-2*-2*(-3)/(-6). Factor 1/4*h**3 - 1/4*h - 1/4 + 1/4*h**q.
(h - 1)*(h + 1)**2/4
Let d(l) be the third derivative of -l**7/70 + l**6/20 - l**4/4 + l**3/2 + 6*l**2. Solve d(s) = 0.
-1, 1
Let l(a) be the second derivative of 7/10*a**5 - 8*a**2 + 13/3*a**4 + a + 20/3*a**3 + 0. Factor l(z).
2*(z + 2)**2*(7*z - 2)
Let t(b) be the second derivative of 1/6*b**4 + 0 - 2*b + 0*b**2 - 1/3*b**3. What is w in t(w) = 0?
0, 1
Let q(c) be the second derivative of 2*c**7/21 + 2*c**6/15 - c**5 + c**4 + 12*c. Suppose q(d) = 0. Calculate d.
-3, 0, 1
Suppose -f + 4 = 2. Let -8*u**4 + 2*u**5 - 2*u**3 + 4*u**4 + f*u**4 + 2*u**2 = 0. What is u?
-1, 0, 1
Suppose -d + 3 = -0*d. Let m = -655 - -657. Factor 1/2*h - m*h**4 + 0 + 9/2*h**d - 3*h**2.
-h*(h - 1)**2*(4*h - 1)/2
Let v(j) be the first derivative of j**9/4536 - j**7/630 + j**5/180 - 2*j**3/3 - 2. Let k(l) be the third derivative of v(l). Find m, given that k(m) = 0.
-1, 0, 1
Let g(b) be the third derivative of b**8/42 + 2*b**7/1