 3*p + p**r.
p**3
Let l(j) be the third derivative of j**8/3024 - j**7/378 + 7*j**6/1080 + j**5/540 - j**4/27 + 2*j**3/27 + 21*j**2. Find n, given that l(n) = 0.
-1, 1, 2
Let y(p) be the third derivative of -p**6/180 - p**5/60 - p**3 + 8*p**2. Let r(d) be the first derivative of y(d). Solve r(h) = 0 for h.
-1, 0
Let n(w) be the second derivative of 0*w**3 + 0*w**4 - 3*w - 1/63*w**7 + 4/135*w**6 - 1/90*w**5 + 0*w**2 + 0. Let n(c) = 0. What is c?
0, 1/3, 1
Let h(i) = i**2 + 7*i - 12. Let y be h(-9). Find z, given that z - 12*z**2 - 6*z**3 + y*z**4 - 2 + 3*z**5 + 2*z + 8 + 0*z = 0.
-2, -1, 1
Let r(w) be the first derivative of -w**4/7 - 4*w**3/7 - 4*w**2/7 - 3. Suppose r(z) = 0. What is z?
-2, -1, 0
Let i(a) be the second derivative of -a**6/1440 - a**5/480 + a**4/48 + a**3/3 - 3*a. Let j(y) be the second derivative of i(y). Let j(m) = 0. What is m?
-2, 1
Let i(f) be the third derivative of -2*f**2 + 0*f**3 - 1/70*f**7 - 1/32*f**4 + 0 + 0*f - 3/80*f**6 - 1/448*f**8 - 1/20*f**5. Let i(x) = 0. Calculate x.
-1, 0
Let p(s) be the third derivative of s**7/490 - s**6/70 + s**5/35 + 16*s**2. Solve p(d) = 0.
0, 2
Let k(q) be the second derivative of -3*q**5/100 + 3*q**4/5 - 18*q**3/5 + 2*q. Factor k(p).
-3*p*(p - 6)**2/5
Let n(j) = -j**2 - 8*j - 9. Let k be n(-6). Factor 11*d + 3*d**2 - 3*d**5 - 9*d**k + 9*d**4 - 11*d.
-3*d**2*(d - 1)**3
Let b(q) be the second derivative of 7*q**6/120 + 3*q**5/20 + q**4/16 - q**3/12 - 2*q. Factor b(i).
i*(i + 1)**2*(7*i - 2)/4
Suppose -7*p = -6*p - 89. Factor -5*c**2 + 12*c - 102*c**3 + 256*c**3 + p*c**3 + 113*c**2.
3*c*(9*c + 2)**2
Let b(o) = 4*o**2 + 2*o. Suppose 0 = 2*g - 0 + 12. Let f(i) = -i**3 - i. Let y(h) = g*f(h) - 2*b(h). Factor y(w).
2*w*(w - 1)*(3*w - 1)
Let j(y) be the first derivative of 0*y**2 + 1/14*y**4 + 1/21*y**6 - 4/35*y**5 + 0*y - 2 + 0*y**3. Factor j(k).
2*k**3*(k - 1)**2/7
Suppose 15*p + 25/4 + 3*p**3 + 23/2*p**2 + 1/4*p**4 = 0. What is p?
-5, -1
Let x(n) be the first derivative of -1/4*n**4 + 0*n**3 + 1/12*n**6 + 0*n**5 + 1/4*n**2 - 3 + 0*n. Factor x(y).
y*(y - 1)**2*(y + 1)**2/2
Let j(a) be the first derivative of -a**2 + 1/3*a**3 + 3 - 3*a. Determine w so that j(w) = 0.
-1, 3
Let t(n) be the first derivative of 49*n**3/12 + 21*n**2/4 + 9*n/4 + 6. Factor t(y).
(7*y + 3)**2/4
Let f(p) = 2*p**2 + 7*p + 5. Let q be f(-4). Let r = q - 7. Factor -r*v**2 + 3*v**3 - v - 3*v**3 + 2 - 4*v**3 + 5*v**3.
(v - 2)*(v - 1)*(v + 1)
Let i(v) be the first derivative of -2/3*v**3 - 2/5*v**5 + v**4 - 2 + 0*v + 0*v**2. Factor i(o).
-2*o**2*(o - 1)**2
Let n = -9 + 13. Suppose -4*q + 8 = n*j, -q = -4*q - 3. Find m such that 0*m - 2/5*m**2 + 6/5*m**4 - 4/5*m**j + 0 = 0.
-1/3, 0, 1
Suppose 5*s = 4*s + 2. Let k(r) be the first derivative of 1/2*r**4 + 0*r + 0*r**3 - r**2 - s. Let k(y) = 0. Calculate y.
-1, 0, 1
Factor -6/5*z - 9/5 - 1/5*z**2.
-(z + 3)**2/5
Let f(g) be the first derivative of -g**6/15 + g**4/5 - g**2/5 - 2. Factor f(u).
-2*u*(u - 1)**2*(u + 1)**2/5
Let c(i) be the first derivative of i**8/672 - i**6/120 + i**4/48 - 2*i**2 - 4. Let r(l) be the second derivative of c(l). Factor r(g).
g*(g - 1)**2*(g + 1)**2/2
Let u be (-332)/249*(-4 + 1). Factor 0*j**u + 3/4*j**5 + 0*j**2 - 3/2*j**3 + 0 + 3/4*j.
3*j*(j - 1)**2*(j + 1)**2/4
Let v(u) be the first derivative of -20*u**3/3 - 14*u**2 - 8*u - 1. Solve v(b) = 0 for b.
-1, -2/5
Let r(d) be the first derivative of 1/12*d**6 + 3/4*d**4 + 1/4*d**2 + 2/3*d**3 + 5 + 0*d + 2/5*d**5. Factor r(w).
w*(w + 1)**4/2
Factor -2/11*n**3 - 4/11*n - 4/11 + 7/11*n**2.
-(n - 2)**2*(2*n + 1)/11
Let q(p) = -p**4 + 11*p**3 + 9*p**2 + 5*p - 1. Let a(g) = -4*g**4 + 34*g**3 + 26*g**2 + 14*g - 4. Let w(o) = -6*a(o) + 20*q(o). Factor w(d).
4*(d + 1)**4
Factor 3/5*t**4 - 6/5*t**5 + 0*t + 12/5*t**3 + 0 - 9/5*t**2.
-3*t**2*(t - 1)**2*(2*t + 3)/5
Let c be (0 - 2) + 1/(-1). Let q = 5 + c. Suppose -3*p**4 - 2*p**2 - 6*p**3 + 0*p**3 + q*p**5 - 4*p**5 - 3*p**4 = 0. What is p?
-1, 0
Let u be 8*(-6)/(-21) - (-2)/(-7). Factor 8/7 - 8/7*p + 2/7*p**u.
2*(p - 2)**2/7
Let t(y) be the second derivative of -5*y**4/12 + y**3/6 + 8*y. Let p(h) = h**2. Let m(x) = -6*p(x) - t(x). Determine s so that m(s) = 0.
-1, 0
Let t be (-24)/(-10) - 16/40. Suppose 1/4*l**t + 1/4*l**3 + 0 - 1/2*l = 0. What is l?
-2, 0, 1
Let r(q) be the first derivative of -q**8/1680 + q**7/1050 + 3*q**2 - 5. Let s(k) be the second derivative of r(k). Factor s(h).
-h**4*(h - 1)/5
Suppose 18 - 45 = -9*x. Determine r, given that -1/3 - 1/3*r + 1/3*r**x + 1/3*r**2 = 0.
-1, 1
Suppose -7*v - 8 = -3*v. Let z be (3/v)/(2/(-4)). Let 1/3*b**5 - 1/3*b - 2/3*b**4 + 2/3*b**2 + 0*b**z + 0 = 0. Calculate b.
-1, 0, 1
Let o(b) be the first derivative of 81*b**5/5 + 81*b**4/2 + 36*b**3 + 12*b**2 + 2. Factor o(t).
3*t*(3*t + 2)**3
Let q = -4 + 9. Suppose 3*l = 3*o, -q*l + 9 + 15 = 3*o. Suppose 2*j**l - 3*j**3 + 2*j**3 - j**2 = 0. Calculate j.
0, 1
Let p(o) be the second derivative of -3*o + 1/51*o**3 + 0 + 1/170*o**5 + 0*o**2 + 1/51*o**4. Determine c so that p(c) = 0.
-1, 0
Let c(o) = -o**3 + o**2 - o + 85. Let d be c(0). Let w = -251/3 + d. Let w + 10/3*j + 8/3*j**2 + 2/3*j**3 = 0. What is j?
-2, -1
Let q(n) be the second derivative of -n**6/1800 - n**5/300 - n**3/2 - 3*n. Let t(j) be the second derivative of q(j). Determine c so that t(c) = 0.
-2, 0
Let s(t) be the third derivative of -t**6/72 + t**5/9 - 25*t**4/72 + 5*t**3/9 + 2*t**2. Find c, given that s(c) = 0.
1, 2
Let g(w) be the third derivative of -w**5/60 - w**4/8 - 13*w**2. Factor g(d).
-d*(d + 3)
Let h(d) = d + 12. Let g be h(-10). Factor -g*t**4 + 16/5*t**3 - 4/5*t + 0 - 2/5*t**2.
-2*t*(t - 1)**2*(5*t + 2)/5
Suppose -3*o = 2*o - 20. Let s(x) = -5*x + 22. Let k be s(4). Factor -4 + 0*n + k*n**3 + 3 + n**o - 2*n + 0*n.
(n - 1)*(n + 1)**3
Let f = -1471 + 1473. Find a, given that 4 - f*a + 1/4*a**2 = 0.
4
Let n(k) = 2*k**3 + 6*k**2 + 20*k + 8. Let q(w) = -w**3 - 4*w**2 - 13*w - 5. Let y(v) = -5*n(v) - 8*q(v). Factor y(j).
-2*j*(j - 2)*(j + 1)
Let y(f) be the third derivative of -f**5/12 + 5*f**4/6 - 5*f**3/2 - 14*f**2. Factor y(n).
-5*(n - 3)*(n - 1)
Factor -3*h**2 - 6*h**2 + 5 - 9*h**2 + 13*h**2.
-5*(h - 1)*(h + 1)
Let j(v) = -v**3 + 9*v**2 + 5. Let x be j(9). Suppose -4*d**5 + 2*d**5 - 4*d**5 + 4*d**x = 0. What is d?
0
Factor 7*z + 3*z**2 - 15*z + 4*z - 10*z**3 + 11*z**2.
-2*z*(z - 1)*(5*z - 2)
Let u = -199 - -399/2. Let q(f) be the first derivative of 0*f + 9/4*f**4 + 2*f**3 + u*f**2 + 2. Solve q(s) = 0 for s.
-1/3, 0
Suppose 0*y = 5*y - 20. Let o(v) be the first derivative of 8/3*v**2 - 1 - 40/3*v**3 + 0*v - 50/3*v**5 + 25*v**y. Let o(j) = 0. What is j?
0, 2/5
Factor 8*v**4 + 10*v**2 - 14*v**3 - 16*v**2 - 12*v**3 - 20*v**2 + 8*v.
2*v*(v - 4)*(v + 1)*(4*v - 1)
Let t(n) be the third derivative of -2*n**2 - 1/15*n**5 + 0 - 3/20*n**6 + 3/4*n**4 + 0*n + 2/3*n**3. Let t(c) = 0. What is c?
-1, -2/9, 1
Factor 0 - 2/17*w**2 + 4/17*w.
-2*w*(w - 2)/17
Let n be -1 + (-3 - -6) + -11. Let p(w) = w**2 + 10*w + 9. Let o be p(n). Let 2/7*i**3 - 2/7*i**2 + 0*i + o = 0. What is i?
0, 1
Let v be 1/(-15)*-6 + (-13)/(-5). Suppose 2/7 - 2/7*a**2 - 2/7*a + 2/7*a**v = 0. Calculate a.
-1, 1
Let y = -59 + 86. Let m be (-12)/(-8)*4/y. Solve 0*n**2 + 2/9*n**3 + 0 - m*n = 0.
-1, 0, 1
Let m(k) be the second derivative of k**7/840 - k**6/240 - k**5/20 - 5*k**4/12 + 6*k. Let h(n) be the third derivative of m(n). Determine o so that h(o) = 0.
-1, 2
Let f(s) be the first derivative of 0*s**3 + 0*s + 8/5*s**5 - 3*s**4 + 2*s**2 - 7. Let f(d) = 0. Calculate d.
-1/2, 0, 1
Let k(y) be the second derivative of -y**7/2520 - y**6/720 + y**4/4 - y. Let a(r) be the third derivative of k(r). Determine l so that a(l) = 0.
-1, 0
Let n be (-9)/6*8/(-6). Suppose -2*p = 10, 2*t + n*p + 1 = -t. Find k, given that 0*k**4 - t*k**4 + 2*k**4 = 0.
0
Let l = 215/573 - 8/191. Factor 2/3*x + l*x**2 - 1.
(x - 1)*(x + 3)/3
Solve 0*j - 2/11*j**2 + 0 - 2/11*j**3 = 0.
-1, 0
Let r(a) be the third derivative of a**7/140 - 3*a**6/80 + 3*a**5/40 - a**4/16 - 9*a**2. Factor r(t).
3*t*(t - 1)**3/2
Let j be 8529/(-84) - 4/(-14). Let z = j + 103. Find o, given that -3/4*o**4 + 0 - 5/4*o**5 + 3/4*o**2 + z*o**3 - 1/2*o = 0.
-1, 0, 2/5, 1
Let -5/4*c**3 + 5/4*c**2 + 3/2*c**5 + 0 - 1/4*c - 5/4*c**4 = 0. Calculate c.
-1, 0, 1/3, 1/2, 1
Suppose 0 = 5*n - 4*n + 3. Let q(y)