Let g = -7 + p. Let g*i**2 + 2*i**5 + 2*i**2 + 2*i**3 + 0*i**2 - 2*i**4 - 4*i**3 = 0. Calculate i.
-1, 0, 1
Let o(u) be the third derivative of -2*u**7/735 - u**6/70 - u**5/35 - u**4/42 - 12*u**2. Determine f, given that o(f) = 0.
-1, 0
Let y(o) be the second derivative of o**5/10 + o**4/3 + o**3/3 - 3*o. Suppose y(w) = 0. Calculate w.
-1, 0
Let i(s) be the first derivative of s**3/3 + 7*s**2/2 + 2*s + 1. Let o be i(-7). Factor -3*l**2 + 0*l**2 + l**o.
-2*l**2
Let i be (65/26)/((-4)/(-94)). Suppose 175/4*p**4 + 145/4*p**2 - 10*p - i*p**3 - 49/4*p**5 + 1 = 0. What is p?
2/7, 1
Factor 4/3*g + 0 - 1/3*g**3 + 0*g**2.
-g*(g - 2)*(g + 2)/3
Let u = 50 + -46. Let h(l) be the second derivative of 1/42*l**u + 0*l**3 + 0 + 0*l**2 - 3*l. Let h(m) = 0. What is m?
0
Let w(b) = -2*b**3 - 9*b**2 + 11*b + 7. Let f(y) = 2*y**2 + 6*y - y**3 + 2 + 2 - 7*y**2. Let z(l) = -7*f(l) + 4*w(l). Factor z(i).
-i*(i - 1)*(i + 2)
Suppose 72*s - 81*s = 0. Let -1/6*q**3 + 0*q**2 + 0*q - 1/6*q**5 + s + 1/3*q**4 = 0. What is q?
0, 1
Let g(q) be the second derivative of 7*q**6/120 + q**5/40 + 30*q. Factor g(h).
h**3*(7*h + 2)/4
Let y(n) be the second derivative of -4*n**3/3 - 2*n**2 - n. Let f(g) = -g**2 + 32*g + 15. Let p(z) = 2*f(z) + 9*y(z). Factor p(k).
-2*(k + 1)*(k + 3)
Let m be 1 + -4 + 11 - 2. Find q, given that 10*q**2 + m*q**3 - 6*q**5 + 4*q - 3*q**4 - 7*q**4 - 4*q**3 = 0.
-1, -2/3, 0, 1
Let h = 18 + -4. Let z(d) = -9*d**2 + 7*d + 7. Let t(n) = -4*n**2 + 3*n + 3. Let q(k) = h*t(k) - 6*z(k). Factor q(m).
-2*m**2
Let z(q) be the third derivative of -q**8/8960 + q**7/10080 + q**6/1440 - q**4/6 - 6*q**2. Let x(m) be the second derivative of z(m). Factor x(b).
-b*(b - 1)*(3*b + 2)/4
Let q(j) be the second derivative of j**5/20 - j**2/2 - 3*j. Let b(d) = 3*d**3 - 2*d**2 + 2*d - 3. Let n(p) = -b(p) + 5*q(p). Find i, given that n(i) = 0.
-1, 1
Find r such that -7*r**2 + 0*r**3 + 0*r**3 + 4*r**3 - 5*r**2 = 0.
0, 3
Let n = -20 - -6. Let s = 14 + n. Factor 2/9 + s*q - 2/9*q**2.
-2*(q - 1)*(q + 1)/9
Let p(a) be the second derivative of -a**9/45360 - a**8/20160 - a**4/12 - 2*a. Let r(k) be the third derivative of p(k). Find z such that r(z) = 0.
-1, 0
Let m = -37/68 + 22/17. Let m*o**2 + o + 1/4*o**4 - 1 - o**3 = 0. What is o?
-1, 1, 2
Let t(y) be the first derivative of 5/22*y**4 + 0*y - 9/11*y**2 - 2/55*y**5 - 2/11*y**3 - 7. What is m in t(m) = 0?
-1, 0, 3
Let n(c) be the first derivative of 0*c + 0*c**5 - 1/9*c**3 - 1/8*c**4 + 0*c**2 + 1/36*c**6 + 6. Factor n(t).
t**2*(t - 2)*(t + 1)**2/6
Let l(f) = f**3 + 2*f**2 - 3*f. Let n = -13 + 10. Let k be l(n). Factor 1/2*w**3 + 0*w + w**2 + k.
w**2*(w + 2)/2
Let j(g) be the third derivative of -g**9/18144 - g**8/10080 - g**3/3 + g**2. Let d(i) be the first derivative of j(i). What is s in d(s) = 0?
-1, 0
Factor -12*u + 106*u**4 + 96*u**2 - 69*u**3 + 41*u**4 - 162*u**3.
3*u*(u - 1)*(7*u - 2)**2
Suppose 0 = -13*n + 8*n. Find o, given that -2/7*o**4 + 2/7*o**3 + 0 + n*o + 0*o**2 = 0.
0, 1
Let c(n) = 2*n**3 - n - 4*n - 5*n**2 - 3*n**3. Let u be c(-4). Factor u*m**3 + 2*m**2 + 2*m**4 - 4 + 4.
2*m**2*(m + 1)**2
Let d be (-2*(3 - 4))/(1 - 0). Factor -2*a - 2 - 1/2*a**d.
-(a + 2)**2/2
Let y(n) be the third derivative of n**9/83160 - n**8/36960 - n**7/13860 + n**6/3960 + n**4/8 - 3*n**2. Let d(i) be the second derivative of y(i). Factor d(j).
2*j*(j - 1)**2*(j + 1)/11
Let i be -2 - (0 + -2) - -2. Find a, given that 0*a**2 - 4 + 3*a + i + 0*a**2 - a**2 = 0.
1, 2
Suppose 0 - 6/7*y - 3/7*y**2 = 0. What is y?
-2, 0
Determine q, given that -987/5*q**2 + 1344/5*q**5 - 36*q - 12/5 - 1296/5*q**4 - 2244/5*q**3 = 0.
-2/7, -1/4, 2
Let v(z) = 4*z**2 + 0 - 5 - z**2 - z. Let c(p) = -p**2 + 2. Suppose -8 = 5*d + 2. Let j(q) = d*v(q) - 5*c(q). Factor j(n).
-n*(n - 2)
Let d = 1 - 0. Suppose s - d = 1. Determine g so that 3*g**s + g**2 - 3*g**2 = 0.
0
Let c(f) be the second derivative of f**5/30 - f**3/9 - 3*f. Factor c(v).
2*v*(v - 1)*(v + 1)/3
Let p(s) be the first derivative of -s**5/10 - s**4/4 + s**2/2 + s/2 + 4. Factor p(x).
-(x - 1)*(x + 1)**3/2
Factor -4/15*j + 2/15*j**4 + 2/15*j**5 - 2/3*j**2 + 0 - 2/5*j**3.
2*j*(j - 2)*(j + 1)**3/15
Let b = 8 - 5. Factor 6*a - 9*a**3 - 6*a**2 - 6*a**b - 3*a**2.
-3*a*(a + 1)*(5*a - 2)
Suppose 0 = 5*h - 10*h. Let a(u) be the third derivative of 0*u - 1/15*u**6 - 1/30*u**7 + 7/144*u**8 + 0 - 1/45*u**5 + 0*u**4 + h*u**3 + 2*u**2. Factor a(n).
n**2*(n - 1)*(7*n + 2)**2/3
Suppose -4/17*q - 2/17*q**2 - 2/17 = 0. What is q?
-1
Let r(q) be the third derivative of -q**7/735 + q**6/210 + q**5/210 - q**4/42 - 5*q**2. Find j such that r(j) = 0.
-1, 0, 1, 2
Determine o so that 44*o**5 - 95*o**5 - 2*o**2 + 5*o**3 + 52*o**5 - 4*o**4 = 0.
0, 1, 2
Let b(w) = 6*w - 30. Let g be b(5). Factor 1/3*z**2 - 1/3 + g*z.
(z - 1)*(z + 1)/3
Let j(k) be the third derivative of 1/120*k**5 + 4*k**2 + 1/12*k**3 + 1/24*k**4 + 0*k + 0. Factor j(w).
(w + 1)**2/2
Let c(y) be the first derivative of -y**4/4 - 3*y**3/2 - 3*y**2 - y + 3. Let j(h) be the first derivative of c(h). Factor j(a).
-3*(a + 1)*(a + 2)
Factor 5/3*x + 10/3 - 5/3*x**2.
-5*(x - 2)*(x + 1)/3
Let l(q) = q - 1. Let b(v) = -2*v**2 + 2*v. Let p(z) = b(z) - 4*l(z). Factor p(s).
-2*(s - 1)*(s + 2)
Let o(z) = -2*z**3 + z**2 - 3*z + 3. Let m(x) = -2*x**3 - 2*x + 2. Let d(h) = 6*m(h) - 4*o(h). Factor d(q).
-4*q**2*(q + 1)
Let d(p) be the third derivative of -1/80*p**6 + 1/32*p**4 + 0 + 1/448*p**8 + 1/4*p**3 - 1/20*p**5 + 1/140*p**7 + 0*p - 10*p**2. Find g, given that d(g) = 0.
-2, -1, 1
Let i = 875/82 - 1/246. Factor 14/3*t**2 + i*t + 8/3.
2*(t + 2)*(7*t + 2)/3
Let h(t) = 2*t**2 + 1. Let g(s) = 2*s**2 + 2. Let r(p) = -3*g(p) + 4*h(p). What is f in r(f) = 0?
-1, 1
Suppose 43 = -s + 140. Find h such that -2 + s*h + 2*h**2 - 97*h = 0.
-1, 1
Determine x so that 7*x**3 + 4*x**2 - 10*x + 2*x + 0*x**2 + 5*x**3 = 0.
-1, 0, 2/3
Let u(o) be the first derivative of -o**5/15 - o**4/6 + o**3/3 + 30. Find d such that u(d) = 0.
-3, 0, 1
Let k(n) be the first derivative of 0*n**2 - 1/12*n**4 - 3 + 0*n + 1/40*n**5 + 1/3*n**3 - 1/360*n**6. Let c(z) be the third derivative of k(z). Factor c(l).
-(l - 2)*(l - 1)
Let q(w) be the third derivative of -2*w**7/105 - w**6/5 - 3*w**5/5 - 9*w**2. Suppose q(p) = 0. What is p?
-3, 0
Let w(u) be the third derivative of -u**6/60 + u**5/30 + 2*u**4/3 - 4*u**3 - 54*u**2. Factor w(m).
-2*(m - 2)**2*(m + 3)
Let g(v) be the first derivative of -v**8/560 - v**7/140 - v**6/120 + 2*v**3 - 1. Let y(s) be the third derivative of g(s). Factor y(i).
-3*i**2*(i + 1)**2
Let c(b) be the second derivative of b**7/2940 - b**5/420 + b**3/2 - b. Let i(k) be the second derivative of c(k). Solve i(u) = 0.
-1, 0, 1
Let x(h) = h + 4. Let u be x(-4). Suppose -5*t + 4*l = 20, 0*t - 4*l = 2*t - 20. Factor 2/3*v**2 - 2/3*v**4 + u*v + 0 + t*v**3.
-2*v**2*(v - 1)*(v + 1)/3
Let z(p) be the first derivative of 2/3*p**3 - 3 + p**2 + 4*p + 1/6*p**4. Let o(j) be the first derivative of z(j). Factor o(d).
2*(d + 1)**2
Factor -6*h**4 - 15*h**2 + 199*h**3 + 3*h**4 - 181*h**3.
-3*h**2*(h - 5)*(h - 1)
Let d(c) be the second derivative of -c**5/30 + c**4/18 + 29*c. Determine g so that d(g) = 0.
0, 1
Let b(o) be the first derivative of o**6/2160 + o**3/3 + 4. Let z(d) be the third derivative of b(d). Factor z(c).
c**2/6
Let j(c) = c**3 - 5*c**2 - 5*c. Let k be j(6). Suppose u = -2*u + k. Factor -11*d**4 + 9*d**4 + u*d**3 + 8*d**4 - 4*d**2.
2*d**2*(d + 1)*(3*d - 2)
Let v(t) be the third derivative of -t**5/20 + t**4/4 + 2*t**2. Let v(b) = 0. Calculate b.
0, 2
Let r be -2 - (4 + 50/(-8)). Let g(k) be the first derivative of 3/2*k**2 + k + r*k**4 + 1 + k**3. Factor g(m).
(m + 1)**3
What is l in 1/4 + 1/2*l**3 - 1/4*l - 1/2*l**2 - 1/4*l**5 + 1/4*l**4 = 0?
-1, 1
Let o be (-29)/2*1*1. Let y = 15 + o. What is f in -f**3 + 0 - 1/2*f**2 - y*f**4 + 0*f = 0?
-1, 0
Let n(p) = -p + 1. Let b(y) = -2*y + 8. Let v be b(9). Let i(h) = -2*h**2 + 9*h - 5. Let f(j) = v*n(j) - 2*i(j). Factor f(u).
4*u*(u - 2)
What is d in 2/3*d**3 + 0 + 0*d + 0*d**2 + 0*d**4 - 2/3*d**5 = 0?
-1, 0, 1
Factor 6/7*z + 3/7*z**2 + 0.
3*z*(z + 2)/7
Let a = 848/9 - 94. Let p(r) be the first derivative of 4 - 8/3*r - a*r**3 - 4/3*r**2. Factor p(m).
-2*(m + 2)**2/3
Let w(t) be the third derivative of 1/420*t**6 + 0*t**3 + 4*t**2 + 1/21*t**4 + 0*t + 2/105*t**5 + 