e v.
0, 2/7
Let v(f) = 145*f**2 - 85*f + 7. Suppose -2 + 5 = -h. Let z(g) = 72*g**2 - 42*g + 3. Let i(w) = h*v(w) + 5*z(w). Suppose i(m) = 0. What is m?
1/5, 2/5
Let c(w) be the second derivative of -w**10/3780 + w**9/7560 + w**4/4 + 3*w. Let i(d) be the third derivative of c(d). Factor i(r).
-2*r**4*(4*r - 1)
Let f(g) be the second derivative of 2*g + 0 + 0*g**2 - 1/2*g**3 + 1/40*g**6 - 1/60*g**5 + 0*g**4. Let d(o) be the second derivative of f(o). Solve d(v) = 0.
0, 2/9
Let s(v) be the third derivative of 0*v**3 + 3*v**2 - 1/6*v**4 + 0*v + 1/30*v**5 + 0. Solve s(r) = 0.
0, 2
Let o(q) be the third derivative of 1/600*q**6 + 5*q**2 + 0*q**4 + 0*q**3 + 1/300*q**5 + 0 + 0*q. Factor o(l).
l**2*(l + 1)/5
Let b(n) be the first derivative of -n**5/40 - n**4/24 + n**3/12 + n**2/4 + n - 2. Let i(j) be the first derivative of b(j). Suppose i(v) = 0. Calculate v.
-1, 1
Let k(h) be the first derivative of -h**4/10 - 2*h**3/15 + h**2/5 + 2*h/5 + 1. Factor k(z).
-2*(z - 1)*(z + 1)**2/5
Suppose -2*x = 3*t + 9, 0*t + 2*t + 25 = 5*x. Let j(g) be the first derivative of -1/12*g**x - 1/4*g + 1/4*g**2 - 2. Factor j(d).
-(d - 1)**2/4
Let f(d) = -4*d**2 - 32*d - 64. Let q(g) = -22*g**2 + 194 - 279 - 235 + 2*g**2 - 160*g. Let m(u) = -14*f(u) + 3*q(u). Determine a, given that m(a) = 0.
-4
Factor 0 + 32/3*b + 1/6*b**3 - 8/3*b**2.
b*(b - 8)**2/6
Let l(a) be the second derivative of 0*a**3 + a + 1/50*a**5 + 0*a**2 + 0 + 1/30*a**4. Find n, given that l(n) = 0.
-1, 0
Let s = 42 - 42. Suppose -3/4*r**5 + 3*r**4 + s - 3/4*r - 9/2*r**3 + 3*r**2 = 0. Calculate r.
0, 1
Factor -w**4 - w**5 + 0*w**5 + 8*w**3 - 6*w**3.
-w**3*(w - 1)*(w + 2)
Let j(t) be the third derivative of -t**8/336 + t**6/30 - t**5/30 - t**4/8 + t**3/3 - 8*t**2. Determine d so that j(d) = 0.
-2, -1, 1
Let s = 25 - 8. Suppose -6 = 3*g - 4*m, -m - 33 = g + 4*g. Let t(x) = 29*x**2 - 8*x - 3. Let k(p) = 10*p**2 - 3*p - 1. Let o(j) = g*t(j) + s*k(j). Factor o(a).
-(a + 1)*(4*a - 1)
Let s(b) be the second derivative of 0 - b + 0*b**4 + 0*b**3 - 1/70*b**5 + 0*b**2. Find n such that s(n) = 0.
0
Let x(y) be the first derivative of -y**7/840 + y**6/360 + 5*y**3/3 - 4. Let s(z) be the third derivative of x(z). Determine d, given that s(d) = 0.
0, 1
Let u(v) be the first derivative of 4 + 0*v**2 + 1/20*v**4 + 0*v - 1/30*v**6 + 1/15*v**3 - 1/25*v**5. Let u(i) = 0. Calculate i.
-1, 0, 1
Suppose -2*i - 4*i = -24. Let x(z) be the first derivative of -6*z**2 - 28/3*z**3 - 18/5*z**5 - 2*z - 8*z**i - 2/3*z**6 + 1. Factor x(m).
-2*(m + 1)**4*(2*m + 1)
Suppose -45 = -4*q - w, 8*w + 12 = 4*w. Factor -q*m**4 - 4*m**5 - 7*m**2 - 12*m**3 + 3*m**2 + 0*m**4.
-4*m**2*(m + 1)**3
Let i(z) be the first derivative of -z**4/36 + z**3/18 - 2*z - 3. Let p(t) be the first derivative of i(t). Solve p(k) = 0 for k.
0, 1
Let g(b) be the third derivative of -6*b**7/5 + 13*b**6/5 - 4*b**5/15 - 7*b**4/3 + 2*b**3 - 14*b**2. Find n, given that g(n) = 0.
-3/7, 1/3, 1
Let p(n) be the third derivative of n**7/630 + n**6/90 + n**5/30 - n**4/4 + 4*n**2. Let s(l) be the second derivative of p(l). Factor s(f).
4*(f + 1)**2
Let z(y) be the second derivative of y**5/50 - y**4/10 + y**3/5 - y**2/5 + 8*y. Let z(k) = 0. What is k?
1
Let h(c) = -c**3 + 2*c - 1. Let f be h(-2). Factor -4/9*a**f + 0*a - 2/9*a**4 - 2/9*a**2 + 0.
-2*a**2*(a + 1)**2/9
Suppose 5*x = 2*g + 3*g - 40, -4*g + 24 = -2*x. Factor s - s**4 + 3*s**3 + 6*s**2 - s**2 - 4*s**2 - g*s**2.
-s*(s - 1)**3
Let c be 0 + 2 - 0 - 0. Suppose -4*z = a + c, -1 = -a - z - 0. Suppose -1/6*q**4 + 1/6*q**3 + 0*q + 1/6*q**a - 1/6*q**5 + 0 = 0. Calculate q.
-1, 0, 1
Let m(n) be the third derivative of -1/24*n**5 - 7/48*n**4 + 4*n**2 + 0 + 1/28*n**7 + 1/6*n**3 + 0*n + 19/240*n**6. Let m(d) = 0. Calculate d.
-1, 1/3, 2/5
Let o be (-12)/(-105) - (-8)/28. Determine q, given that -o*q**2 - 2/5*q**4 + 0*q + 0 - 4/5*q**3 = 0.
-1, 0
What is h in -3/2*h + 3/2*h**4 + 0 - 3/2*h**2 + 3/2*h**3 = 0?
-1, 0, 1
Let n(f) = -f**4 + 5*f**3 - 5*f**2 - 5*f - 3. Let d(t) = 31*t**2 - 6*t**2 + 6*t**4 - 26*t**3 + 26*t + t**2 + 16. Let m(p) = -3*d(p) - 16*n(p). Factor m(z).
-2*z*(z - 1)*(z + 1)**2
Let i(v) be the first derivative of v**8/560 - 3*v**7/280 + v**6/40 - v**5/40 - 4*v**3/3 + 3. Let l(s) be the third derivative of i(s). Factor l(n).
3*n*(n - 1)**3
Factor -2*a**4 - 954*a**5 - 4*a**3 + 950*a**5 + 10*a**4.
-4*a**3*(a - 1)**2
Let y(n) be the third derivative of n**6/24 - n**5/12 - 5*n**4/12 + 16*n**2. Solve y(r) = 0.
-1, 0, 2
Let i(z) be the second derivative of z**4/12 - 23*z**3/18 - 4*z**2/3 - 47*z. Find c such that i(c) = 0.
-1/3, 8
Let l(b) be the second derivative of -5*b**5/8 + 5*b**4/12 - b**3/12 - 10*b. Determine n so that l(n) = 0.
0, 1/5
Let h(v) = -v**3 + v**2. Let j(z) = -6*z**5 + 16*z**4 - 12*z**3 - 8*z**2 + 14*z - 4. Let b(u) = 4*h(u) - j(u). Suppose b(p) = 0. Calculate p.
-1, 2/3, 1
Factor 35*s + 29*s + 72*s**2 + 82*s**2 + 8 + 98*s**3.
2*(s + 1)*(7*s + 2)**2
Factor -2/9*c**3 - 2/9*c**2 + 2/9 + 2/9*c.
-2*(c - 1)*(c + 1)**2/9
Let p(g) = -g**2 + 9*g + 1. Let u be p(10). Let a be u/3 - (-6 + 1). Let 4*j**3 + 18*j**a - 19*j**2 - 5*j**3 = 0. What is j?
-1, 0
Let q(p) be the first derivative of 9*p**4/4 - p**3 - 9*p**2/2 + 3*p - 13. Determine o, given that q(o) = 0.
-1, 1/3, 1
Let q(b) = 11*b - 24*b**3 - 5*b**2 + 0 - 6*b**2 - 1. Let v = 0 - -1. Let c(l) = l**2 + l - 1. Let g(u) = v*q(u) + c(u). Factor g(k).
-2*(k + 1)*(3*k - 1)*(4*k - 1)
Let c be (103 - 97) + 3/((-51)/100). Find s, given that 2/17 - c*s**2 + 0*s = 0.
-1, 1
Let j(w) = 3*w**3 + 2*w**2 - 4*w + 5*w - 2*w. Let o(x) = -x**3 - x**2. Let k(i) = j(i) + 4*o(i). What is m in k(m) = 0?
-1, 0
Let n(b) be the second derivative of 0 - 3/20*b**5 - 4*b + 1/2*b**3 - 1/10*b**6 + 1/4*b**4 + 0*b**2. Factor n(c).
-3*c*(c - 1)*(c + 1)**2
Let y(m) = 5*m + 4 + 4 - 1 - 4*m. Let h be y(-7). Factor 0*w**2 - 2/3*w**3 + h + 2/3*w**5 + 0*w + 0*w**4.
2*w**3*(w - 1)*(w + 1)/3
Suppose 0 = -5*g - s + 7, -2*s - 8 = -g - 0. Factor d**g + 4 + 2*d**2 + 6*d - 1.
3*(d + 1)**2
Let a(v) = v**2 - 9*v + 16. Let y be a(7). Let -2/3*z**y + 2/3*z + 0 = 0. What is z?
0, 1
Let f = 109 + -106. Let r(j) be the third derivative of j**2 + 1/18*j**f + 0 - 1/144*j**4 - 1/360*j**5 + 0*j. Factor r(l).
-(l - 1)*(l + 2)/6
Let w(y) be the third derivative of -3*y**7/70 - y**6/10 + 4*y**5/15 + 2*y**4/9 - 8*y**3/9 + 23*y**2. Find t such that w(t) = 0.
-2, -2/3, 2/3
Factor 20/3*v + 0 - 4/3*v**2.
-4*v*(v - 5)/3
Let o = 1 + 2. Determine t, given that -t + 1 - 3*t**o - t**2 + 5*t - t = 0.
-1, -1/3, 1
Let m = -15 + 11. Let v be (0 - 4)*m/56. Factor 0 - 4/7*a**2 - v*a**3 - 2/7*a.
-2*a*(a + 1)**2/7
Let h(l) be the first derivative of 2*l + 2/9*l**4 + 0*l**2 + 1/30*l**5 + 4/9*l**3 + 2. Let g(n) be the first derivative of h(n). Suppose g(y) = 0. Calculate y.
-2, 0
Let 2229*i**4 + i**5 - 2*i**3 + 5*i**3 - 2233*i**4 = 0. What is i?
0, 1, 3
Let n(o) = 3*o**3 + 2*o**2 + 13*o. Let j(k) = -k**3 - k**2 - 4*k. Let s(w) = 7*j(w) + 2*n(w). Let s(c) = 0. Calculate c.
-2, -1, 0
Let a(q) = 23*q**4 + 12*q**3 + 6*q**2 - 17*q + 17. Let f(v) = 4*v**4 + 2*v**3 + v**2 - 3*v + 3. Let b(w) = -6*a(w) + 34*f(w). What is t in b(t) = 0?
-1, 0
Let s(c) be the first derivative of 9*c**5/40 + 7*c**4/8 + c**3/8 - 9*c**2/4 - c/2 + 51. Factor s(r).
(r - 1)*(r + 2)**2*(9*r + 1)/8
Let l(s) be the third derivative of s**5/180 - s**3/18 + 7*s**2. Find r, given that l(r) = 0.
-1, 1
Let m(v) be the second derivative of -v**7/63 + v**6/15 - 2*v**4/9 - v. Factor m(s).
-2*s**2*(s - 2)**2*(s + 1)/3
Let z(t) be the third derivative of t**6/160 - t**5/40 + 3*t**2. Factor z(w).
3*w**2*(w - 2)/4
Let m be (2/(-2) + 1)/(-2). Let p(z) be the second derivative of 1/30*z**6 + 0*z**5 - 1/12*z**4 + 0 + m*z**2 + 0*z**3 - 2*z. Factor p(n).
n**2*(n - 1)*(n + 1)
Let q(i) be the second derivative of -2*i + 0*i**4 - 1/150*i**6 + 0*i**3 + 0 - 1/100*i**5 + 0*i**2. Determine f, given that q(f) = 0.
-1, 0
Let t be (6/14)/(2/7). Factor -t - k - 1/6*k**2.
-(k + 3)**2/6
Let b(h) = -9*h**3 - 9*h**2 + 12. Let c(z) = z**3. Let v(a) = -b(a) - 12*c(a). Factor v(g).
-3*(g - 2)**2*(g + 1)
Suppose 2*a - 56 = 138. Find c such that a*c**5 - 98*c**4 + 4*c**5 - 106*c**3 - 8 + 123*c**2 - 3*c**5 - 17*c**2 + 8*c = 0.
-1, -2/7, 2/7, 1
Let z = -151/3 - -51. Factor z*g**3 - 2/3*g + 2/3 - 2/3*g**2.
2*(g - 1)*