ird derivative of p(q). What is n in u(n) = 0?
0, 2
Let n(o) be the second derivative of o**6/135 + o**5/30 + o**4/18 + o**3/27 + 7*o. Factor n(s).
2*s*(s + 1)**3/9
Factor -h**3 - 70*h**2 - 2560 + 15*h**2 - 960*h - 65*h**2 - 4*h**3.
-5*(h + 8)**3
Determine p, given that -6*p**3 - 2*p**2 - 6*p**2 + 0*p**3 - 2*p = 0.
-1, -1/3, 0
Let n be (-4)/22 + 1572/(-308). Let w = 39/7 + n. Determine d so that -w*d**2 - 8/7 + 8/7*d = 0.
2
Let n be ((-6)/14)/((-155)/(-35) - 5). Determine k, given that 1/4*k**3 + n*k**4 + 3*k - 11/4*k**2 - 1 - 1/4*k**5 = 0.
-2, 1, 2
Suppose 2/7*l + 4/7 - 2/7*l**2 = 0. Calculate l.
-1, 2
Let c(y) be the first derivative of -1/24*y**4 + 2 + 0*y**2 + y + 0*y**3. Let h(d) be the first derivative of c(d). What is i in h(i) = 0?
0
Let q(y) be the second derivative of -y**6/120 - y**5/80 + y**4/48 + y**3/24 - 8*y. Solve q(o) = 0 for o.
-1, 0, 1
Let i(j) be the third derivative of j**9/20160 + j**8/3360 + j**7/1680 - j**5/10 + 8*j**2. Let y(t) be the third derivative of i(t). What is g in y(g) = 0?
-1, 0
Suppose -5/6*u - 1/2 + 1/6*u**3 - 1/6*u**2 = 0. Calculate u.
-1, 3
Let f(p) be the first derivative of p**3/2 - 3*p/2 - 2. Factor f(n).
3*(n - 1)*(n + 1)/2
Let h be (-77)/(-540) - (-12)/(-90). Let z(o) be the third derivative of 0*o**3 - o**2 + 0 + 1/90*o**5 + 0*o + h*o**6 - 1/54*o**4. Find c such that z(c) = 0.
-1, 0, 2/5
Let o = 143/2 - 71. Solve 1/4*s**3 + o*s**2 + 0 + 0*s = 0 for s.
-2, 0
Suppose 101*i - 100*i = 2. Find f, given that 1/2*f**3 - 4 + 6*f - 3*f**i = 0.
2
Let c = 1 - -3. Let p = -24/19 + 139/95. Suppose -p*i + 0 - 3/5*i**2 - 3/5*i**3 - 1/5*i**c = 0. What is i?
-1, 0
Let r(m) be the second derivative of m**5/70 + m**4/42 - 7*m. What is q in r(q) = 0?
-1, 0
Factor 1/2 + 3/4*o + 1/4*o**2.
(o + 1)*(o + 2)/4
Suppose -2 = -g + 3. Let k(o) be the second derivative of 1/10*o**g + 0 - 1/45*o**6 - 1/6*o**4 - 2*o + 1/9*o**3 + 0*o**2. Factor k(s).
-2*s*(s - 1)**3/3
Let n(m) = m**2 - 4*m - 8. Let l be n(6). Let v be 1/(2/l + 2). Factor -1/5*p - 1/5*p**5 - 1/5*p**4 + v*p**2 - 1/5 + 2/5*p**3.
-(p - 1)**2*(p + 1)**3/5
Find o, given that 4*o**2 - 1 - 3*o**2 + 5*o**2 + 5 + 14*o = 0.
-2, -1/3
Let s = -1588/15 - -46969/420. Let v = s + -40/7. Factor -1/4 + v*c**3 - 1/4*c + 1/4*c**2.
(c - 1)*(c + 1)**2/4
Let t(a) = -a - 7. Let o be t(-4). Let b(d) = d**2 + 2*d. Let c be b(o). What is l in -4*l**2 - 3*l**c + 7*l**4 + 2*l**5 + 4*l - 3*l**4 - 3*l**5 = 0?
-1, 0, 1, 2
Suppose 3*s = 5*d + 7*s - 49, 0 = -5*s + 5. Factor 31*a**4 - 9*a**3 - 34*a**4 - d*a**2 - 3*a + 0*a**2.
-3*a*(a + 1)**3
Let n = 25 - 22. Factor -12*i - 70*i**n - 4*i**4 - 4*i**2 + 0*i + 82*i**3 + 8.
-4*(i - 2)*(i - 1)**2*(i + 1)
Let x(j) be the second derivative of 1/42*j**7 - 1/2*j**2 + 1/6*j**3 + 0 - 1/10*j**5 + 1/6*j**4 - 1/30*j**6 + j. Solve x(i) = 0 for i.
-1, 1
Let y(w) be the second derivative of -w**4/30 + 2*w**3/15 + 3*w**2/5 + 3*w. Factor y(s).
-2*(s - 3)*(s + 1)/5
Let g(y) be the third derivative of -1/280*y**6 + 1/70*y**5 + 0*y**3 + 0*y + 0*y**4 + 0 + y**2. Find l such that g(l) = 0.
0, 2
Suppose -41*j + 62 + 61 = 0. Solve 3/5*p**j - 3/5 + 3/5*p**2 - 3/5*p = 0.
-1, 1
Let u(q) be the second derivative of 3*q**5/40 + q**4/8 - q**3/4 - 3*q**2/4 + 6*q. Factor u(w).
3*(w - 1)*(w + 1)**2/2
Let h(k) be the first derivative of k**4/6 + 2*k**3/9 + 6. Factor h(u).
2*u**2*(u + 1)/3
Let 1/4*x**4 + 1/2*x + 0*x**3 + 0 - 3/4*x**2 = 0. What is x?
-2, 0, 1
Let b(u) be the second derivative of -u**7/42 - u**6/30 + u**5/20 + u**4/12 - 10*u. Find y such that b(y) = 0.
-1, 0, 1
Let m(x) be the third derivative of -x**6/90 + 2*x**5/45 - 30*x**2 - x. Solve m(t) = 0 for t.
0, 2
Let i(f) be the first derivative of 0*f + 0*f**3 + 4 - 2*f**2 + 1/20*f**5 + 1/8*f**4. Let z(m) be the second derivative of i(m). Factor z(g).
3*g*(g + 1)
Suppose -3*s = 3*a + 3, -4*a + 4*s = -s - 32. Let y be (-12)/(a - 6) + -2. Factor 6/5*h**y - 2/5*h**4 + 4/5*h**3 - 8/5*h - 8/5.
-2*(h - 2)**2*(h + 1)**2/5
Let i(y) = y**3 + 16*y**2 + 2*y + 37. Let c be i(-16). Solve 0*m**3 + 1/2*m + 0 + m**4 - 1/2*m**c - m**2 = 0 for m.
-1, 0, 1
Let u(x) be the third derivative of -1/24*x**4 + 0 - 3*x**2 - 1/360*x**6 + 0*x + 1/60*x**5 + 1/18*x**3. Factor u(a).
-(a - 1)**3/3
Let j(d) be the second derivative of -d**4/16 - d**3/4 - 3*d**2/8 - 3*d. Factor j(g).
-3*(g + 1)**2/4
Suppose -3/4*f**2 - 3/2*f + 0 + 3/4*f**3 = 0. Calculate f.
-1, 0, 2
Let c(x) = -5*x**2 + 10*x - 5. Let g(l) = 5*l**2 - 10*l + 5. Let m(q) = 5*c(q) + 6*g(q). Let m(d) = 0. Calculate d.
1
Let i(u) be the first derivative of 5*u**3/3 + 5*u**2/2 + 33. Factor i(p).
5*p*(p + 1)
Let v(r) be the first derivative of -6 + 0*r + 0*r**2 - 4/3*r**3. Solve v(y) = 0 for y.
0
Let n(v) be the second derivative of -2*v**7/21 - v**6/3 - 2*v**5/5 - v**4/6 - 8*v. Suppose n(d) = 0. What is d?
-1, -1/2, 0
Suppose 0*h**3 + 2/3*h - 2/3*h**5 + 4/3*h**4 + 0 - 4/3*h**2 = 0. Calculate h.
-1, 0, 1
Let r(v) be the second derivative of -v**6/30 - v**5/20 + 11*v. Factor r(z).
-z**3*(z + 1)
Let c = 9 - 9. Let a be (2 + c)*(-6)/(-4). Solve 4/3*b**2 + 2/3*b + 2/3*b**a + 0 = 0.
-1, 0
Let q be (-19)/(-2)*(-7)/14. Let g = q + 61/12. Let 0 + 1/3*o**2 - g*o = 0. Calculate o.
0, 1
Suppose 5/3*w - 25/3*w**3 - 5/3*w**2 - 5*w**4 + 0 = 0. What is w?
-1, 0, 1/3
Let g(t) = 2*t. Let w be g(0). Determine r so that -1/4*r**3 + w*r**2 - 1/4*r**5 + 0*r + 0 + 1/2*r**4 = 0.
0, 1
Let d(s) = -s**4 + s**3 - s - 1. Let n(p) = 5*p**4 - 3*p**3 - 2*p**2 + 4*p + 4. Let m(r) = 4*d(r) + n(r). Factor m(a).
a**2*(a - 1)*(a + 2)
Let s(v) be the second derivative of -v**5/5 + 8*v**3 + 32*v**2 + 10*v. Factor s(z).
-4*(z - 4)*(z + 2)**2
Suppose 2*l = 3*f + 4*l - 6, 4*f - 5*l - 8 = 0. Determine x so that f*x**2 + x + 1 - x**2 + x = 0.
-1
What is j in 0 + 2*j + 2*j - 3 + j**2 + 7 = 0?
-2
Let w be (-3)/(1/(-2) - 1). Let u(g) = g + 1. Let r be u(7). Factor 0*c**w + r + 0*c**2 + 3*c**2 - 5*c**2.
-2*(c - 2)*(c + 2)
Let p(y) be the second derivative of -2*y**6/75 - y**5/25 + y**4/5 + 2*y**3/15 - 4*y**2/5 - 19*y. Find u such that p(u) = 0.
-2, -1, 1
Let m(s) be the third derivative of -1/21*s**3 + 0 + 0*s - 3/14*s**4 - 18/35*s**6 - 18/35*s**5 - s**2. Factor m(i).
-2*(6*i + 1)**3/7
Let s(u) = 4 + 2*u - u - 8*u**2 - 1 + 2*u - 16*u**3. Let w(o) = -48*o**3 - 24*o**2 + 10*o + 8. Let g(v) = 11*s(v) - 4*w(v). Suppose g(f) = 0. Calculate f.
-1, 1/4
Suppose 10 = 7*i - 2*i. Factor -6 - 5*y + 3*y**3 - 6*y + i*y + 0*y.
3*(y - 2)*(y + 1)**2
Let y = 437/669 + 3/223. Factor 1/3*z**2 + 0 + y*z.
z*(z + 2)/3
Let r(a) be the third derivative of -a**8/588 + a**7/245 - a**6/420 - 17*a**2. Factor r(w).
-2*w**3*(w - 1)*(2*w - 1)/7
Let f(i) be the first derivative of i**3/9 - 7*i**2/6 - 15. Factor f(v).
v*(v - 7)/3
Let l(v) be the second derivative of v**7/630 + v**6/90 + v**5/30 + 7*v**4/12 + 2*v. Let q(x) be the third derivative of l(x). Factor q(k).
4*(k + 1)**2
Let m be (-1 + 1)/1 + 3. Let t = -267/4 + 69. Factor 3/2 + t*a**m - 3/2*a**2 - 9/4*a.
3*(a - 1)*(a + 1)*(3*a - 2)/4
Let g(r) = r**5 + r**4 + r**3 + r**2 - r - 1. Let k(j) = 6*j**5 + 3*j**4 + 5*j**3 + 7*j**2 - 6*j - 5. Let c(v) = 5*g(v) - k(v). What is z in c(z) = 0?
-1, 0, 1
Let d(r) be the second derivative of 1331*r**7/21 + 1936*r**6/15 + 11*r**5/10 - 235*r**4/3 + 116*r**3/3 - 8*r**2 + 10*r + 1. Factor d(n).
2*(n + 1)**2*(11*n - 2)**3
Let v(k) be the first derivative of k**3/2 + 3*k**2/2 - 9*k/2 - 1. Factor v(s).
3*(s - 1)*(s + 3)/2
Let n = 7 - 7. Let g(k) be the second derivative of -k + n - 1/50*k**5 + 0*k**2 + 1/75*k**6 + 0*k**3 - 1/30*k**4 + 1/105*k**7. Factor g(i).
2*i**2*(i - 1)*(i + 1)**2/5
Let m(o) be the third derivative of o**8/1512 - 4*o**7/945 + o**6/540 + o**5/27 - o**4/27 - 8*o**3/27 - 8*o**2. Factor m(b).
2*(b - 2)**3*(b + 1)**2/9
Let x(g) be the third derivative of -g**6/280 + g**5/70 - 4*g**2. What is d in x(d) = 0?
0, 2
Let y(a) be the second derivative of 2*a**7/21 + 8*a**6/15 + 4*a**5/5 - 2*a**4/3 - 10*a**3/3 - 4*a**2 + 5*a. Factor y(p).
4*(p - 1)*(p + 1)**3*(p + 2)
Let y be (-8)/(-8)*4/2. Let w(b) be the first derivative of 2 + 0*b**4 - 2/3*b**3 + 0*b**y + 0*b + 2/5*b**5. Factor w(o).
2*o**2*(o - 1)*(o + 1)
Find f such that 1 - f + 1/4*f**2 = 0.
2
Let w(f) = f + 3. Let y be w(-3). Let v = 83 - 413/5. What is l in -1/5*l**3 + y - v*l - 3/5*l**2 = 0?
-2, -1, 0
Let j be (-18)/(-3)