0 - 3*u**2. Let x(s) be the third derivative of l(s). Determine q so that x(q) = 0.
0, 1
Determine c so that 24/7*c + 16/7 + 2/7*c**3 + 12/7*c**2 = 0.
-2
Let r(d) be the third derivative of d**6/120 - d**5/10 + 3*d**4/8 - 2*d**3/3 - 19*d**2. Factor r(x).
(x - 4)*(x - 1)**2
Factor 16/3 - 6*f + 2/3*f**2.
2*(f - 8)*(f - 1)/3
Let b(c) be the first derivative of 4*c**5/5 + 3*c**4 + 4*c**3 + 2*c**2 - 3. Factor b(l).
4*l*(l + 1)**3
Let l(z) = z**2 + 14*z + 3. Let k be l(-14). Let m(c) be the first derivative of -1/3*c**k - c**2 - c + 4. Factor m(s).
-(s + 1)**2
Let g be 8/4 + -3 - -9. Let y(l) be the first derivative of -24*l**2 - 2 - 49/3*l**6 + 73/2*l**4 - g*l - 34/3*l**3 + 42/5*l**5. Find p, given that y(p) = 0.
-1, -2/7, 1
Let m(w) = 3*w**2 - 15*w + 4. Let q be m(5). Let f = 1/62 - -108/31. Factor 3/2*y + 3/2*y**2 - 1 - f*y**3 + 3/2*y**q.
(y - 1)**3*(3*y + 2)/2
Let z(w) be the second derivative of w**7/126 + w**6/90 + 6*w. Find y such that z(y) = 0.
-1, 0
Let a(b) = -2*b - 2. Let d be a(3). Let f be (-4)/3*2/d. Let -1/3*l**3 + 0*l + 1/3*l**5 + 1/3*l**2 + 0 - f*l**4 = 0. What is l?
-1, 0, 1
Let d(q) = q**2 + 9*q - 1. Let j(a) = -2*a**2 - 8*a. Let p(m) = 2*d(m) + 3*j(m). Factor p(o).
-2*(o + 1)*(2*o + 1)
Let 1/2 - 7/4*g + 5/4*g**2 = 0. What is g?
2/5, 1
What is l in 3/7*l**2 - 9/7*l + 0 = 0?
0, 3
Let u(d) = -d**3 - 5*d**2 - 11*d - 4. Let f(m) = 4*m**3 + 20*m**2 + 43*m + 16. Let p(a) = 6*f(a) + 22*u(a). Factor p(n).
2*(n + 1)*(n + 2)**2
Determine l so that -39/2*l + 6*l**2 + 9/2 = 0.
1/4, 3
Let t(m) = -1. Let u(q) = 2*q**3 - 2*q**2 - 10. Let f = 23 + -33. Let b(r) = f*t(r) + u(r). Factor b(l).
2*l**2*(l - 1)
Let q(x) = x**2 + 2*x + 3. Let n(m) = -m**2 - 2*m - 4. Let v(p) = -6*n(p) - 7*q(p). Factor v(s).
-(s - 1)*(s + 3)
Let o(v) = v + 12. Let t be o(-8). Suppose q = 8*u - 4*u + 7, 0 = -2*q - t*u + 2. Factor g + 0*g**q + g**5 + 0*g**3 - 2*g**3.
g*(g - 1)**2*(g + 1)**2
Let k(b) be the first derivative of 3*b**5/5 + 9*b**4/16 - b**3/4 - 5. Determine n, given that k(n) = 0.
-1, 0, 1/4
Suppose 11 = 3*o - 1. Let -b**o - 4*b**3 - 2*b**3 + 4*b**3 + b**2 + 2*b**5 = 0. What is b?
-1, 0, 1/2, 1
Suppose 6*x = 7*x - 3. Factor 0*z + 2/3*z**2 - 2/3*z**x + 0.
-2*z**2*(z - 1)/3
Let t(j) be the second derivative of 2*j**6/75 + j**5/50 - j**4/15 - j**3/15 + 5*j. Solve t(w) = 0 for w.
-1, -1/2, 0, 1
Let l be 4*1 - 3832/960. Let n(f) be the third derivative of 0 + l*f**5 - 1/48*f**4 + 0*f - 1/6*f**3 - 3*f**2. Factor n(m).
(m - 2)*(m + 1)/2
Let v(p) be the first derivative of -p**5/240 + p**4/96 + p**3/12 - 2*p**2 - 6. Let s(j) be the second derivative of v(j). Let s(w) = 0. Calculate w.
-1, 2
Let f(t) be the first derivative of t**4/20 + t**3/15 + 6. Factor f(l).
l**2*(l + 1)/5
Let m be 0/(-1) + (9 - 6). Factor m*i - 3*i - i**3 + i.
-i*(i - 1)*(i + 1)
Let b = -15 + 22. Let l be 1 - (-3 - (1 + -3)). Factor 0 - 4 + 2*t - 5*t - 8*t**2 - l*t**3 - b*t.
-2*(t + 1)**2*(t + 2)
Let p(o) be the second derivative of o**5/270 + 2*o**4/27 + 16*o**3/27 + 3*o**2 - 9*o. Let u(z) be the first derivative of p(z). Factor u(j).
2*(j + 4)**2/9
Let h(o) = -o**2 + 6*o + 19. Let r be h(8). Let j(t) be the first derivative of 0*t + 0*t**r + 0*t**2 + 1/5*t**5 + 0*t**4 + 2. Solve j(n) = 0.
0
Let d(f) be the third derivative of f**8/20160 - f**7/630 + f**6/45 + f**5/20 - 8*f**2. Let u(w) be the third derivative of d(w). Determine l so that u(l) = 0.
4
Let h = -187/5 + 2077/55. Factor -2/11*q**2 + h*q - 2/11.
-2*(q - 1)**2/11
Let i(t) = -t - 2. Let l be i(-4). Let o be (3 + (-10)/4)*6. Factor -1/2*h**5 - l*h**2 + 0 - o*h**3 - 1/2*h - 2*h**4.
-h*(h + 1)**4/2
Let w(u) be the third derivative of u**6/720 + u**5/180 - 5*u**2. Factor w(s).
s**2*(s + 2)/6
Let s be 9/((30/(-28))/(-5)). Suppose s = 5*b + 7. Factor c**3 + c**5 + 5*c**5 - b*c**5.
-c**3*(c - 1)*(c + 1)
Let i(s) = -s - 5. Let p be i(-7). Let -2 - 2*j + 2*j**2 - 4*j**p + 2 = 0. What is j?
-1, 0
Let 0*f + 4/9*f**2 + 2/9*f**3 - 2/9*f**4 + 0 = 0. What is f?
-1, 0, 2
Let r(t) be the first derivative of -2/3*t**3 - 1/4*t**4 + 2 + 0*t - 1/2*t**2. Suppose r(v) = 0. Calculate v.
-1, 0
Determine y so that 2/5*y + 0 - 2/5*y**3 + 2/5*y**2 - 2/5*y**4 = 0.
-1, 0, 1
Let o be ((-2)/(-9))/((-6)/(-18)). Let u(h) be the first derivative of -11/6*h**2 + o*h + h**3 - 1. Suppose u(i) = 0. Calculate i.
2/9, 1
Let r(a) be the second derivative of 1/21*a**7 - 1/6*a**4 + 0*a**3 - a + 1/15*a**6 + 0 - 1/10*a**5 + 0*a**2. Solve r(k) = 0 for k.
-1, 0, 1
Let k be (-1 - (4 - 8))*2. Let a(j) be the second derivative of -3*j + 1/84*j**7 + 0*j**4 + 1/60*j**k + 0 + 0*j**5 + 0*j**3 + 0*j**2. Solve a(q) = 0.
-1, 0
Suppose 2*t + 2*q = 4*t - 10, 23 = 5*t - 4*q. Suppose -5*u - t*k = -0*u, 5*k = 5*u - 40. What is x in 3*x**u - 4*x**3 - 4*x**2 + 6*x**2 - 3*x**2 = 0?
-1, 0
Let a(y) be the second derivative of -y**5/5 - 2*y**4/3 + 2*y**3/3 + 4*y**2 + 9*y. Factor a(i).
-4*(i - 1)*(i + 1)*(i + 2)
Let j(k) be the second derivative of k**4/28 + 2*k**3/7 + 6*k**2/7 + 6*k. Solve j(h) = 0 for h.
-2
Let m**2 + 4*m**2 - 5*m**4 + m + 7*m**3 + m**5 - 4*m**3 - 5*m**5 = 0. Calculate m.
-1, -1/4, 0, 1
Factor -16*o - 15*o**3 + 43*o**3 + 12 - 6*o**2 - 4*o**4 - 12*o**3 - 2*o**2.
-4*(o - 3)*(o - 1)**2*(o + 1)
Let t(u) be the second derivative of u**5/200 + u**4/120 - u**3/30 + 3*u. Let t(p) = 0. What is p?
-2, 0, 1
Suppose 5*h - 4 - 11 = 0. Let k(d) be the third derivative of 0*d**h + 0*d**5 - 1/210*d**7 + 2*d**2 + 0*d + 1/120*d**6 + 0 + 0*d**4. What is m in k(m) = 0?
0, 1
Determine h, given that -2/3*h + 1/3*h**2 + 1/3 = 0.
1
Let t(p) be the third derivative of -p**10/6048 - p**9/1890 - p**8/6720 + p**7/1260 - p**4/8 + 3*p**2. Let h(w) be the second derivative of t(w). Factor h(j).
-j**2*(j + 1)**2*(5*j - 2)
Let l(f) be the third derivative of -f**6/1440 + f**5/240 - f**4/96 + f**3/6 - 2*f**2. Let a(y) be the first derivative of l(y). Factor a(o).
-(o - 1)**2/4
Suppose a - 10 = -4*h, -6*a - 19 = -3*h - a. Let r(o) be the first derivative of 1/2*o**2 + 0*o + 5/6*o**h + 1/8*o**4 - 1/5*o**5 - 3. Factor r(f).
-f*(f - 2)*(f + 1)*(2*f + 1)/2
Let l = -7 + 7. Let q be (l + 0/(-2))/(-1). Factor -i**4 + 1/3*i**3 + q + 0*i + 2/3*i**2.
-i**2*(i - 1)*(3*i + 2)/3
Let h(m) = -m**2 + 13*m + 5. Let s(c) = -c**2 + 25*c + 11. Let o(i) = 5*h(i) - 3*s(i). Factor o(r).
-2*(r + 1)*(r + 4)
Let k(n) be the second derivative of 1/50*n**5 + 1/75*n**6 - 1/30*n**4 + 2*n - 1/15*n**3 + 0*n**2 + 0. Solve k(w) = 0.
-1, 0, 1
Let v(j) be the second derivative of 2*j**6/15 - 7*j**5/5 + 5*j**4/3 + 14*j**3/3 - 12*j**2 - 74*j. What is k in v(k) = 0?
-1, 1, 6
Let b = 153/644 - -2/161. Let z(r) be the second derivative of 0 + b*r**3 - 1/8*r**4 - 2*r + 1/40*r**5 - 1/4*r**2. Find q such that z(q) = 0.
1
Let p = 4 + -4. Factor 2*h**5 + h + 6*h**3 - h**5 + 0*h**3 + 4*h**2 + 4*h**4 + p*h.
h*(h + 1)**4
Let v(q) be the third derivative of 0*q + 0 + 1/300*q**5 + 1/60*q**4 - 2*q**2 + 1/30*q**3. Factor v(d).
(d + 1)**2/5
Suppose -2*m = 14*m - 32. Solve -4/5 - 2/5*z**m + 6/5*z = 0 for z.
1, 2
Let y be ((-63)/28*-2)/3. Let -3/2*b**2 - 1/2 + 1/2*b**3 + y*b = 0. What is b?
1
Let d(y) be the first derivative of -3*y**2/2 + y + 1. Let u be d(-1). Determine m so that 0*m**2 + 0 + 0*m**u - 4/9*m**3 + 2/9*m + 2/9*m**5 = 0.
-1, 0, 1
Suppose 0 = 5*d - r - r - 6, 2*d - 3*r = 9. Let a(y) be the second derivative of -2/3*y**3 - 1/6*y**4 - y**2 + 2*y + d. Factor a(x).
-2*(x + 1)**2
Suppose g + g - 8 = 0. Factor -3*r**3 + 2*r**5 - 8*r**4 - g*r**2 + 0*r**5 + 9*r**3 + 4*r**3.
2*r**2*(r - 2)*(r - 1)**2
Let c(j) be the second derivative of -j**7/14 - j**6/2 - 27*j**5/20 - 7*j**4/4 - j**3 - 11*j. Find t such that c(t) = 0.
-2, -1, 0
Let b(n) be the second derivative of n**4/4 - n**3/2 + 9*n. Factor b(p).
3*p*(p - 1)
Let q(l) be the second derivative of l**4/6 + l**3/2 + l**2/2 + 11*l. Factor q(v).
(v + 1)*(2*v + 1)
Let x = 108/7 - 15. Let h(q) be the first derivative of -x*q**4 + 2 + 0*q - 1/21*q**6 + 8/21*q**3 - 1/7*q**2 + 8/35*q**5. Factor h(b).
-2*b*(b - 1)**4/7
Let w(z) be the third derivative of 2*z**2 + 1/3*z**3 + 0*z + 0 - 1/1440*z**6 + 1/48*z**4 - 1/480*z**5. Let o(q) be the first derivative of w(q). Factor o(i).
-(i - 1)*(i + 2)/4
Let b(m) be the third derivative of -m**6/120 - m**5/30 - m**4/12 + 3*m**2. Let h be b(-2). Factor -2*i**3 - 2*i**3 + 0*i**4 - 14*i*