et d = 67 - 61. Let h(w) be the third derivative of -1/18*w**3 + 2*w**2 + 1/90*w**5 + 0*w**4 + 0*w**d + 0 + 0*w - 1/630*w**7. Factor h(j).
-(j - 1)**2*(j + 1)**2/3
Let i be 60/112 + 4/(-48)*3. Let k be ((-10)/(-6))/((-1)/(-3)). Find p, given that i*p**2 + 0*p + 0 - 2/7*p**4 + 2/7*p**k - 2/7*p**3 = 0.
-1, 0, 1
Let z = 4 + 10. Suppose 5*h - z = -4. Factor 5*w**2 - w**2 - 2*w**5 + 0*w + h*w - 4*w**4.
-2*w*(w - 1)*(w + 1)**3
Let x be 2/168*46 - 0. Let q = x - 1/21. Factor 1/2*k**2 + 1/2*k**3 - q*k + 0 - 1/2*k**4.
-k*(k - 1)**2*(k + 1)/2
Let k(l) be the third derivative of -1/672*l**8 + 3*l**2 + 0*l**4 + 0*l**5 + 0*l + 1/420*l**7 + 0 + 0*l**6 + 0*l**3. Factor k(i).
-i**4*(i - 1)/2
Let d = -8 + 13. Let -o**2 + 5 + 2*o**2 + o - d = 0. Calculate o.
-1, 0
Let h(s) = s**2 + 6*s + 4. Let n be h(-6). Let 0*c**4 - 5*c**4 + n*c**4 + c**3 = 0. What is c?
0, 1
Let b(c) be the second derivative of -5*c**4/21 - 2*c**3/3 - 4*c**2/7 + 11*c. Factor b(p).
-4*(p + 1)*(5*p + 2)/7
Let b be 1/(-3) + 20/24. Let f be 4 + (-332)/80 + 4/10. Determine y, given that 1/4*y**2 + f - b*y = 0.
1
Let a(o) be the second derivative of -1/210*o**7 + 0*o**2 - 1/50*o**6 + 0 + 0*o**3 - 1/60*o**4 + 3*o - 3/100*o**5. Determine u, given that a(u) = 0.
-1, 0
Let a(x) be the first derivative of 1/6*x**3 + 0*x**2 - 2/3*x + 1/24*x**4 + 10. Factor a(j).
(j - 1)*(j + 2)**2/6
Let b be (-1)/(-6)*(-44)/(-33). Let n(g) be the first derivative of 5/6*g**4 + 0*g - 8/15*g**5 - 3 - b*g**3 + 0*g**2. Factor n(p).
-2*p**2*(p - 1)*(4*p - 1)/3
Let z(h) = h + h + 1 - 17*h**2 + 22*h**2. Let q be z(-1). Let 2/7*m**3 + 0 - 2/7*m**5 + 0*m + 0*m**q + 0*m**2 = 0. Calculate m.
-1, 0, 1
Let c(g) be the second derivative of -g**6/10 - g**5/2 - g**4 - g**3 - g**2/2 + g. Factor c(v).
-(v + 1)**3*(3*v + 1)
Let z(d) be the second derivative of -d**5/4 + 5*d**4/4 - 5*d**3/3 - 10*d. Find o, given that z(o) = 0.
0, 1, 2
Solve 0*q**2 + 4/3*q**3 + 0 + 0*q - 1/3*q**4 = 0 for q.
0, 4
Let i(z) be the third derivative of -z**7/3780 - z**6/270 - z**5/45 - z**4/12 - 3*z**2. Let o(t) be the second derivative of i(t). Solve o(s) = 0 for s.
-2
Suppose k**4 + 1/3*k**5 + 0 + 0*k + k**3 + 1/3*k**2 = 0. Calculate k.
-1, 0
Suppose 4*z + 5*p - 30 = -12, z + 4*p - 10 = 0. Suppose -2*x - z*b + 12 = 0, -x + 4*b = -0*b + 14. Factor -1 - n**3 - 2*n**x + 2 - 1 - n.
-n*(n + 1)**2
Let i(q) be the first derivative of -q**5/20 + q**4/6 - q**3/6 - 6*q + 3. Let c(k) be the first derivative of i(k). Factor c(m).
-m*(m - 1)**2
Let a(v) be the third derivative of -v**7/42 + v**5/12 + 5*v**2. Factor a(f).
-5*f**2*(f - 1)*(f + 1)
Let i(h) be the first derivative of h**6/540 + h**5/90 + 7*h**3/3 + 9. Let m(f) be the third derivative of i(f). Factor m(n).
2*n*(n + 2)/3
Let i = -224 - -899/4. What is j in -i*j**3 - j**4 - 1/4 + 3/4*j + 5/4*j**2 = 0?
-1, 1/4, 1
Let r = -2 - -4. Let b be 2/24*24/9. Find g such that -b + 0*g**3 + 4/9*g**r - 2/9*g**4 + 0*g = 0.
-1, 1
Let o(l) be the third derivative of l**7/15120 - l**5/720 - l**4/12 - 4*l**2. Let j(x) be the second derivative of o(x). Factor j(c).
(c - 1)*(c + 1)/6
Let o(a) = a**3 - 5*a**2 + 2. Let v be o(5). Factor 2*s**2 + 2 - v - 6*s + 4.
2*(s - 2)*(s - 1)
Let h(p) = 0*p + 0 - p + 7. Let j be h(5). Find s, given that 2*s**2 - 1 - s**5 + j*s**3 - s - 2*s - s**4 + 2*s = 0.
-1, 1
Suppose -2*x - 30 = -3*x + 5*b, -5 = b. Let 10*r**3 + 30*r**2 - 8 + r - 17*r - 22*r**4 + x*r**5 + r**5 = 0. Calculate r.
-1, -1/3, 1, 2
Suppose -13*a + 23 = -16. Determine s, given that 0*s**2 + 0*s + 1/2*s**a + 0 + 1/2*s**4 = 0.
-1, 0
Let b(k) be the first derivative of -1/4*k**4 - 2*k + 2 + 1/2*k**2 + 2/3*k**3. Factor b(c).
-(c - 2)*(c - 1)*(c + 1)
Let d(x) = -3*x**2 - 5*x - 3. Let m(k) = 4*k**2 - 13 - 14*k**2 - 2*k**2 - 21*k. Let j(z) = 26*d(z) - 6*m(z). Factor j(f).
-2*f*(3*f + 2)
Let g(a) be the third derivative of a**6/200 + a**5/100 - a**4/40 - a**3/10 - 9*a**2. Determine m, given that g(m) = 0.
-1, 1
Let z(q) be the third derivative of -1/40*q**5 - 3*q**2 - 1/4*q**3 - 1/8*q**4 + 0 + 0*q. Find n, given that z(n) = 0.
-1
Let o(q) = 3*q**3 + 9*q**2 - 6. Let w(a) = 4*a**3 + 10*a**2 - 7. Let k be 1/2 - (-26)/4. Let r(z) = k*o(z) - 6*w(z). What is g in r(g) = 0?
0, 1
Let m = 1071 + -1068. Factor -1/4*j**4 - j**m - 1/2*j**2 + j + 3/4.
-(j - 1)*(j + 1)**2*(j + 3)/4
Let x = 22/91 - -4/91. Let 0 + 6/7*v**3 - 6/7*v**2 - x*v**4 + 2/7*v = 0. What is v?
0, 1
Let z(q) be the second derivative of q**8/336 + q**7/210 - 3*q**2/2 - 3*q. Let s(d) be the first derivative of z(d). Solve s(v) = 0.
-1, 0
Let x(w) = -7*w + 6. Let t be x(5). Let l = 31 + t. Let 2/11*m**l + 2/11*m**3 + 0 - 2/11*m - 2/11*m**4 = 0. What is m?
-1, 0, 1
Let a(w) be the third derivative of -w**8/5040 - w**7/630 - w**5/20 + 3*w**2. Let l(i) be the third derivative of a(i). Factor l(t).
-4*t*(t + 2)
Let u(n) be the second derivative of n**6/120 + 3*n**5/80 + n**4/16 + n**3/24 + 2*n. Factor u(v).
v*(v + 1)**3/4
Determine b so that -4*b**5 + 7*b**5 + 20*b**4 + 16*b - 28*b**3 + 16 + 9*b**5 - 36*b**2 = 0.
-2, -1, -2/3, 1
Factor 0 + 2/9*q**2 - 2/9*q.
2*q*(q - 1)/9
Let m be (-1 - 0)*(-10 - -6). Let x(z) be the second derivative of 2*z**3 + 1/4*z**m + 2*z + 6*z**2 + 0. Solve x(i) = 0 for i.
-2
Let h(c) be the third derivative of -c**8/1008 - c**7/210 + c**6/60 + c**5/18 - 7*c**4/24 + c**3/2 - 27*c**2. Let h(f) = 0. Calculate f.
-3, 1
Let t(m) be the first derivative of 1/40*m**5 - 2 + m**2 - 2*m - 1/8*m**4 + 0*m**3. Let y(u) be the first derivative of t(u). Determine a, given that y(a) = 0.
-1, 2
Let y(l) be the first derivative of -7*l**3 + 27*l**2/2 - 6*l - 7. Factor y(j).
-3*(j - 1)*(7*j - 2)
Let i(s) = 3*s**2 + 2*s + 1. Let j be i(-1). Factor -13 - 6 - m**j - m + 21.
-(m - 1)*(m + 2)
Let r(p) be the first derivative of -2*p**3/21 + p**2/7 + 4*p/7 - 46. Factor r(o).
-2*(o - 2)*(o + 1)/7
Let x(w) be the second derivative of -25*w**7/168 - 19*w**6/24 - 139*w**5/80 - 97*w**4/48 - 4*w**3/3 - w**2/2 + 3*w. Find b such that x(b) = 0.
-1, -2/5
Let d be ((-6)/9)/((-10)/30). Suppose 1/3*p**2 + 3 + d*p = 0. What is p?
-3
Let t(n) = -7*n**2 + 3*n**2 + 0*n - 2 - 2*n. Suppose -v = 1, -2*s + 2 = -v + 3. Let p(j) = -j**2 + j - 1. Let i(u) = s*t(u) + 2*p(u). What is z in i(z) = 0?
-2, 0
Suppose 12*u**2 - 11*u**2 + 0*u + 0*u - 3*u + 2 = 0. What is u?
1, 2
Let n(h) be the second derivative of h**5/240 - h**4/48 + h**2/2 + 5*h. Let q(o) be the first derivative of n(o). Factor q(w).
w*(w - 2)/4
Let t(b) = -2*b**4 - b**3 + 6*b**2 - 5*b - 2. Let a(u) = -4*u**4 - u**3 + 11*u**2 - 11*u - 5. Let r(f) = -4*a(f) + 10*t(f). Solve r(k) = 0 for k.
-3, 0, 1/2, 1
Let p(s) = -2*s - 7. Let j be p(-6). Let m(n) = n**2 - 3*n - 5. Let v be m(j). Find b, given that 2 + 2*b - 7*b**2 + v*b**2 - 2 = 0.
0, 1
Factor 0*t - 3/5 + 3/5*t**2.
3*(t - 1)*(t + 1)/5
Suppose 0 = -l - 3*i - 2*i - 8, 2*l + 6 = -5*i. Suppose -4*b + 6 = -l*b. Factor 4*q**4 - 5*q**4 + q**b + 0*q**3.
-q**3*(q - 1)
Find f, given that 0 + 24/5*f**2 + 0*f + 3/5*f**5 - 18/5*f**3 - 9/5*f**4 = 0.
-2, 0, 1, 4
Let z(f) = 2*f - 12. Let s be z(6). Let b(h) be the second derivative of 1/2*h**2 - h - 1/6*h**4 + 1/30*h**6 + 0*h**3 + 0 + s*h**5. Factor b(q).
(q - 1)**2*(q + 1)**2
Let l(s) be the second derivative of s**4/30 - 4*s**3/15 + 4*s**2/5 - 44*s. Let l(x) = 0. What is x?
2
Let g(l) = -l**2 - 11*l - 8. Let y be g(-8). Suppose s + 3*s - y = 0. Factor 0*u**5 + 2*u**s + 2*u**5 + u - 2*u**2 + 3*u**5 - 6*u**5.
-u*(u - 1)**3*(u + 1)
Let q(v) = 2*v**3 - v. Let w be q(-1). Let k = w - -3. What is a in 0*a**3 - k*a**2 + 2*a**4 - 4*a**4 + 4*a**3 = 0?
0, 1
Let q(d) be the second derivative of -d**7/56 - d**6/12 - 3*d**5/20 - d**4/8 - d**3/24 + 11*d. Factor q(u).
-u*(u + 1)**3*(3*u + 1)/4
Suppose 2*g = -5*o + 28, 3*g - 12 - 19 = -2*o. Let x = -4 + g. Determine m, given that -3*m**2 + m**2 + 3*m**5 + 2*m**3 + 2*m**4 - x*m**5 + 0*m**2 = 0.
-1, 0, 1
Let g(i) be the second derivative of -3*i**5/70 + 5*i**4/28 + 3*i**3/14 + 6*i. Factor g(k).
-3*k*(k - 3)*(2*k + 1)/7
Let w(r) be the second derivative of 12*r**6/25 - 33*r**5/50 + r**4/3 - r**3/15 + 10*r. Determine l, given that w(l) = 0.
0, 1/4, 1/3
Suppose -2 - 3 = 5*t. Let v be t*(-7 + -2 + 4). Solve -28/3*y**2 + 8/3*y**3 + 8*y**4 + 2*y + 4/3 - 14/3*y**v = 0.
-1, -2/7, 1
Let f(o) be the first derivative of -1/30*o**4 - 1/15*o*