h. Factor -2*a**5 + 3*a + 3*a**4 + j*a**5 - 2*a**3 - 2*a**2 - 2*a**5 - 1.
-(a - 1)**4*(a + 1)
Suppose -8 = -m - 3*m. Factor -m*q**2 - q**4 + 4*q**4 + 2 - q**4 - 2*q**2.
2*(q - 1)**2*(q + 1)**2
Suppose 9 - 3/2*a**2 - 15/2*a = 0. Calculate a.
-6, 1
Let d(z) = 5*z**3 + 45*z**2 - 5*z - 20. Let s(v) = v**2. Let l(k) = -d(k) + 25*s(k). Determine j so that l(j) = 0.
-4, -1, 1
Suppose -734*v = -731*v - 15. Determine p, given that -175/4*p**4 - 1 - 10*p - 145/4*p**2 - 235/4*p**3 - 49/4*p**v = 0.
-1, -2/7
Let t(y) be the second derivative of y**6/900 - y**5/150 - y**3/2 + 2*y. Let n(s) be the second derivative of t(s). Factor n(f).
2*f*(f - 2)/5
Let i(b) be the first derivative of b**4/8 + 3*b**3/2 + 2*b**2 + 22. Suppose i(n) = 0. Calculate n.
-8, -1, 0
Let a(h) be the second derivative of h**4/4 - h**3/2 - 3*h**2 + 3*h. Factor a(q).
3*(q - 2)*(q + 1)
Let y(o) be the first derivative of 5*o**3/3 - 5*o**2 - 15*o - 3. Factor y(m).
5*(m - 3)*(m + 1)
Let c(l) be the third derivative of 0*l**3 + 0*l - 1/90*l**5 - 1/36*l**4 + 0 - 3*l**2. Factor c(q).
-2*q*(q + 1)/3
Let q be -76*5/(-840) - 1/6. Let -q + 6/7*c**3 + 10/7*c - 2*c**2 = 0. What is c?
1/3, 1
Factor 56/5*g - 22/15*g**2 + 24/5 + 10/3*g**4 - 28/3*g**3.
2*(g - 2)**2*(5*g + 3)**2/15
Let c be 2/(-4) - 18/(-4). Let z be (-1)/2*(c + -5). Factor -3/4*k - 1/4*k**2 - z.
-(k + 1)*(k + 2)/4
Let n be ((-4)/((-80)/(-15)))/((-6)/14). Let m(k) be the first derivative of -3/2*k**3 + n*k**2 - 1/10*k**5 + 2 - k + 5/8*k**4. Let m(j) = 0. Calculate j.
1, 2
Let v(y) be the first derivative of y**6/9 - 4*y**5/9 + 2*y**4/3 - 4*y**3/9 + y**2/9 + 7. Suppose v(p) = 0. What is p?
0, 1/3, 1
Let g(u) = -9*u**2 + 16*u - 16. Let r(h) = -4*h**2 + 8*h - 8. Let p(n) = 2*g(n) - 5*r(n). Solve p(b) = 0.
2
Factor 4/7*l - 2/7*l**4 + 8/7*l**3 - 10/7*l**2 + 0.
-2*l*(l - 2)*(l - 1)**2/7
Let b be (2/(-1))/(-2) - 1. Let a = 0 - b. Let a*s - 2/5*s**3 + 0*s**2 + 0 = 0. Calculate s.
0
Find d, given that 2/11*d**2 + 0 - 4/11*d + 4/11*d**3 - 2/11*d**4 = 0.
-1, 0, 1, 2
Let g(s) be the first derivative of s**9/15120 - s**7/2100 + s**5/600 + s**3/3 - 3. Let l(k) be the third derivative of g(k). Find z, given that l(z) = 0.
-1, 0, 1
Let g(x) be the second derivative of x**7/14 + x**6/5 - 3*x**5/20 - x**4/2 - 6*x + 3. Let g(o) = 0. What is o?
-2, -1, 0, 1
Let g = -28 + 30. Solve 3*y**2 - 8*y**g + y**2 + 0*y**2 = 0 for y.
0
Let c = 17/22 + 30/11. What is u in c*u**3 - 6*u**2 + 3/2*u + 1 = 0?
-2/7, 1
Let j(r) be the second derivative of -r**7/189 + r**6/135 + r**5/90 - r**4/54 - 51*r. Factor j(m).
-2*m**2*(m - 1)**2*(m + 1)/9
Let z(b) be the first derivative of -2*b**6/21 + 16*b**5/35 - 6*b**4/7 + 16*b**3/21 - 2*b**2/7 - 19. Factor z(l).
-4*l*(l - 1)**4/7
Let y = -2/1203 + 9638/8421. Factor 10/7*s**3 + 6/7*s**2 - 24/7*s + y.
2*(s - 1)*(s + 2)*(5*s - 2)/7
Let d(w) be the second derivative of -w**6/60 + w**4/4 + 2*w**3/3 + 2*w**2 - 3*w. Let b(c) be the first derivative of d(c). Let b(i) = 0. Calculate i.
-1, 2
Let c(w) be the second derivative of 2/3*w**2 + 1/9*w**3 - w + 0 - 1/18*w**4. Solve c(i) = 0.
-1, 2
Suppose 0*v - 4 = -2*v. Let -3*k + 3*k**v + 4*k + 0*k + 0*k - 4*k**3 = 0. What is k?
-1/4, 0, 1
Let l(d) = 3*d - 7 - 2*d + 8 - 2*d. Let r(q) = q**2 - 1. Let c(j) = 3*l(j) + 3*r(j). Factor c(x).
3*x*(x - 1)
Let l(b) be the third derivative of b**5/15 - 7*b**4/3 + 98*b**3/3 - 12*b**2. Factor l(z).
4*(z - 7)**2
Let d(x) be the first derivative of 4 + 2*x**2 + 0*x**4 + 1/270*x**5 + 0*x + 1/180*x**6 + 0*x**3. Let n(y) be the second derivative of d(y). Factor n(l).
2*l**2*(3*l + 1)/9
Let m be ((-4)/((-80)/30))/((-27)/(-4)). Factor -m*o**2 + 0 - 4/9*o.
-2*o*(o + 2)/9
Suppose -2*a**2 - 7 - 26*a - 2*a**2 + 15 - 3*a**2 = 0. Calculate a.
-4, 2/7
Let u(n) be the first derivative of -5*n**3/3 - 5*n**2 + 42. Suppose u(c) = 0. Calculate c.
-2, 0
Suppose 0 = d - 4 - 1. Suppose -8 + 6 = -h. Factor 2*j**4 + d*j**h + 6*j**3 + j**2 - 5*j + 7*j.
2*j*(j + 1)**3
Let a be (-5)/((-20)/24) + 1. Let w = 9 - a. What is x in 2*x + 2 + 1/2*x**w = 0?
-2
Let m be ((-7)/(-4) - 2)*(-2 + -6). Let d(s) be the first derivative of 1 - 2/5*s + 3/5*s**m + 1/10*s**4 - 2/5*s**3. Factor d(c).
2*(c - 1)**3/5
Let y(l) = 1. Let d(g) be the second derivative of -3*g**4/2 - 4*g**3 - 7*g**2 + 3*g. Let b = -15 + 9. Let t(r) = b*y(r) - d(r). Factor t(s).
2*(3*s + 2)**2
Let u(v) be the first derivative of -5*v**3/3 + 21*v**2/2 + 6*v + 3. Let s(d) = -d**2 + 4*d + 1. Let n(t) = 22*s(t) - 4*u(t). Factor n(z).
-2*(z - 1)**2
Let z(i) be the third derivative of -i**6/60 - i**5/20 + 2*i**2. Let v be z(-2). Factor 0 - 11*p**2 + v*p**2 + 5 + 5*p - 3.
-(p - 1)*(7*p + 2)
Let j be 21/(-18) + (-11)/(22/(-3)). Solve 4/3 + j*b**3 - b**2 + 0*b = 0.
-1, 2
Determine d, given that 6/13 + 4/13*d + 2/13*d**4 - 4/13*d**3 - 8/13*d**2 = 0.
-1, 1, 3
Let r(a) be the first derivative of -16/5*a**5 - 14*a**2 - 13*a**4 + 1 - 20*a**3 - 4*a. Solve r(w) = 0.
-1, -1/4
Suppose -2*j + 5*j = 0. Let w(y) be the second derivative of y + 0*y**2 + j - 1/18*y**3 - 1/36*y**4. Factor w(r).
-r*(r + 1)/3
Let o(q) be the second derivative of -q**8/1050 - q**7/300 + q**6/450 + q**3/3 + 2*q. Let a(t) be the second derivative of o(t). Find m such that a(m) = 0.
-2, 0, 1/4
Let v(y) be the third derivative of y**6/30 - 2*y**5/5 + 3*y**4/2 - 8*y**3/3 + 12*y**2. Factor v(k).
4*(k - 4)*(k - 1)**2
Suppose l - 13 = -2*r, 3*l = -l + 3*r - 3. Let s(i) be the first derivative of 1/4*i**l + 1/4*i + 3/8*i**2 + 2 + 1/16*i**4. Suppose s(b) = 0. Calculate b.
-1
Let 12*l - 15*l + 9*l + 5*l - l**2 = 0. What is l?
0, 11
Let o(b) = -6*b**3 - 8*b**2 - 10*b - 4. Let n(p) = 7*p**3 + 8*p**2 + 11*p + 5. Let y(f) = 4*n(f) + 5*o(f). Solve y(t) = 0 for t.
-3, -1, 0
Let w = 12 + -7. Let g(d) be the second derivative of 4/5*d**4 + 0 - 4/15*d**3 + 0*d**2 - 1/15*d**7 + 2/5*d**6 + 3*d - 43/50*d**w. Find s, given that g(s) = 0.
0, 2/7, 1, 2
Let o(h) be the second derivative of 2*h**6/75 - 7*h**4/15 - 4*h**3/5 + 60*h. Solve o(d) = 0.
-2, -1, 0, 3
Let t(o) be the first derivative of 3*o**5/10 + o**4/4 - 2*o**3/3 - o**2/2 + o/2 + 41. Determine p, given that t(p) = 0.
-1, 1/3, 1
Let c(n) be the second derivative of 0 + 0*n**2 - 6*n - n**3 - 1/4*n**4 + 3/20*n**5. Let c(l) = 0. Calculate l.
-1, 0, 2
Let d(h) = 6*h**4 + 5*h**3 + 25*h**2 + 4*h. Let a(t) = t**4 + t**3 + 5*t**2 + t. Let v(o) = 33*a(o) - 6*d(o). Solve v(z) = 0.
-1, 0, 3
Let n be 20 - 3/(-1)*-1. Suppose -4*h = -20, 4 - n = -4*b - h. Let 1/3*o**4 + 0 + 0*o - 1/3*o**3 + 0*o**b = 0. Calculate o.
0, 1
Let j(q) = 4*q**2 + 20*q - 30. Let b(l) = -11*l**2 - 59*l + 89. Let x(s) = -6*b(s) - 17*j(s). Let x(n) = 0. Calculate n.
3, 4
Let s be ((-6)/15 - -1)*145/87. Factor 2/3*h - 1/3*h**2 + s.
-(h - 3)*(h + 1)/3
Let g = -7 + 9. Determine q, given that -5*q**2 - 15*q**4 - g*q**3 - 22*q**3 + q**2 + q**2 + 6*q = 0.
-1, 0, 2/5
Let y(i) be the third derivative of -i**5/30 + i**4/4 - 10*i**2. Determine z so that y(z) = 0.
0, 3
Let 4/13*d - 10/13*d**4 + 14/13*d**5 + 0 + 10/13*d**2 - 18/13*d**3 = 0. What is d?
-1, -2/7, 0, 1
Let w(l) be the third derivative of l**7/10080 + l**6/2880 + l**4/24 - l**2. Let h(n) be the second derivative of w(n). Solve h(x) = 0 for x.
-1, 0
Let q(i) = 2*i**3 - 2*i**2 + 5*i. Let j(v) = v. Let o(g) = -5*j(g) + q(g). Determine z, given that o(z) = 0.
0, 1
Let f(n) = n**2 + 6*n + 9. Let q be f(-5). Suppose 3/4*d**3 + 0 + 0*d**2 + 0*d - 3/4*d**q = 0. Calculate d.
0, 1
Let i(h) be the first derivative of -h**3/15 + 2. Suppose i(l) = 0. What is l?
0
Factor 9*r**3 + 12 + 13*r**3 + 3*r**4 + 45*r**2 + 936*r - r**3 - 897*r.
3*(r + 1)**3*(r + 4)
Let t be (-2 + 5 + -3)*1. Let n(c) be the third derivative of -1/9*c**3 + c**2 + t*c + 0*c**4 + 0 + 1/90*c**5. Factor n(u).
2*(u - 1)*(u + 1)/3
Solve -15*x**2 + 27*x**2 - 8*x**2 + 6*x**3 + 2*x**4 = 0 for x.
-2, -1, 0
Let f = 11 + 8. Let l = 19 - f. Factor l - 1/2*o - 1/4*o**2.
-o*(o + 2)/4
Let p be (3/2)/((-5)/(-10)). Factor -4*y**2 - 1 + y + 5*y**2 - 2*y**p + y**3.
-(y - 1)**2*(y + 1)
Factor 3/7*m - 3/7*m**2 + 6/7.
-3*(m - 2)*(m + 1)/7
Let k be 180/(-54)*6/(-4). Factor 2/7*o**2 + 0*o - 2/7*o**k + 0 - 6/7*o**3 + 6/7*o**4.
-2*o**2*(o - 1)**3/7
Suppose f = -f + 10*f. Let q(p) be the third derivative of 0*p + 1/45*p**5 + f*p**3 + 1/60*p**6 + 3*p**2 + 0 + 0*p**4. Determine c so that q(c) = 0